MULTIPLICATION.

WRITTEN EXERCISES.

349. 1. Multiply 8 cd. 5 cd. ft. 9 cu. ft. by 4.

ANALYSIS.-Write the multiplier under the lowest denomination of the multiplicand, and begin at the right to multiply.

4 times 9 cu. ft. are 36 cu. ft., equal to 2 cd. ft. 4 cu. ft. Write the 4 cu. ft. under the cubic feet in the product, and reserve the

2 cd. ft. to add to the product of cord feet.

4 times 5 cd. ft. are 20 cd. ft., and 2 cd. ft. added make 22 cd. ft., equal to 2 cd. 6 cd. ft. Write the 6 cd. ft. under the cord feet in the product and reserve the 2 cd. to add to the product of cords. 4 times 8 cd. are 32 cd. and 2 cd. added make 34 cd., which write under the cords.

RULE.-I. Write the multiplier under the lowest denomination of the multiplicand.

II. Multiply each denomination separately, as in simple numbers, and if the product is less than a unit of the next higher denomination, write it under the term multiplied.

III. When the product of any denomination is equal to, or greater than a unit of the next higher denomination, reduce it to that denomination and write the excess, if any, under the term multiplied, and add the quotient to the product of the next higher denomination.

When the multiplier is a composite number and more than 12, we may multiply first by one of the factors, and that partial product by another, and so on (88).

What is the result

4. Of £9 10s. 84d. × 6? by 7? 5. Of 6 hhd. 20 gal. 3 qt. x 5? 6. Of 2 rd. 4 yd. 2 ft. 6 in. × 6?

by 9?

by 8? by 15?

by 18?

7. Of 9 cu. yd. 15 cu. ft. 520 cu. in. × 7? by 14?

8. Of 783 53 10 18 gr. x 9? by 250?

9. Of 5 hr. 42 min. 50 sec. × 12? by 36?

10. Of 26 cd. 3 cd. ft. 12 cu. ft. x 18? 24?

11. 14 A. 26 P. x 24? 36? 42?

12. How much paper will be required to print 10 editions of a book, each requiring 40 reams 7 quires 12 sheets? 13. What amount of cranberries in 16 boxes, each box containing 1 bu. 2 pk. 6 qt.?

14. How many bushels of wheat in 42 sacks, each containing 145 lb. ?

15. What is the weight of 1 doz. spoons, each weighing 1 oz. 12 pwt. 16 gr.?

16. How much hay in 7 stacks, each containing 6 T. 250 lb.?

17. If 5 lb. 8 oz. of grapes be required to fill a box, what will be the weight of enough to fill a half-gross of boxes of the same capacity?

18. How much land in 3 farms, each farm being divided into 10 fields, and each field containing 14 A. 20 P.?

19. What will be the cost of 4 pieces of cloth, each piece containing 30 yards, at 16s. 9d. a yard?

20. If a pipe discharge 4 hdd. 26 gal. 3 qt. of water in 1 hour, how much will it discharge in 48 hours?

DIVISION.

WRITTEN EXERCISES.

350. 1. Divide 88 bu. 3 pk. 7 qt. by 6.

OPERATION.

bu.

pk. qt. pt.

6)88

3

0

14 3

2

1

ANALYSIS.-Write the divisor at the left of the dividend, as in simple numbers. The object in this example is to find of a compound number.

1 sixth of 88 bu. is 14 bu. and a re

mainder of 4 bu. Write the 14 bu. in the quotient, and reduce the 4 bu. to pecks. 4 bu. equal 16 pk., plus 3 pk. make 19 pk.

1 sixth of 19 pk. is 3 pk. and a remainder of 1 pk. Write the 3 pk. in the quotient and reduce the 1 pk. to quarts. 1 pk. equals 8 qt., plus 7 qt. make 15 qt.

1 sixth of 15 qt. is 2 qt. and a remainder of 3 qt. Write the 2 qt. in the quotient, and reduce the 3 qt. to pints. 3 qt. equal 6 pt. 1 sixth of 6 pt. is 1 pt., which write in the quotient.

4. Divide 88 bu. 3 pk. 7 qt. by 14 bu. 3 pk. 2 qt. 1 pt.

OPERATION.

88 bu. 3 pk. 7 qt. = 5694 pt.

11 bu. 3 pk. 2 qt. 1 pt. 949 pt.

5694 pt. 949 pt.

=

= 6

ANALYSIS.-The object

in this example is to divide one compound number by another.

88 bu. 3 pk. 7 qt. are

equal to 5694 pints; and 14 bu. 3 pk. 2 qt. 1 pt. are equal to 949 pt.;

and 949 pt. is contained in 5694 pt., 6 times.

5. Divide 31 lb. 8 oz. by 2 lb. 10 oz. Troy.

6. Divide £98 16s. by £4 2s. 4d.

RULE.-When the divisor is a simple number.

I. Write the divisor at the left of the dividend, and begin with the highest denomination and divide as in simple numbers.

II. When there is a remainder after dividing any denomination, reduce it to the next lower denomination, and to the result add the given number of that denomination, if any, and divide as before.

When the divisor is a compound number.

Reduce both dividend and divisor to the lowest denomination contained in either, and divide as in simple numbers.

What is the quotient of

7. 376 gal. 3 qt. 1 pt.÷9? 10. 9 hhd. 28 gal. 2 qt.÷12? 8. 328 yd. 1 ft. 3 in.÷6? 11. 153° 16′ 12′′ ÷ 9 ?

9. 281 A. 85 P. = 14?

12. £98 16s. 24?

13. 3 da. 11 hr. 10 min. ÷ 7 hr. 45 min. 50 sec.?

14. A teamster drew 19 cd. 2 cd. ft. 11 cu. ft. of wood at 15 loads: how much did he average per load?

15. Bought 6 spoons, which weighed 11 oz. 3 pwt.: what was the weight of each spoon ?

16. If a man feed his horse 1 pk. 4 qt. of oats a day, how long will 5 bu. 2 pk. 4 qt. last him?

17. How many iron rails, each 18 ft. long, will be required to lay 3 miles of railroad track?

18. The total weight of 18 hhd. of sugar is 7 T. 15 cwt. 66 lb. 4 oz. what is their average weight?

19. If a township of land 3 miles square be divided equally into farms of 120 A. each, what number of farms will it make?

351.

MEASUREMENTS.

RECTANGULAR SURFACES.*

WRITTEN EXERCISES.

1. What is the area of a floor 27 ft. long and 18 ft. wide? (297.)

2. How many feet wide is a hall that is 36 ft. long, and contains 252 square feet? (298.)

3. What is the area of a rectangle whose length is 13 ch. and breadth 9 ch. ?

4. A hall floor 8 ft. 4 in. wide contains 450 sq. ft. What is its length?

5. What will it cost to cover the floor with carpeting yd. wide, at $2.25 a yard?

6. How many acres in a piece of land 60 rd. square? 7. What is the difference between the area of a floor 25 ft. square and that of two others 12 ft. 6 in. square?

8. What will be the cost of a piece of land 80 rd. long and 75 rd. wide, at $68 an acre?

9. A rectangular field 120 rd. long contains 24 A. What is its width?

10. What will be the cost of covering the floor of a hall 45 ft. long and 6 ft. 6 in. wide, with oilcloth, at $1.35 a square yard?

11. What will be the cost of glazing 5 windows, each 8 ft. 2 in. by 4 ft., at $.75 a square foot?

12. How many small squares, each containing 6 sq. in., are equal to one large one, 3 feet square.

*For Definitions, Illustrations, etc., see pages 197, 198, and 199.