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SIMPLE NUMBERS.*

1. Four, 6, 8, 10, 12, etc., are multiples of 2. 2. Six, 9, 12, 15, 18, etc., are multiples of 3. 3. Twelve is a multiple of 2. 3, and of 4, and of 6.

12 is also a multiple of

4. Twelve is a common multiple of 2, 3,

5. Fifteen is a common multiple of

and

and

6. Common multiples of 4 and 6 are, 12, 24, The least common multiple of 4 and 6 is 12.

etc.

7. Common multiples of 6 and 8 are, 24, 48,

etc.

etc.

The least common multiple of 6 and 8 is

8. Common multiples of 8 and 12 are, The least common multiple of 8 and 12 is 9. Common multiples of 6 and 9 àre, The least common multiple of 6 and 9 is

10. The prime factors of 18 are

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11. The prime factors of 70 are

and

(a) What are the prime factors of 140. (c) Of 135? (d) of 175?

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(b) Of 160?

(e) Of 250 ?

(f) Of 225?

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Divide.

(i) 1536 lb. by 12.†

(1) 1445 lb. by 12.

(0) 1374 lb. by 12.

(q) 873 lb. by 56 lb.

(r) 1653 lb. by 12.

(s) 836 by 55.

(t) 965 lb. by 56 lb.

(u) 1738 lb. by 12.

* Do much oral work in preparation for this page. By using these terms, make the pupil as familiar with multiple, common multiple, and least common multiple, as he is with house, schoolhouse, and stone schoolhouse.

†Tell the meaning. Tell a number story.

COMMON FRACTIONS.

L. c. m. is the abbreviation for least common multiple.

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(t) 6)756 dollars. This means, find 1 sixth of $756. Story.

This means, find how many times $61 are contained in $375.

DECIMAL FRACTIONS.

1. One tenth of $432 is

2. One hundredth of $432 is

.2 of $432 =

.02 of $432

=

(a) Multiply $432 by .25. This means, find 2 tenths of

$432, plus 5 hundredths of $432.

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If 1 acre of land is worth $432,

1 hundredth of an acre is worth

5 hundredths of an acre are worth

1 tenth of an acre is worth

2 tenths of an acre are worth
25 hundredths of an acre are worth

(b) Multiply $325 by .23.
(d) Multiply $278 by .43.
(f) Multiply $536 by .07.
(h) Multiply $249 by 2.6.

(c) $482 × .32.
(e) $356 x .36.
(g) $351 x .7.

(i) $426 x 45.

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*The pupil should understand that he multiplies $4.32 (not $132) by 5, and should be taught to write the decimal point in the partial product immediately after writing the tenths' figure, 6, of the partial product.

The pupil should understand that he multiplies $13.2 (not $432) by 2, and should be taught to write the decimal point in the partial product immediately after writing the tenths' figure, 4, of the partial product.

DENOMINATE NUMBERS.

1. Sixteen and one half feet are 1 rod.

2. Three hundred twenty rods are 1 mile.

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(a) How far is it from the first telegraph pole to the thirty-third ?

9. The roads in the country are usually 4 rods wide. A 4-rod road is

10. A 100-foot street is

feet wide.

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(d) Change 28 rd. to yards.

(c) Change 40 rd. to feet. (e) Change 7 mi. to rods.

REVIEW.

12. When hay is $12 a ton, 3000 lb. cost 13. When oats are 30¢ a bushel, 96 lb. cost

14. When wheat is 80¢ a bushel, 180 lb. cost

(f) When corn (not shelled) is 45¢ a bushel, how much will 3640 lb. cost?

(g) When coal is $5.40 a ton, how much will 2600 lb. cost?

* Discover by actual measurement the number of yards in a rod.

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1. A pile of wood 8 feet long, 4 feet wide, and 4 feet high (or its equivalent) is called a cord.

(a) How many cubic feet in a rectangular solid 8 feet by 4 feet by 4 feet?

2. A pile of wood 16 feet long, 4 feet wide, and 4 feet high contains cords.

(b) How many cubic feet in 2 cords?

3. A pile of wood 8 feet long, 4 feet wide, and 6 feet high contains

cords.

(c) How many cubic feet in 1 cords? (d) In & of a cord? (e) How many cubic feet in 54 cords? (f) In 63 cords?

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(g) Find the area of a surface 12 ft. by 24 ft.*

(h) Find the volume of a solid 12 ft. by 8 ft. by 4 ft.†

*Take care that the pupil understands that he does not (cannot) multiply 24 ft. by 12 ft., but 24 square feet by 12, or 12 square feet by 24.

+In this problem the pupil multiplies 12 cubic feet by 8, and the product thus obtained by 4.

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