# Fractions example sentences

**Word suggestions** (1): Fractions

## Fractions

[ˈfrakSH(ə)n]

#### NOUN

### Synonyms

fragment, snippet, snatch, smattering, selection, little, bit, touch, hint, trifle,### "Fractions" Example Sentences

1. |
2 We have given the fractions in the order in which they occur in the modern system. |

2. |
Napier thus had complete command over decimal fractions and the use of the decimal point. |

3. |
2), with a float plate on its upper side, carrying three indicating dials, recording respectively fractions, units and tens of miles (up to a hundred). |

4. |
The idea of (-5) as a number with which we can perform such operations as multiplication comes later (ï¿½ 49)ï¿½ (ii.) On the other hand, the conception of a fractional number follows directly from the use of fractions, involving the subdivision of a unit. |

5. |
The deductions follow directly from the definitions, and such mechanical processes as "clearing of fractions " find no place (ï¿½ 21 (ii.)). |

6. |
(iii.) There are important theorems as to the relative value of fractions; e.g. |

7. |
We find that fractions follow certain laws corresponding exactly with those of integral multipliers, and we are therefore able to deal with the fractional numbers as if they were integers. |

8. |
Dephlegmation of the vapours arising from such mixtures as coaltar fractions, petroleum and the "wash" of the spirit industry, is very important, and many types of apparatus are employed in order to effect a separation of the vapours. |

9. |
The frequency ratios in the diatonic scale are all expressible either as fractions, with i, 2, 3 or 5 as numerator and denominator, or as products of such fractions; and it may be shown that for a given note the numerator and denominator are smaller than any other numbers which would give us a note in the immediate neighbourhood. |

10. |
(c) the standard gallon (and multiples and fractions of it), declared to contain 10 lb of water at 62° F., being in volume 277.274 cub. |

11. |
In order to separate the distillate into various fractions, and to remove as much of it as possible free from condensed steam, it is now usual to employ condensing appliances of special form with outlets for running off the different fractions. |

12. |
African mines the diamonds are not only crystals of various weights from fractions of a carat to 150 carats, but also occur as microscopic crystals disseminated through the blue ground. |

13. |
Beneath are the official Liverpool quotations of " futures," as they appeared on the morning of the 19th of April 1906: A merican Deliveries, any port, basis of middling, good ordinary clause (the fractions are given in moths of a penny). |

14. |
(v.) The use of the solidus / separating two numbers is for convenience of printing fractions or fractional numbers. |

15. |
This was arranged for by a movable leaf carrying the sighting V, worked by means of a mill-headed screw provided with a scale in degrees and fractions to the same radius as the elevation scale, and an arrowb head for reading. |

16. |
Logistic or Proportional Logarithms. - The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign. |

17. |
Which Gives The Series Of Approximating Fractions, I 7 8 31 132 163 &C. |

18. |
Decimal fractions had been employed for the extraction of square roots. |

19. |
For forty years after the death of its founder it remained united under the authority of a series of grand khans chosen from among his descendants, and then it began to fall to pieces till the various fractions of it became independent khanates. |

20. |
Obviously, therefore, liquids are comparable when the pressures, volumes and temperatures are equal fractions of the critical constants. |

21. |
In astronomical practice the masses of the planets are commonly expressed as fractions of the mass of the sun, the latter being taken as unity. |

22. |
Unfortunately these eclipses are not sudden but slowly changing phenomena, so that they cannot be observed without an error of at least several seconds, and not infrequently important fractions of a minute. |

23. |
The Army of the North was to concentrate in three fractions - around Solre, Beaumont and Philippeville - as close to Charleroi as was practicable; and he arranged to screen the initial movements of the troops as much as possible, so as to prevent the allies from discovering in time that their centre was aimed at. |

24. |
The size of the angle between the median planes of two consecutive leaves in an alternate arrangement is their divergence; and it is expressed in fractions of the circumference of the axis which is supposed to be a circle. |

25. |
(iii.) The general statement of the laws of operation of fractions is perhaps best deferred until we come to fractional numbers, when letters can be used to express the laws of multiplication and division of such numbers. |

26. |
ï¿½; the successive terms of this series, after the first, are alternately positive and negative, and consist of fractions with numerators I and denominators continually increasing. |

27. |
So persistently does the human ear rebel against the division of the tetrachord into two greater tones and a leimma or hemitone, as represented by the fractions 9, 9, 26, that, centuries before the possibility of reconciling the demands of the ear with those of exact science was satisfactorily demonstrated, the Aristoxenian school advocated the use of an empirical scale, sounding pleasant to the sense, in preference to an unpleasing tonality founded upon immutable proportions. |

28. |
Benzene is manufactured from the low-boiling fractions of the coal-tar distillate. |

29. |
The fractions are agitated with strong sulphuric acid, and then washed with a caustic soda solution. |

30. |
Generally the components of a mixture will be vaporized in the order of their boiling-points; consequently if the condensates or "fractions" corresponding to definite ranges of temperature be separately collected, it is obvious that a more or less partial separation of the components will be effected. |

31. |
For the purpose of collecting the distillates in fractions, many forms of receivers have been devised. |

32. |
On the side of the defence, each colonel had been left to retire as best he could, and thus certain fractions of the retreating Russians encountered Inouye's advancing troops and were destroyed after a most gallant resistance. |

33. |
If we express the pressure, volume and temperature as fractions of the critical constants, then, calling these fractions the " reduced " pressure, volume and temperature, and denoting them by 7r, 0 and 0 respectively, the characteristic equation becomes (7+3/0 2)(30-i) =80; which has the same form for all substances. |

34. |
For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF. |

35. |
The amounts of Turkish gold, silver and debased coinage in circulation are approximately £T16,500,000, in gold, £T8,70o,000 (940,000,000 piastres at 108) in silver mejidies and fractions, and 200,000,000 piastres in beshlik and metallik. |

36. |
The Liber abaci, which fills 459 printed pages, contains the most perfect methods of calculating with whole numbers and with fractions, practice, extraction of the square and cube roots, proportion, chain rule, finding of proportional parts, averages, progressions, even compound interest, just as in the completest mercantile arithmetics of our days. |

37. |
We have to multiply a01; -alas+a2 by ao, -aif32+a2 and we obtain ao (3 - aoal(f31N2 +01133) +aoa2(SI+13) -i-a?31a2 - aIa2(31 + 02) + al, 131+02 = b, 131132 = b t'i +s2 = 2bob2, and clearing of fractions R 1,5 = (a o b 2 - a2 b o) 2 + (a i b o - aobi) (aib2 - a2b1). |

38. |
In algebra he discovered the method of approximating to the real roots of an equation by means of continued fractions, and imagined a general process of solving algebraical equations of every degree. |

39. |
(ii.) Perhaps the worst thing we can do, from the point of view of intelligibility, is to " clear of fractions " by multiplying both sides by 6. |

40. |
If each of the fractions (3) is put equal to i/4h, it is readily found, from the first property of the normal state, that, of the s molecules of the first kind, a number sal (h3m3 /13)e hm (u2+v2+w2)dudvdw (4) Velocities. |

41. |
STYROLENE, C 6 H 5 CH:CH 2, also known as phenylethylene or vinylbenzene, an aromatic hydrocarbon found to the extent of 1 to 4% in storax; it also occurs with crude xylene in coal tar fractions. |

42. |
He studied at Berlin University, where he obtained the degree of doctor of philosophy in 1825, his thesis being an analytical discussion of the theory of fractions. |

43. |
(arithmetic) elementary lessons on the notation of decimal fractions. |

44. |
3 Besides his connexion with logarithms and improvements in the method of prosthaphaeresis, Byrgius has a share in the invention of decimal fractions. |

45. |
Fractions except * were all primary, i.e. |

46. |
With the numerator unity: in order to express such an idea as ~ the Egyptians were obliged to reduce it to a series of primary fractions through double fractions 1~+~1rt~r+1~w+ 1~ 4(1+ |

47. |
Rabies and rule to facilitate the employment of fractions. |

48. |
FLUORANTHENE, C15H10, also known as idryl, a hydrocarbon occurring with phenanthrene, pyrene, diphenyl, and other substances in "Stupp" fat (the fat obtained in working up the mercury ores in Idria), and also in the higher boiling fractions of the coal tar distillate. |

49. |
Fractions of the day are disregarded to avoid dispute, though sometimes the law will consider fractions, as where it is necessary to show the first of two acts. |

50. |
The law pays no regard to fractions of a day except to prevent injustice. |

51. |
In the recording acts relating to real property, fractions of a day are of the utmost importance, and all deeds, mortgages and other instruments affecting the property, take precedence in the order in which they were filed for record. |

52. |
The Aµ from C to F being taken as unity in each case then the AA's for the other regions of the spectrum are expressed in fractions A A (C to F) and are given under the asterisks. |

53. |
Soc., 1904, 26, p. 922) divided the product into three fractions according to their volatility. |

54. |
Should B or C, or both, be at once inconveniently large, and orime, then, instead of the exact ratio B/C some ratio anproxlmat:ng to that ratio, and capable of resolution into convenient factors, is to be found by the method of continued fractions. |

55. |
Then, if possible, B and, C themselves are to be resolved each into rnI factors (counting 1 as a factor), which factors, or multiples of them, shall be not less than t nor greater than 6t; or if B and C contain inconveniently large prime factors, an approximate velocity ratio, found by the method of continued fractions, is to be substituted for B/C as before. |

56. |
Let a denote the arc of contact expressed in turns and fractions of a turn; then O=62832a 6 |

57. |
Or, if n a,27- = a/6.2832 be the number of turns or fractions of a turn in a second, g 0.8165 ft. |

58. |
At first it was only levied at irregular intervals; afterwards, in 378 B.C., it became a permanent tax based on elaborate valuation under which the richer members paid on a larger quota of their capital; in the case of the wealthiest class the taxable quota was taken as one-fifth, smaller fractions being adopted for those belonging to the other divisions. |

59. |
The iron ore raised in the various countries, and in the most productive counties, is here shown: The number of furnaces in blast (fractions showing the proportion of the year furnaces were in blast) was: in England 298162, Wales 19,; Scotland 852, total 403 i '. |

60. |
CONTINUED FRACTIONS. |

61. |
If b 2 /a 2, 3 /a 3 ..., the component fractions, as they are called, recur, either from the commencement or from some fixed term, the continued fraction is said to be recurring or periodic. It is obvious that every terminating continued fraction reduces to a commensurable number. |

62. |
A2 a3 a 4 Ia2 la3 la4 The terminating continued fractions b 2 b2 b 3 b, b, b4 al, a1 + ?2, al-1 7:2+Z' al' + a2 reduced to the forms ala2a3+b2a3+ b2a1 a2 a2a3 b3 ala2a3a4+b2a3a4+b3a,a4+b4a,a2 +b2b4 a2a,a4+a4b3+a2b4 ' are called the successive convergents to the general continued fraction. |

63. |
Simple Continued Fractions. |

64. |
The numerators and denominators of the successive convergents obey the law p n g n _ l - pn-1qn = (- O n, from which it follows at once that every convergent is in its lowest terms. The other principal properties of the convergents are The odd convergents form an increasing series of rational fractions continually approaching to the value of the whole continued fraction; the even convergents form a decreasing series having the same property. |

65. |
The chief practical use of the simple continued fraction is that by means of it we can obtain rational fractions which approximate to any quantity, and we can also estimate the error of our b4 as a4 b5 approximation. |

66. |
For the application of continued fractions to the problem " To find the fraction, whose denominator does not exceed a given integer D, which shall most closely approximate (by excess or defect, as may be assigned) to a given number commensurable or incommensurable," the reader is referred to G. |

67. |
Chrystal's Algebra, where also may be found details of the application of continued fractions to such interesting and important problems as the recurrence of eclipses and the rectification of the calendar. |

68. |
Lagrange used simple continued fractions to approximate to the solutions of numerical equations; thus, if an equation has a root between two integers a and a+1, put x=a+I/y and form the equation in y; if the equation in y has a root between b and b+i, put y = b + I /z, and so on. |

69. |
The solution in integers of the indeterminate equation ax+by=c may be effected by means of continued fractions. |

70. |
An interesting application of continued fractions to establish a unique correspondence between the elements of an aggregate of m dimensions and an aggregate of n dimensions is given by G. |

71. |
Applications of simple continued fractions to the theory of numbers, as, for example, to prove the theorem that a divisor of the sum of two squares is itself the sum of two squares, may be found in J. |

72. |
Recurring Simple Continued Fractions. |

73. |
The Evaluation of Continued Fractions. |

74. |
The Incommensurability of Infinite Continued Fractions. |

75. |
The Conversion of Series and Products into Continued Fractions. |

76. |
Where a (a+I)y (a+n-I)(y+n-2) =y, (33= (Y+ I)(y+2),..., 132n-1 - (y+2n-3)(7+272-2)' (32= y-a, N4 = 2(y+I-a) ?..., N2 - 71(7-I-a) Y(' y + I) (7+2) (7+3)' (y+2n-2)(y+2nFrom this we may express several of the elementary series as continued fractions; thus taking a= I, 7=2, and putting x for -x, have log (I +x) = x I 2 x I 2 x 2 2 x 2 2 X 3 2 x 32x we +2 + 3 +4+5+ 6-I-7 +. |

77. |
Ascending Continued Fractions. |

78. |
The invention of continued fractions is ascribed generally to Pietro Antonia Cataldi, an Italian mathematician who died in 1626. |

79. |
- For the further history of continued fractions we may refer the reader to two papers by Gunther and A. |

80. |
For the application of continued fractions to the theory of O o O b 3 O O a3 b4 O - I a 4 b5 b2 irrational numbers there is P. Bachmann's Vorlesungen fiber die Natur der Irrationalzahnen (1892). |

81. |
For the application of continued fractions to the theory of lenses, see R. |

82. |
It is obtained from the higher boiling fractions, after separation of naphthalene and anthracene, by fractional distillation, the portion boiling between 290-340° C. being taken. |

83. |
Fractions |

84. |
Historical Development of Fractions and Decimals |

85. |
Continued Fractions |

86. |
Thus the fractions must be reduced to a common denominator. |

87. |
This denominator must, if the fractions are in their lowest terms (§ 54), be a multiple of each of the denominators; it is usually most convenient that it should be their L.C.M. |

88. |
We must regard the ratio of a to b as being the same as the ratio of c to d, if the fractions 12 b and d are equal. |

89. |
Complex Fractions. |

90. |
- In order to deal, by way of comparison or addition or subtraction, with fractions which have different denominators, it is necessary to reduce them to a common denominator. |

91. |
To avoid this difficulty, in practical life, it is usual to confine our operations to fractions which have a certain standard denominator. |

92. |
The modern method is to deal with fractions which have ioo as denominator; such fractions are called percentages. |

93. |
Hence, to find a percentage of a percentage, we multiply the two numbers, put o's in front if necessary to make up four figures (not counting fractions), and prefix the point. |

94. |
Decimal Fractions. |

95. |
These two fractions are equal to each other, and also to 1530. |

96. |
A fraction written in this way is called a decimal fraction; or we might define a decimal fraction as a fraction having a power of To for its denominator, there being a special notation for writing such fractions. |

97. |
Fractions other than decimal fractions are usually called vulgar fractions. |

98. |
The fractions used in ancient times were mainly of two kinds: unitfractions, i.e. |

99. |
fractions representing aliquot parts (§ 103), and fractions with a definite denominator. |

100. |
The Egyptians as a rule used only unit-fractions, other fractions being expressed as the sum of unit-fractions. |

101. |
The Greeks originally used unit-fractions, like the Egyptians; later they introduced the sexagesimal fractions of the Babylonians, extending the system to four or more successive subdivisions of the unit representing a degree. |

102. |
They also, but apparently still later and only occasionally, used fractions of the modern kind. |

103. |
In the sexagesimal system the numerators of the successive fractions (the denominators of which were the successive powers of 60) were followed by', ", "', ", the denominator not being written. |

104. |
Since represented 60, and o was the next letter, the latter appears to have been used to denote absence of one of the fractions; but it is not clear that our present sign for zero was actually derived from this. |

105. |
In the case of fractions of the more general kind, the numerator was written first with ', and then the denominator, followed by ", was written twice. |

106. |
The Romans commonly used fractions with denominator 12; these were described as unciae (ounces), being twelfths of the as (pound). |

107. |
Hindu treatises on arithmetic show the use of fractions, containing a power of io as denominator, as early as the beginning of the 6th century A.D. |

108. |
Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions. |

109. |
Fractions of Concrete Quantities. |

110. |
- The British systems of coinage, weights, lengths, &c., afford many examples of the use of fractions. |

111. |
Also most fractions cannot be expressed exactly as decimals; and this is also the case for surds and logarithms, as well as for the numbers expressing certain ratios which arise out of geometrical relations. |

112. |
For multiplication by a proper fraction or a decimal, it is sometimes convenient, especially when we are dealing with mixed quantities, to convert the multiplier into the sum or difference of a number of fractions, each of which has i as its numerator. |

113. |
The fractions should generally be chosen so that each part of the product may be obtained from an earlier part by a comparatively simple division. |

114. |
In the form L(a+f), where f is a fraction (or the sum of several fractions); we then say that the cost, being nXL(a-l-f), is equal to (a+f)XLn, and apply the method of compound practice, i.e. |

115. |
The theory of continued fractions gives a method of expressing a number, in certain cases, as a continued product. |

116. |
Any exact fraction can be expressed as a continued fraction, and there are methods for expressing as continued fractions certain other numbers, e.g. |

117. |
Square roots, whose values cannot be expressed exactly as fractions. |

118. |
That grantee, the tenant-in-chief, has the right to demand from his sub-tenants, to whom he has given out fractions of his estate, the same dues that the king exacts from himself. |

119. |
As the process of the partition of lands continued, the fractions grew smaller and smaller, and many of the tenants-in-chief were ere long very small and unimportant persons. |

120. |
The solubility of naphthalene by various oils has led some engineers to put in naphthalene washers, in which gas is brought into contact with a heavy tar oil or certain fractions distilled from it, the latter being previously mixed with some volatile hydrocarbon to replace in the gas those illuminating vapours which the oil dissolves out; and by fractional distillation of the washing oil the naphthalene and volatile hydrocarbons are afterwards recovered. |

121. |
Enneper, and the expression of continued fractions as determinants by Jacobi, V. |

122. |
Most of the elements are small numerical fractions: e, the eccentricity of the moon's orbit, about 0.055; e', the eccentricity of the earth's orbit, about o 017: y, the sine of half the inclination of the moon's orbit, about 0.046; m, the ratio of the mean motions of the moon and earth, about 0.075. |

123. |
A divided cylinder is fixed to the turning knob, which thus makes it possible to measure fractions of the revolution. |

124. |
With the help of this scale the total revolutions of the screw can be read; fractions of the revolution can be read from the divided cylinder d. |

125. |
As fractions of intervals can only be estimated in this method, a measurement with such an eyepiece scale can of course not be as exact as with a screw micrometer ocular. |

126. |
It was urged that studies should focus on the fine and ultrafine fractions of the ambient aerosol and on effects on sensitive individuals. |

127. |
Algebraic manipulation, fractions. |

128. |
All the crude extracts and the fractions exhibited a very good level of broad spectrum antibacterial activity. |

129. |
It only take fractions of a second for a child to get severely burnt. |

130. |
Decimal fractions. |

131. |
Denominators of the two fractions. |

132. |
Elute with 14 ml of EB into 7x2 ml fractions. |

133. |
Finally the protein was eluted with 15 MLS of eluted with 15 MLS of Elute buffer with 2 ml fractions collected into eppendorf tubes. |

134. |
fractions of millimeters and seconds, she is quite inconsolable. |

135. |
Procedure: The eluted fractions from the Ni-affinity Histrap columns were loaded on the gel filtration column in GF buffer at 0.80 ml/min. |

136. |
Adding and subtracting Before adding or subtracting fractions, they must be transformed so that they all have a common denominator. |

137. |
His defining moment was when he showed his teacher how to multiply mixed fractions. |

138. |
Algebra 2 Pages 66 to 69 Cancelation and four rules with algebraic fractions. |

139. |
Effect of enalapril on survival in patients with reduced left ventricular ejection fractions and congestive heart failure. |

140. |
C. Series, ' The modular surface and continued fractions ' J London Math. |

141. |
Elute with 14 ml of EB into 7x2 ml fractions. |

142. |
All teachers have heard the old gripes, why should I have to learn fractions? |

143. |
Only hyphenate compass points and fractions if they make a compound, eg southeast England, two-thirds full. |

144. |
Use of symbols, basic algebraic manipulation, fractions. |

145. |
Methanol extract suggesting that the active compounds might be found in the polar fractions. |

146. |
Multiply mixed fractions. |

147. |
Dundee One surgeon performing open radical prostatectomy; radical radiotherapy - external beam 50 gray in 20 fractions; brachytherapy referred to Edinburgh. |

148. |
Mathematical Expressions use the solidus whenever possible in preference to built-up fractions. |

149. |
Square roots of rational fractions. |

150. |
Subtract fractions by writing them with a common denominator. |

151. |
T1 t2 t3 translation vector in fractions of ROTATING cell edge. |

152. |
The sum of the twin fractions must be 1.0 Twin Data stored by CRYSTALS For a twinned crystal the following equation holds. |

153. |
You also want to look for whey that contains the greatest amounts of those important whey protein fractions. |

154. |
The symmetrical separation of the edges is produced and measured by a single screw; the fractions of a revolution of the screw are obtained by an index attached to one end of the screw, reading on a dial divided into loo equal parts. |

155. |
To Napier seems to be due the first use of the decimal point in arithmetic. Decimal fractions were first introduced by Stevinus in his tract La Disme, published in 1585, but he used cumbrous exponents (numbers enclosed in circles) to distinguish the different denominations, primes, seconds, thirds, &c. Thus, for example, he would have written 123.456 as [email protected] |

156. |
In the Rabdologia Napier gives an "Admonitio pro Decimali Arithmetica," in which he commends the fractions of Stevinus and gives an example of their use, the division of 861094 by 43 2. |

157. |
This single instance of the use of the decimal point in the midst of an arithmetical process, if it stood alone, would not suffice to establish a claim for its introduction, as the real introducer of the decimal point is the person who first saw that a point or line as separator was all that was required to distinguish between the integers and fractions, and used it as a permanent notation and not merely in the course of performing an arithmetical operation. |

158. |
Laurent generally agreed, except when the theory compelled the adoption of formulae containing fractions of atoms; in such cases he regarded the molecular weight as the weight occupying a volume equal to four unit weights of hydrogen. |

159. |
Leonardo, making use of fractions of the sexagesimal scale, gives X = IÃ‚° 221 7 42" i 33 iv 4v 40 vi, after having demonstrated, by a discussion founded on the 10th book of Euclid, that a solution by square roots is impossible. |

160. |
The deductions follow directly from the definitions, and such mechanical processes as "clearing of fractions " find no place (Ã¯¿½ 21 (ii.)). |

161. |
(ii.) The elements of the theory of numbers belong to arithmetic. In particular, the theorem that if n is a factor of a and of b it is also a factor of pa= qb, where p and q are any integers, is important in reference to the determination of greatest common divisor and to the elementary treatment of continued fractions. |

162. |
The idea of (-5) as a number with which we can perform such operations as multiplication comes later (Ã¯¿½ 49)Ã¯¿½ (ii.) On the other hand, the conception of a fractional number follows directly from the use of fractions, involving the subdivision of a unit. |

163. |
(iii.) Another application of the method is to proving the law of formation of consecutive convergents to a continued fraction (see Continued Fractions). |

164. |
Ã¯¿½; the successive terms of this series, after the first, are alternately positive and negative, and consist of fractions with numerators I and denominators continually increasing. |

165. |
Continued fractions, one of the earliest examples of which is Lord Brouncker's expression for the ratio of the circumference to the diameter of a circle (see Circle), were elaborately discussed by John Wallis and Leonhard Euler; the convergency of series treated by Newton, Euler and the Bernoullis; the binomial theorem, due originally to Newton and subsequently expanded by Euler and others, was used by Joseph Louis Lagrange as the basis of his Calcul des Fonctions. |

166. |
Benzene is manufactured from the low-boiling fractions of the coal-tar distillate '(see' Coal-Tar). |

167. |
Baker this would seem to point to the fact that the tellurium used was insufficiently purified, since his work showed that there was no difference between the first and last fractions (see Chem. |

168. |
.; so that, marking off duodecimal fractions by commas, the area in the above case is 4 of 3, I, 8, 4, 8 X15, 3 X15, 3 sq. |

169. |
An essential accompaniment therefore of the potentiometer is a series of standard low resistances, say of o 1, o oi, o ooi ohm, and also a series of higher resistances divided into known fractions. |

170. |
(c) the standard gallon (and multiples and fractions of it), declared to contain 10 lb of water at 62Ã‚° F., being in volume 277.274 cub. |

171. |
In Ptolemaic times the artaba (2336.), modified from the Persian, was general in Egypt, a working equivalent to the Attic metretes -- value 2 apet or 1/2 tama; medimnus=tama or 2 artabas, and fractions down to 1/400 artaba (35). |

172. |
'NAPHTHALENE, C 1 oH 8, a hydrocarbon discovered in the "carbolic" and "heavy oil" fractions of the coal-tar distillate '(see Coal-Tar) in 1819 by A. |

173. |
(b) Conversions of compound fractions (e.g. |

174. |
Most of the theorems concerning continued fractions can be thus proved simply from the properties of determinants (see T. |

175. |
The theory of the convergence of continued fractions is due to Oscar Schldmilch, P. F. |

176. |
Van Vleck have written on the convergence of infinite continued fractions with complex elements. |

177. |
It is obtained from the higher boiling fractions, after separation of naphthalene and anthracene, by fractional distillation, the portion boiling between 290-340Ã‚° C. being taken. |

178. |
Sedanolic acid, C12H2003, which is found along with sedanonic acid, C12H18031 in the higher boiling fractions of celery oil, is an orthooxyamyl-A 5 -tetrahydrobenzoic acid, sedanonic acid being orthovaleryl-A l -tetrahydrobenzoic acid (G. |

179. |
Such fractions are called aliquot parts (from Lat. |

180. |
She has nearly finished Colburn's mental arithmetic, her last work being in improper fractions. |

181. |
Mathematical Expressions Use the solidus whenever possible in preference to built-up fractions. |

182. |
This is my Root Rational Fraction program, which does exact arithmetic on quantities that are square roots of rational fractions. |

183. |
Add and subtract fractions by writing them with a common denominator. |

184. |
Alternative: TRANslate FRAC t1 t2 t3 translation vector in fractions of ROTATING cell edge. |

185. |
The volume fractions have subsequently been successfully fitted using a novel model for transformation kinetics. |

186. |
Savings bonds can also be purchased at different fractions of the face value of the bond, or at the face value of the bond itself. |

187. |
All fields of math are represented, from algebra to chemistry to geometry and from finance to fractions to statistics. |

188. |
This lets you pick half, quarter and eighth of an inch thickness without having to convert fractions to decimals. |

189. |
If you're patient and open to opportunity, you can get good games from wholesalers for fractions of the original prices. |

190. |
Free fractions worksheets, addition problems, and advanced algebra are all available. |

191. |
Fraction worksheets can help your child through difficult math concepts, such as dividing fractions, by providing extra practice. |

192. |
There are many different printed and bound books available that focus on fractions exclusively. |

193. |
Many of the upper elementary grade workbooks include fractions in a variety of forms. |

194. |
One of the disadvantages of these printed books is that they sometimes contain material other than just fractions. |

195. |
This can help you see if your child even understands fractions before you start printing off fraction worksheets for him or her to perform. |

196. |
For example, your child may understand how to add fractions, but need some additional help with multiplying before being given worksheets covering this concept. |

197. |
The Internet abounds with free printable worksheets and items to help your child learn fractions. |

198. |
Math Drills - This site offers not only fraction worksheets but printable manipulatives to help your child learn fractions hands on. |

199. |
TeachNology - Tons of free worksheets featuring fractions of different sizes and types. |

200. |
You'll even find pizza fractions and similar items to help make learning fun. |

201. |
Whichever method you choose for locating the worksheets you'll use to teach your child fractions, remember that daily practice is vital when it comes to math. |

202. |
Fraction Worksheet -Includes a fraction worksheet generator that produces like or unlike fractions. |

203. |
Counting on fingers and toes, for example, helps children learn how to count, but more in-depth concepts such as decimals and fractions can be made easier through the use of games and tools. |

204. |
If you have not worked on fractions, stick with whole numbers, such as dollars or five dollars to avoid confusing your child. |

205. |
Using models can help children to understand basic mathematical concepts such as fractions and percentages. |

206. |
Fractions lesson plans represent a challenging milestone in your child's academic career. |

207. |
It is often around the time that a student is introduced to fractions and more complicated mathematical concepts that confusion may begin to settle in. |

208. |
This isn't necessarily because fractions are so difficult in and of themselves, but the concept can be more abstract for children and more complicated to absorb. |

209. |
There is no shortage of fractions lesson plans available on the web. |

210. |
Fractions do not always seem as tangible a concept to young students as the mathematical fundamentals of addition, subtraction, multiplication, and division. |

211. |
However, fractions are a mathematical fundamental that is necessary for most types of advanced math. |

212. |
Solidifying the concept of fractions is essential for a child's mathematical development. |

213. |
Introducing the idea that fractions are highly applicable to a person's day-to-day activities is important. |

214. |
This helps fractions come to life in the everyday environment. |

215. |
LessonPlanet.com offers many worksheets and activities regarding the introduction of fractions. |

216. |
Fractions appear at the second grade level. |

217. |
This isn't necessarily a site for full fractions lesson plans, but it is an excellent resource for honing skills. |

218. |
This is why the Life of Fred: Fractions textbook can be a great tool for struggling students. |

219. |
When it comes to introducing fractions to stressed students, lessons will always be benefited by the supplementation of as much hands-on experience as possible. |

220. |
An excellent way to supplement your homeschooler's fractions lessons is to bake with your child, showing him how two-half cups are equivalent to a full cup and so forth. |

221. |
Even small basic concepts like fractions pave the way for a successful study of math. |

222. |
This is why, regardless of time and costs, ensuring that your child comprehends his fractions lessons thoroughly is fundamental before the child can be expected to advance. |

223. |
The jewelry industry maintains strict regulations on the ranges of carat weights that may be grouped into particular fractions to help uphold the high quality standards of the industry. |

224. |
A game that focuses on learning fractions through fun. |

225. |
After you are done cooking, use meal time to introduce fractions. |

226. |
This is a great way to show how fractions work. |

227. |
Not only is this hands-on game lots of fun, it also helps teach early mathematic skills such as adding, subtracting, and even fractions! |

228. |
While it is certainly helpful to have a basic understanding of French numbers, there is a whole world of percentages, fractions, money and measurements that is worth studying. |

229. |
The accuracy of a meter is tested by drawing calibration curves showing the percentage departure from absolute accuracy in its reading for various decimal fractions of full load. |

230. |
Was to divide his territories among his sons, whereby Poland was partitioned into no fewer than four, and ultimately into as many as eight, principalities, many of which (Silesia and Great Poland, for instance) in process of time split up into still smaller fractions all of them more or less bitterly hostile to each other. |

231. |
He extended the "law of continuity" as stated by Johannes Kepler; regarded the denominators of fractions as powers with negative exponents; and deduced from the quadrature of the parabola y=xm, where m is a positive integer, the area of the curves when m is negative or fractional. |

232. |
Be proper fractions, and the value of every one of the interminate continued fractions l!1 a2. |

233. |
Thus, if we have an equation P=Q, where P and Q are numbers involving fractions, we can clear of fractions, not by multiplying P and Q by a number m, but by applying the equal multiples P and Q to a number m as unit. |

234. |
Both the fractions into which they were divided by the Nerbudda river laid claim to antiquity: while the northern, however, did not trace their origin further back than the period of the early Mahommedan kings of Delhi, the southern fraction not only claimed an earlier and purer descent, but adhered also with greater strictness to the rules of their profession. |

235. |
The time between the breaks could be measured in seconds by the clock signals, and in fractions of a second by the tuning-fork record. |

236. |
Thus, whilst the detachment was still disposed as a series of rearguards, the foremost fractions of it stood to fight on the Yalu, against odds of four to one. |

237. |
Calling in the brigade detached to the assistance of Nozu as well as all other available fractions of his scattered army, he himself attacked 1 The 5th division of the 2nd Army had been sent to join the 10th as the latter approached Hsimucheng. |

238. |
The point separating the integers from the decimal fractions seems to be the invention of Bartholomaeus Pitiscus, in whose trigonometrical tables (1612) it occurs and it was accepted by John Napier in his logarithmic papers (1614 and 1619). |

239. |
AS, the Roman unit of weight and measure, divided into 12 unciae (whence both "ounce" and "inch"); its fractions being deunx i 2, dextans, dodrans 4 i bes 3, septunx T7-2-, semis z, quincunx A, triens 3 i quadrans 4, sextans s, sescuncia $, uncia r i g. |

240. |
Leonardo, making use of fractions of the sexagesimal scale, gives X = I° 221 7 42" i 33 iv 4v 40 vi, after having demonstrated, by a discussion founded on the 10th book of Euclid, that a solution by square roots is impossible. |

241. |
There are extensions of the binomial theorem, by means of which approximate calculations can be made of fractions, surds, and powers of fractions and of surds; the main difference being that the number of terms which can be taken into account is unlimited, so that, although we may approach nearer and nearer to the true value, we never attain it exactly. |

242. |
2 an embolismic The result so obtained would in general be more accurate than the Jewish calculation, from which it may differ a day, as fractions of a day do not enter alike in these computations. |

243. |
Thus, to take the latter one, if we suppose that of two editors of equal competence A requires a probability of four-fifths to admit a reading into his text and B a probability of three-fifths only, then in all the cases in which the probability lies between these two fractions B will be right seven times to A's three, while outside these limits there will be no difference between them. |

244. |
Recorde published several works upon mathematical subjects, chiefly in the form of dialogue between master and scholar, viz.: - The Grounde of Artes, teachinge the Worke and Practise of Arithmeticke, both in whole numbers and fractions (1540); The Pathway to Knowledge, containing the First Principles of Geometry. |

245. |
Learn and practise finding equivalent fractions. You can use images to help you work out which fractions are equivalent. Here we have two identical rectangles but each rectangle is split into ... |

246. |
Give students practice dividing fractions within real-world contexts with this Dividing Fractions: Word Problems worksheet. Word problems are a great way to help students see the relevance of their ... |

247. |
3.3(A) - represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number ... |

248. |
Now, for the first time, scientists and archaeologists believe that they have decrypted symbols denoting numerical fractions in the Linear A writing system. The alphabet called Linear A was first ... |

249. |
Sep 16, 2020 (The Expresswire) -- “Milk Fat fractions Market" is valued at 2735.1 million USD in 2020 is expected to reach 5098.5 million USD by the end of 2026, growing at a CAGR of 9.2% during ... |

250. |
However, if you rotate your iPhone into landscape mode, then the calculator application offers many more options, which will be useful for business calculations such as percentages and fractions. |

251. |
The comprehensive research report titled Global Milk Fat fractions Market To Record Exponential Growth During Projected Timeframe by Zion Market Research supports the reader by assisting to accumulate ... |

252. |
INTERNATIONAL ATOMIC ENERGY AGENCY, Certification of Polycyclic Aromatic Hydrocarbon Mass fractions in IAEA-477 Sediment Sample, Analytical Quality in Nuclear Applications Series No. 61, IAEA, Vienna ... |

253. |
INTERNATIONAL ATOMIC ENERGY AGENCY, Certification of Trace Element Mass fractions in Marine Sediment IAEA-475, Analytical Quality in Nuclear Applications Series No. 62, IAEA, Vienna (2020). |

254. |
fractions sentence examples. 2 We have given the fractions in the order in which they occur in the modern system. 17. 16. Napier thus had complete command over decimal fractions and the use of the decimal point. 9. 8. |

255. |
Examples of fractions in a sentence: 1. Sur une généralisation des fractions continues. 2. It is estimated at fractions of one per cent. 3. La compagnie fut partagée en deux fractions égales. |

256. |
· Reducing fractions · Adding and subtract- ing fractions · Multiplying fractions · Dividing fractions · Adding and subtract- ing mixed numbers · Multiplying mixed numbers · Dividing mixed numbers |

257. |
fractions form an important part of our daily lives. There are many examples of fractions you will come across in real life. We have to willingly or unwillingly share that yummy pizza amongst our friends and families. Three people, four slices. If you learn and visualize fractions in an easy way, it will be more fun and exciting. |

258. |
In this post, I show you examples of how we have used language to understand fraction concepts. Become Familiar with the Vocabulary. The first day in working with fractions, we made fraction strips. This activity helped students become familiar with the language of fractions though hands on cutting. |

259. |
Today we are going to look at some examples of word problems with fractions. Although they may seem more difficult, in reality, word problems involving fractions are just as easy as those involving whole numbers. The only thing we have to do is: Read the problem carefully. Think about what it is asking us to do. Think about the information we need. |

260. |
Let's look at some more examples of fractions. In examples 1 through 4 below, we have identified the numerator and the denominator for each shaded circle. We have also written each fraction as a number and using words. Example 1: One-half |

261. |
Rule: Always spell out simple fractions and use hyphens with them. Example: One-half of the pies have been eaten. Rule: A mixed fraction can be expressed in figures unless it is the first word of a sentence. Example: We expect a 5 1/2 percent wage increase. Example: Five and one-half percent was the maximum allowable interest. Rule: Hyphenate all compound numbers from twenty-one through ninety |

262. |
fractions on a number line: fractions can be represented on a number line, as shown below. For examples, Real life examples. The most common examples of fractions from real life are equal slices of pizza, fruit, cake, a bar of chocolate, etc. Non-examples. When the parts of the whole are unevenly divided, they don’t form fractions. Types of |

263. |
· Reducing fractions · Adding and subtract- ing fractions · Multiplying fractions · Dividing fractions · Adding and subtract- ing mixed numbers · Multiplying mixed numbers · Dividing mixed numbers |

264. |
With Fraction Designer you can make your own fraction examples. Let's say you wish to see how the fractions 3/4 and 3/5 compare in size. With Compare with Circles just enter the two fractions, press the button and there they are: |

265. |
fractions at the Beginning of a Sentence. Even if you are writing fractions as numerals elsewhere, you should not start a sentence with a numeral. For example, the following would be incorrect: 22/7 is a good approximation of pi. To avoid this, you would either need to write the fraction as words or rephrase the sentence so that it does not |

266. |
One of the best times to practice using fractions is during cooking. At the beginning, your child can simply be shown how fractions are used in recipes: Example: 1/3 cup of sugar; 1/2 fl oz of syrup; 3 1/4 cups of flour; Knowing how fractions work in this can help to measure out the required quantities. |

267. |
Some examples of fractions include: ½, ¾, 5 . The top number is referred to as the numerator, and the bottom number is your denominator. fractions are important because they tell you what |

268. |
fractions can be of two types Proper fractions and Improper fractions. If both the numerator and denominators are positive and numerator less than denominator such fractions are called proper fraction. Ex: \(\frac{3}{8},\frac{9}{11}\) etc. Whereas fractions having numerator greater than the denominator is called improper fraction. |

269. |
In this post, we are going to look at some sequenced examples of exercises with equivalent fractions. Remember that what we mean by equivalent fractions are those fractions that although they are different, represent the same quantity.. If you need to dig deeper into the concept take a look at this previous blog entry, examples of equivalent fractions. |

270. |
In the previous blog post, I gave you examples using sentence frames in multiplication.Today, I want to give you a some more examples, but this time using fractions. Here is how we have used vocabulary and sentence frames in our classroom to learn about fractions. |

271. |
Pre-Algebra giving you a hard time? Shmoop's free fractions & Decimals Guide has all the explanations, examples, and exercises you've been craving. |

272. |
In general, 1/n is a unit fraction. Unit Fractions: Part of the Number One. When it comes to unit fractions, each unit fraction is a part of the number 1. For example, 1/2 is a half of 1, 1/3 is a |

273. |
Sentence examples for or fractions thereof from inspiring English sources. 6. exact 54. similar 15. related RELATED or parts thereof. or patches thereof. or percentages thereof. or elements thereof. or ratios thereof. or composites thereof. or fragments thereof. or segments thereof |

274. |
Examples of Fraction in Excel. Below are the different examples of fractions in excel. Example #1 – One-Digit Fraction Formatting in Excel. In this example, we will see how to convert the actual decimal numbers to fraction formatting by following the below steps. Consider the below example which has some sort of decimal numbers as shown below. |

275. |
Suggestions: Start with adding like fractions such as 1 3 ⁄ 6 and 2 2 ⁄ 6.Then enter 1 1 ⁄ 2 and 2 1 ⁄ 3 to see how the common denominator of 6 is used.. Enter 5 ⁄ 6 and 5 ⁄ 6 to see how the mixed number 1 2 ⁄ 3 results. Then add 1 5 ⁄ 6 and 3 5 ⁄ 6 to see how the mixed number 5 2 ⁄ 3 results. |

276. |
Complex Fractions: More Examples (page 2 of 2) Simplify the following expression: Can I start by hacking off the x – 3's? Can I cancel the 4 with the 12? Or the 3 with the 9 or the 12? (Hint: No!) The common denominator for this complex fraction would be x – 3 |

277. |
Subtracting Mixed fractions. I have a special page on Adding and Subtracting Mixed fractions.. Making the Denominators the Same. In the previous example it was easy to make the denominators the same, but it can be harder so you may need to use either the |

278. |
Comparing and contrasting examples and non-examples of unit fractions allows students to develop a conceptual understanding of fractions. Plan your 60-minute lesson in Math or fractions with helpful tips from Diane Siekmann. Students use the sentence stems: This is an example because _____ . |

279. |
Once the fractions have the same denominator, we can add or subtract as usual. Click through the slideshow to learn how to add fractions with different denominators. Let's add 1/4 and 1/3. Before we can add these fractions, we'll need to change them so they have the same denominator. |

280. |
Fractional definition, pertaining to fractions; comprising a part or the parts of a unit; constituting a fraction: fractional numbers. See more. |

281. |
These 10 multiplying fractions word problems are a great way to work on multiplying fractions using real-life examples. Get them FREE today. Have you ever heard, “I will never use this”? It is important for children to see how math is used in everyday life. And word problems are one way to do this. |

282. |
Percents and fractions. Knowing how to write percents as fractions and vice versa can help you in your everyday life. For example, let's say you earned a grade of 80% on a test. You can convert 80% into a fraction to find out how many of your answers were correct. When your teacher grades the test, she may do the opposite. |

283. |
An algebraic fraction is the indicated quotient of two algebraic expressions.As with fractions of integers, the denominator of an algebraic fraction cannot be zero. Two examples of algebraic fractions are + − and + −.Algebraic fractions are subject to the same field properties as arithmetic fractions.. If the numerator and the denominator are polynomials, as in + −, the algebraic |

284. |
Translations of the phrase THESE fractions from english to spanish and examples of the use of "THESE FRACTIONS" in a sentence with their translations: These fractions correspond to different collection containers. |

285. |
Complex fractions If the numerator, denominator, or both contain fractions, then the expression is called a complex fraction. The fraction bar indicates division. |

286. |
One of the simplest examples of equivalent fractions is the number 1. If the numerator and the denominator are the same, then the fraction has the same equivalent value as 1. Here are some equivalent fractions for 3/4. The equivalent fractions are all multiples of 3/4. Take 15/20 for example. 3x5 = 15 and 4x5 = 20. |

287. |
How to decompose fractions as a sum of unit fractions using tape diagrams, Draw a number bond and write the number sentence to match each tape diagram, Common Core Grade 4, examples and step by step solutions, Decomposition and Fraction Equivalence |

288. |
Shmoop's free fractions & Decimals Guide has all the explanations, examples, and exercises you've been craving. Menu. Log In. fractions & Decimals. Home / Pre-Algebra / fractions & Decimals / Examples / Decimals Word Problems Examples ; Examples / Decimals Word Problems Examples |

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