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58. To multiply a whole number by a fraction.

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Recite thus: Since of 16 is 4, § of 16 are 3 times 4,

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or 12. Since of 28 is 4, of 28 are 5 times 4, or 20, etc.

RULE.

Divide the whole number by the denominator of the fraction, and multiply the quotient by the numerator.

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2. Find the value of 24×2; 18×3; 27x3; 35x; 132x7; 80×70. Ans. 14; 14; 18, etc. 3. Find the value of 169×5; 196×1; 225×7; 256 ×76; 289×1; 324×5; 361×15. Ans. 65; 126, etc. 4. Find the value of 400 x 30; 441x5; 484 × 529×1; 576×13; 625×28.

Ans. 60; 105, etc. 5. Copy and recite the following exercises:

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Recite thus: Since of 16 is 3, § of 16 are 3 times 31, or 98.

REMARK.-When the whole number does not contain the denominator of the fraction without a remainder, it is often more convenient first to multiply the whole number by the numerator of the fraction, and divide the product by the denominator. Thus: 3 times 16 are 48, and 5 in 48, 9g times.

6. Find the value of 12x; 15x ; 25x7; 39× Ans. 4; 81; 11; 101; 131.

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42×28. 7. Find the value of 28ק; 34x; 25×6; 126x}; 3167 × 2. Ans. 15; 711; 81; 84; 23751.

8. Multiply 20 by ; by 20.

Ans. 15.

FRACTIONS.

19

9. Multiply 57 by 5; 10. Multiply 28 by

5 by 57.

by 28.

;

Ans. 15.

Ans. 91.

11. If a yard of calico is worth 20 cents, what are å Ans. 15 cents. of a yard worth?

12. If a bushel of apples can be had for 57 cents, what will of a bushel cost? Ans. 15 cents. 13. What will 20 bushels of corn cost at 3 of a dollar Ans. 15 dollars. per bushel? 14. What will 5238 bushels of apples cost at of a

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Ans. $3492.

59. To multiply one fraction by another.

EXAMPLES.

1. Copy and recite the following exercises:

(1)

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(2)

(3)

Recite thus: Since of is, of 1 are, and of are 5 times, or 1.

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RULE.

Place the product of the numerators over that of the

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REMARK 1.—The word of between two fractions is to be treated

as a sign of multiplication.

REMARK 2 —If a mixed number is to be multiplied by a fraction, it may be reduced to an improper fraction, and then multi

plied.

REMARK 3.—In the multiplication of fractions, if any number is observed to be common to both a numerator and denominator, it should always be CANCELED; that is, mark the number in botn numerator and denominator, and give it no further attention.

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of it

11. If I have of a watermelon, and give

away, what part of the whole melon do I have left?

1 of 2=3, and 3—3—3.

Ans..

12. If a yard of cloth is worth 5 dollars, what is of a yard worth? of a yard? of a yard? of a yard? Ans. $27; $45; $35; $531⁄2·

13. If corn is worth will 3 bushels cost? 4

els? 13 bushels?

of a dollar per bushel, what bushels? 7 bushels? 10 bush

Ans. $3; $314, etc.

14. At 93 dollars per barrel, what will 74 barrels of

flour cost? 15 barrels? 22

barrels?

barrels? 30 barrels? 371⁄2

First Ans. 73 dollars.

DIVISION OF FRACTIONS.

60. To divide a fraction by a whole number.

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Recite thus: 3 in 6 sevenths, 2 sevenths; 4 in 12 thir

teenths, 3 thirteenths, etc.

RULE.

(1.) Divide the numerator by the whole number, if it is divisible without a remainder, and place the quotient

over the denominator. (See 53. 2. Find the value of 18÷6;

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REMARK 1.)

46-23; §÷3; 12÷4;

2

Ans. ; ; ; ; 8; 13.

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3. Find the value of 2÷3; 25÷5; 36÷4; 38÷19;

28÷7; 144÷12.

12

Ans. 1; 1; 1; ; ; 13.

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4. Find the value of 287; 369; 72÷9;
1÷3; 95÷5.
5. Copy and recite the following exercises:

(1)

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Ans. ; ; ; ;
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Recite thus: 1 third divided by 2 is 1 sixth; since 1 sixth divided by 3 is 1 eighteenth, 5 sixths divided by 3 are 5 eighteenths, etc.

RULE.

(2.) Multiply the denominator by the whole number, and place the product under the numerator.

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8. Find the value of 15÷20; 12÷16; §÷12; 14÷21;

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9. Divide 252 by 2; 3; 4; 5; 6; 7; 8; 9.

Ans. 9; 6; 411; 37, etc.

10. Divide 360 by 2; 3; 4; 5; 6; 7; 8; 9; 10; 12;

15; 18; 24; 30; 36.

Ans. 9, etc. 11. Divide 480 by 2; 3; 4; 5; 6; 8; 10; 12; 16; 20; 24; 48.

23

Ans. 1019, etc.

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61. To divide a mixed number by a whole number.

EXAMPLES.

1. Copy and recite the following exercises:

(1)

(2) .

(3)

31÷4=7÷4=7 41÷9=2÷9=1⁄2 51÷12=16÷12={ Recite thus: 31⁄2 divided by 4=1÷4=7, etc.

RULE.

Reduce the mixed number to an improper fraction, and

then divide as in 60.

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RECITATION.

(1) PROBLEM.-Divide 251 by 2.

(2) DIVISION.-2 in 2 (tens), 1 (ten); 2 in 5 (units), 2 times (units) and 1 (unit) over; 2 in 1 ( of a unit), (of a unit).

(3) RESULT.-Hence, 2 in 251, 12 times.

REMARK 1.—Hence, when the dividend is larger than the divisor, the whole number may be divided first, then divide the remainder (if there be one) united to the fractional part of the divi

dend.

9. Divide 12 by 2 and by 3. 10. Divide 183 by 3 and by 5.

Ans. 61; 41.
Ans. 61; 31.

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