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3. Divide 42 mi. 160 rd. 5 yd. by 5.

4. How many years, months (30 da.), and days are there from April 29, 1759, to July 4, 1832 ?

5. If .25 of a yard of cloth cost $1.60, how much will 78 yards cost ?

6. Find the sum of four hundred thirty-three thousand six hundred thirty-four dollars and twenty-nine cents; eighty-nine thousand three hundred dollars and seventytwo cents; forty-six thousand three hundred fifty-two dollars and thirty-six cents; sixty-five thousand seven hundred nine dollars and forty-five cents.

7. From 3 billion 444 million 236 thousand 164 dollars and 93 cents take 2 billion 542 million 370 thousand dollars and 98 cents.

8. How many miles are there in 52,800 feet?

9. How many yards of Brussels carpet yd. wide will cover the floor of a room 36 ft. long and 27 ft. wide ?

10. If a boy steps 2 ft. 9 in., how many steps will he take in going from his home to school, a distance of 11 miles ?

11. Divide 853.24 by 102.8; 2088.48 by 15.2. 12. Multiply 845 by .25; by .07; by .006. 13. How many dozen are there in 60 score? 14. Change 124 gross to dozens. 15. Change 13 quires to sheets. 16. Find the cost of 9480 ft. of hemlock boards at $18

per M.

CANCELLATION

LESSON 33

Cancellation is an operation to shorten work in division by striking out common factors from both dividend and divisor.

Striking out a factor from any number divides the number by that factor. Thus, to strike out, or to cancel, 7 from 21, is to divide 21 by 7.

Striking out equal factors from both dividend and divisor simply divides both dividend and divisor by those numbers. 1. Divide 210 by 30.

1 1 1

210 MODEL. 210 30 = 7

2 x 3 x 5 x 7 7

=7. Ans. 30 2 X 3 X 5

1 1 1 It will be seen from the preceding operation that equal factors may be rejected from both dividend and divisor without altering the quotient. 2. Divide 150 by 25.

1 1
150 2 x 3 x 5 x 5_6
MODEL.

= 6. Ans.
25

3 x 8

1 3. Divide 24 x 28 x 32 by 12 x 14 x 16.

2 2 2

24 x 28 x 32 8 MODEL.

8. Ans. 12 x 14 x 16 1

1 1 1 4. Divide 48 x 18 x 20 by 12 x 8 x 10. 5. Divide 40 x 64 x 70 by 8 x 10 x 32.

1

Х

Х

Х

=

Ans.

VI

18 x 36 x 48

24 x 32 x 81 6.

?
7.

?
24 x 9 x 12

6 X 8 X 9 3 x 2 x 12 x 8 x 24

20 x 25 x 15 x 27 8.

? 9. 4 x 6 x 36 x 4

15 x 18 x 10 x 25 10. Find the value of } xxx bp by cancellation.

1 1

4 2 5 MODEL.

4 318 63

1 1 9 11. Find the value of } x x x by cancellation. 12. Find the value of $ x 12 x x } by cancellation. 13. 6 x 3 x 8 x 3

=?

14. f *1 x 18 x 19 = ? 15. Divide 99 x 66 x 21 x 6 by 33 x 22 x 7. 16. Divide 36 x 72 x 96 x 144 by 24 x 36 x 48 x 72. 17. Divide 48 x 27 x 13 x 9 by 18 x 16 x 3 x 26. 18. Divide 125 x 96 x 57 x 15 by 16 x 19 x 25.

19. If 28 tons of coal cost $84, how much will 35 tons cost ?

If 28 tons cost $ 84, one ton will cost it of $ 84, or $ 4, and 35 tons will cost 35

$3
$3
35 x $ 84

x
times $ %, or
or $105.

. 28

28 1 20. At $ 3 a day, how many weeks must a stone mason work to pay for 21 tons of coal at $ 4 a ton ?

21. How much must be paid for 42 gallons of molasses when $18 are paid for 36 gallons ?

22. A farmer sold a barrel of cider, containing 31 gallons, for 14 cents a gallon. How many pounds of sugar, at 7 cents a pound, can he buy for what he receives for the cider ?

OPERATION

PERCENTAGE

LESSON 34

Instead of saying tôo, 167, 1ér, etc., we may use the term per cent for the denominator, hundredths; thus, 2 per cent, 5 per cent, 9 per cent; etc.

The sign % is generally used for the term per cent ; thus, 2%, 5%, 9%, etc. Therefore 1% means ido; 2%, Tõo; 3%, 1; 4%, ifj; etc.

The per cent may be expressed in the form of a common fraction, or of a decimal. Thus, 5% = 160= .05.

The process of computing by hundredths is called Percentage.

3

10?

100?

[ocr errors]

90 ? 100

100

1. What per cent of a number is ito of it? Tir? 167? 16? 16%? 25.?

2. What part of a number is 1% of it? 2%? 3% ? 5% ? 10%? 20%? 30%? 40% ? 50%? 75% ? 80% ? 90%? 100%?

3. What per cent of a number is į of it ?

MODEL. The number equals 100%. į of the number equals 1 of 100%, or 50%

4. What per cent of a number is 1 of it? ? 3? s? } ? ? ? ? ? ?? 3? ? ? 10 ? ? 16? 18? 11? 12 ? 26? 27? 30? 5. What common fraction equals 25%?

MODEL. 25 % equals too, or .

6. What common fraction equals 5%? 4%? 10% ? 20% ? 30% ? 35% ? 50% ? 75% ? 80% ? 90% ? Memorize thoroughly : 61% = 1

81% il 13. 371% = 3 8. 121% = 11. 331% 5 14. 623% = 9. 163% = 1 12. 663%

15. 871% = }

7.

10.

LESSON 35

Express as a decimal, and as a common fraction in lowest terms:

1. 25% = .25 = 1 7. 40% 13.32% 19.62% 2. 15%

8. 4% 14. 26% 20.65% 3. 12%

9. 45% 15. 55% 21. 76% 4. 8%

10. 50% 16. 42% 22. 90% 5. 30%

11. 10% 17. 85% 23. 36% 6. 35% 12. 28% 18. 88% 24.

5%

Find :

25. 10 of 400. MODEL. Ito of 400 is 4, and Tøy of 400 are 6 times 4, or 24 Ans. 26. .06 of 300

30. 6% of 200 34. 5% of 100 27. .06 of 400 31. 6% of 600

35. 5% of 200 28. 6% of 400 32. 6% of 300

36. 5% of 300 29. 6% of 500 33. 6% of 50

37. 5% of 500 38. Find 4 % of 100, 200, 125, 175, 150, 225, 300, 275. 39. Find 12}% of 16, 24, 168, 48, 72, 88, 96, 248. 40. Find 50% of 8, 10, 14, 28, 80, 85, 125, 350.

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