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SIMPLE NUMBERS.

1. Seventeen is an integral number.

2. Five eighths is a fractional number.

3. Seventeen and five eighths is a mixed number.

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7. A number is exactly divisible by 2 if the right-hand figure is 0, 2, 4, 6, or 8. Tell which of the following are exactly divisible by 2: 241, 136, 274, 393, 247, 826.

8. A number is exactly divisible by 5 if its right-hand figure is 0 or 5. Tell which of the following are exactly divisible by 5: 184, 275, 320, 145.

9. The following are exactly divisible by 2: 16, 38, 54, 68,

10. The following are exactly divisible by 5: 85, 140, 175, 180,

11. The following are exactly divisible by 10: 30, 40, 80, 120,

12. There are twice as many 5's as there are 10's in a number. 90 is

tens.

90 is (a) Divide $2150 by 50.* (c) Divide $2295 by 51. (e) Divide $2058 by 49. (g) Divide $3276 by 52. (i) Divide $2496 by 48.

fives.

(b) Divide $215.00 by 50.
(d) Divide $290.70 by 51.†
(f) Divide $156.80 by 49.
(h) Divide $322.40 by 52.
(j) Divide $254.40 by 48.

* This means, find 1 fiftieth of $2150. 1 fiftieth of $2150 is If 50 acres of land cost $2150, 1 acre cost.

dollars. Story

In solving such problems as (b), (d), etc., require the pupil to write the decimal point in the quotient, immediately after writing the units' figure of the quotient. If the pupil thinks what the problem means, he will easily "point off" correctly.

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2. Add and . (Change toths.)*

(d) Find the sum of 2488 and 467.

3. From subtract 3. (Change to

-ths.)†

(e) Find the difference of 8373 and 2848.

4. Divide 6 by . This means, find how many times are contained in 6. I can change 6 to thirds. 6 thirds are contained in

thirds

times.

=

3•

Story.‡

(f) Find the quotient of 48 divided by . Story.§

5. Divide 8 feet by 2.

feet. 1 half of 81 feet =

2

This means, find 1 half of 81

Story.

(g) Find the quotient of 86 miles divided by 2. Story.||

(h) 31 miles)154 miles.

This means, find how many times 3 miles are contained in 154 miles.

Story-A canal-boat moved at the

(Change 3 and 154 to halves.)
rate of 31⁄2 miles an hour; to move 154 miles would require
hours.

(i) 3)165 miles.

This means, find 1 third of 165 miles. Story A train moved 165 miles in 3 miles an hour.

hours; it moved at the rate of

* See page 12, problem 6.

† See page 12, problem 7.

See note (4), page 6.

248 feet of ribbon was cut into pieces of a foot long; there were || A train moved 86 miles in 2 hours; this was at the rate of

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(a) Multiply $374 by .3. This means, find 3 tenths of 374.

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* By means of problems 5 to 10 and other similar exercises, lead the pupil to see that he can obtain 1 tenth of an integral number by "pointing off" one figure on the right, and of a mixed decimal by removing the point one place to the left.

†The pupil should understand that he multiplies $37.4 (not $374) by 3, and should be taught to write the decimal point in the product immediately after writing the tenths' figure of the product. See page 10, paragraph 3.

This means, find how many times 5 hundredths are contained in 85 hundredths.
This means, find 1 fifth of 85 hundredths.

DENOMINATE NUMBERS.

A bushel of oats weighs 32 lb.

A bushel of wheat weighs 60 lb.

A bu. of corn (shelled) weighs 56 lb.

A bu. of corn (not shelled) weighs 70 lb.*

lb.; 5 bu. weigh

1. Two bushels of oats weigh (a) How much more than 1 ton do 75 bu. of oats weigh? 2. Two bu. of wheat weigh; 3 bu. weigh (b) Seventy-five bushels of wheat weigh how much more than two tons? (c) How much less than three tons?

3. Two bushels of shelled corn weigh; 3 bu. weigh

(d) Forty-five bushels of shelled corn weigh how much more than 14 tons? (e) How much less than 1 tons? 4. Two bushels of corn (not shelled) weigh bushels weigh -; 4 bushels weigh

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(f) How much more than three fourths of a ton do 25 bushels of corn (unshelled) weigh? (g) How much less than one ton?

5. One hundred pounds of oats are

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bushels and

32nds bushels.

(h) Five hundred pounds of oats are how many bushels? (i) How many bushels in one and one half tons of wheat? (j) How many bushels in two tons of unshelled corn?

(k)

(1)

(m)

(n)

32 lb.)768 lb. 32 lb.)769 lb. 32 lb.)770 lb. 32 lb.)772 lb.

* Explain to the pupil that the expression "a bushel of corn (not shelled)," means, the amount of unshelled corn required to make 1 bushel of shelled corn.

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or

or

(or its equivalent) is called a square square feet.

(or its equivalent) is called a cubic cubic feet.

3. The area of a 4-foot square is

and

square yards.

4. The solid content of a 4-foot cube is

(a) How many cubic yards in a 4-foot cube? 5. The area of a 5-foot square is

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6. The solid content of a 5-foot cube is

(b) How many cubic yards in a 5-foot cube?

7. The area of a 6-foot square is

square yards.

8. The solid content of a 6-foot cube is

(c) How many cubic yards in a 6-foot cube?

9. Find the area of

(1) A 7-foot square.
(2) An 8-foot square.
(3) A 9-foot square.

square feet,

cubic feet,

square feet.

cubic feet.

square feet,

cubic feet.

Find the solid content of—

(d) A 7-foot cube.

(e) An 8-foot cube.
(f) A 9-foot cube.

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