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20

1. Tell which of the following are odd numbers and which are even numbers: 14, 17, 19, 20, 24, 27.

2. The fractions 1, Is, and 1 have a denominator.

3. Change ğ and to equivalent fractions having a common denominator. I can change thirds and fifths to 23 을 A

4. Add \ and ž I can change 7ths and 3ds to 4 1

twenty-firsts and twentyfirsts

twenty-firsts. 5. Divide by . This means, find how many times

is contained in I can change 5ths to One twentieth is contained in twentieths times.

6. Multiply 6.05 by 3. Three times
(a) Find the product of 34.02 multiplied by 4.
7. Divide $6.28 by 2. This means,

10* (b) Find the quotient of $475.65 divided by 5. 8. When hay is $12 a ton, 1500 lb. cost dollars. 9. When coal is $7 a ton, 3000 lb. cost

dollars. 10. A 2-inch square is how many times as large as a 1-inch square ?

11. A 2 inch cube is how many times as large as a 1-inch cube?

(c) How many square inches in an oblong 9 inches by 23 inches ?

12. Three fourths of 20 are 1 half of
(d) Three fourths of 84 are 1 half of what number?

* See note 10, page 9

acres.

MISCELLANEOUS. 1. Mr. A owned 15į acres of land; he sold 64 acres ; ho then had

(a) Mr. B owned 5464 acres of land; he sold 228 acres. How many acres had he remaining ?

2. A bushel of oats weighs 32 lb.; 2 bushels of oats weigh pounds; 3 bushels weigh pounds.

(b) Sixty bushels of oats weigh how many pounds less than one ton ?

3. Two pounds of coffee @ $.23 a pound cost (C) Find the cost of 84 pounds of coffee @ $.23 a pound.*

4. From a piece of cloth containing 12 yards there were sold 5} yards and 24 yards; there were left yards.

(d) From a piece of cloth containing 55 yards, there were sold 24; yd. and 17 yd. How many yards were left?

5. A boarding-school uses one gallon of milk each day; at 5¢ a quart the milk for one week costs

(e) A boarding-school uses 4 gal. of milk each day; at 5¢ a quart how much will the milk for the month of October cost ?

6. John bought 20 oranges at 3¢ each and sold them at 5¢ each; he gained cents.

(f) John's father bought 25 bushels of potatoes at 32¢ a bushel and sold them at 45° a bushel. How much did he gain?

*In multiplication of decimal fractions, require the pupil to locate the decimal point in the product immediately after he has written the figure to the right of the decimal point in any whole or partial product. Thus, in the

$.23 multiplication of $.23 by 84 he writes (and thus locates) the decimal point of the product immediately after writing the figure 9 in the first partial product. This will be quite clear to the pupil if he understands that he first finds 4 times .23; then 80 times .23; then the sum of these two partial $19.32 products.

84

.92 18.4

SIMPLE NUMBERS.

1. Seventeen is an integral number.
2. Five eighths is a fractional number.
3. Seventeen and five eighths is a mixed number.

51 is a

4. 25 is an
5. 1 is a
6. .8 is a

number. number. number.

3.5 is a
18 is an

number number. number.

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 fives.

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(a) Divide $2150 by 50.* (b) Divide $215.00 by 50. (c) Divide $2295 by 51. (d) Divide $290.70 by 51. (e) Divide $2058 by 49. (f) Divide $156.80 by 49. (g) Divide $3276 by 52. (h) Divide $322.40 by 52. (i) Divide $2496 by 48. (j) Divide $254.40 by 48.

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

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

COMMON FRACTIONS.

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Reduce to equivalent fractions having a common denominator : 1. 1 and (Change to —.) 4 } (a) f and (b) i and (c) and . 2. Add $ and (Change to -ths.) * (d) Find the sum of 248% and 467}. 3. From subtract . (Change to —ths.) (e) Find the difference of 8373 and 284..

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

2 thirds are contained in thirds times. Story. +

3

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

5. Divide 84 feet by 2. feet. 1 half of 8 feet =

This means, find 1 half of 8.1
Story.

(g) Find the quotient of 864 miles divided by 2. Story |

(h) 34 miles)154 miles. This means, find how many times

31 miles are contained in 154 miles. (Change 3} and 154 to halves.) StoryA canal-boat moved at the rate of 3} miles an hour; to move 154 miles would require hours.

(i) 3)1654 miles. This means, find i third of 165} miles.

Story A train moved 165miles in 3 hours; it moved at the rate of miles an hour.

* See page 12, problem 6. † See page 12, problem 7. I See note (4), page 6. 8 48 feet of ribbon was cut into pieces į of a foot long; there were — pieces. | A train moved 862 miles in 2 hours; this was at the rate of miles an hour.

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

Explanation. $3747

One tenth of $374 = .3

Three tenths of $374 $112.2

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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 hundred'hs. ? This means, find 1 fifth of 85 hundredths.

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