12. Add +++38.

The fractions being added, are 24, which being added to the sum of the whole numbers is 2211.

13. Add, and 5, together.

14. Find the sum of 31 +5+§ +163. 15. Add 54+ of 25 +17% +432.

16. Add 2875,2% +105%.

17. What is the sum of £3 + £§ + fs. + fd. ?

h. +

min. + sec.

18. Add 3 yr. + da. +
19. Add bu. + pk. + qt.

20. Add 18.9 gal.+.45 gal.+.17 qt. + .416 pt.
21. Add & yd. + qr. + 1⁄2 na.

22. Add cwt.+qr. + lb. + oz.

II. 23. Add mile + rd.& ft.

24. Bought 4 house-lots; the first contained

of an acre,

the second of an acre, the third .275 of an acre, and the fourth .8706 of an acre. How much land was there in the whole?

90.

SUBTRACTION OF COMMON FRACTIONS.

RULE 1. Prepare the fractions as in addition: subtract the numerator of the subtrahend from that of the minuend, and write the remainder over the common denominator.

RULE 2. If the fractional part of the minuend is less than that of the subtrahend, add to the fractional part of the minuend a unit reduced to the same denominator; then subtract and add a unit to the subtrahend. (21.)

3. How much is 8-57? 8-67? 1575-411? 418 -13? 16-819?

4. Subtract 35 from 10. Solution. 10+8=108; 35+1 =4§; 108 — 4ğ=6g.

5. From 25 subtract 57; 3; 15; 20; 18; 22; 12; 16.

6. How much is +=+.

? Solution. = &; }

=

7. How much is — }? ƒ—Į? — § ? } of § -√? f of - of g?

8. How much is 48-14 16-118? 25-16? 254 -168-581 82-5?

9. How much is - of? 5-24? 10. How much is 34-? 348-167? 11. Subtract of 4 of from

12. Subtract of 6 of 81 from

of of §.

of 28.

13. What is the difference between of a pound and of a shilling?

14. Subtract .13d. from £.17; .354 lb. from .257 cwt.

15. From 100 subtract 25;

16. Subtract of a yd. from 17. Subtract of a min. from

184; 74.
of a mile.

of a wk.

MULTIPLICATION OF FRACTIONS.

91. The learner has already had, in the preceding articles, some exercises in multiplication of fractions. The following general rule will apply to all possible cases.

Reduce the multiplier and multiplicand to the form of common fractions, and cancel like factors in the numerators and denominators; then multiply the numerators together for the numerator of the product, and the denominators together for the denominator of the product.

3. Multiply by ;
4. Multiply of by
5. Multiply 5 by
6. How much is 46 X
7. What cost of a

bushel?

;

17 by .

of 271?

? 25×15? 35 bushel of corn, at of a dollar per

8. What will 3ğ lb. of butter cost, at 153 cts. per lb. ? 9. At $10 per barrel, what will 15 barrels of beef come to?

10. If 8 bushels of potatoes cost $43, what will 15 bushels cost?

NOTE. Fifteen bushels will cost 15 as much as 8 bushels.

11. Multiply of 4 of 63 by off of 94.

NOTE. Cancel before performing the multiplication.

12. How much is 4 × 5 × 187 × 35? 13. How much is 5X

X 3.8 x .05?

14. If of of of an acre of land is worth $50, how much can be bought for $15.75 ?

15. How much is of 3 of 3.07 X 15.008?

92.

DIVISION OF FRACTIONS. COMPLEX FRACTIONS.
1 is contained in 8 eight times; being
contained in 8, 5 times as many times as 1,
Therefore, dividing by is the same as

Divide 8 by . as large, must be or 5 times 8 times. multiplying by †. Again. Divide but if & be divided by as large, or § of

by . divided by 4 is of, or; of 4, or 4, the quotient must be 5 times . Hence the following

GENERAL RULE. Reduce the dividend and divisor to the form of common fractions, then INVERT THE DIVISOR, and proceed as in multiplication of fractions.

2. Divide 37 by 54. Solution. 30 X=1. 3. Divide by ; by ; 1 by 8.

of of

by 1 of 45.

÷ 9?

of 25 ÷ § of

4. Divide 9 by 34; 418 by 4;
5. How much is 34 ÷ 16? 16 ÷ 14? 64
6. How much is 3÷4%? % ÷ 2?

25

171 ?

7. How much is

A fraction that has a fraction for its numerator or denominator is called a Complex fraction.

Complex fractions are reduced to simple fractions by performing the division expressed by them. (76.)

93. PARTICULAR RULE. To divide a whole number by a mixed number, reduce both the divisor and dividend to the denomination denoted by the fractional part of the divisor, and then divide as in whole numbers; the remainder, if any, will be of the same denomination as that to which the dividend was reduced.

2. In 381770 feet how many rods? Divide by 161.
3. In 5847 square yards how many square rods?
4. In 5146 inches how many nails?

5. In 814768 days how many years?

NOTE. 365 days=1 yr.

6. In 81641807 square feet how many square rods? 2721 sq. ft. 1 sq. rod.

7. Divide 1400700 by 44; by 87; by 3581; by 2758

To divide a mixed number by a whole number, see Arts. 79, 80, 81.

94. MISCELLANEOUS EXERCISES IN FRACTIONS.

1. Reduce to their lowest terms &£; †2; 88; 75; £8.

2. Express in common fractions and reduce to their lowest terms .6; .8; .04; .25; .75; .28; .85; .002; .405; .816; .15; .45. 3. Reduce these improper fractions to whole or mixed numbers: £; 7; 25; 25; 48; 87; 18; 87; 188; 288; 516.

4. Change to decimals; ;£; £; 20; 25; 28; 28; 2; 18.

5. Express in a fractional form 47; 94; 14; 75; 1163 ; 584; 1016; 4; 8; 25; 10085; 4.5; 16.3; 5.16; 80.101; 30.106; 4.54.

6. Reduce to 5ths; to 9ths; to 8ths; to 7ths; to 25ths.