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280. Written Exercises.

1. From 9} subtract 4g. MODEL: 91

Since the fraction in the minuend

is less than the fraction in the sub-43 43

trahend, add or 1 to the fraction

of the minuend. s and are Add 1 to 4. 5 and 4 are 9.*

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f 9} 7} 8} 143 22; 341 403 -43 - 4 - 2 - 23 – 6

- 63 -4– 153 - 17 - 103

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4. Find the sum of each of the above exercises.

5. From a piece of cloth containing 74 yd. of silk a merchant sold 3; yd. How many yards remained ?

6. A grocer bought 36 doz. eggs. He sold 44 doz. to one customer and 3 doz. to another. How many dozen did he sell to both ?

7. A girl bought 64 yd. of lace. She used 23 yd. to trim a dress. How much lace had she left?

* After the pupils have become familiar with this method, they may be taught to subtract the fraction of the subtrahend from 1, and to add the difference to the fraction in the minuend, thus: į and į make 1. } (the difference) and } (the fraction in the minuend) make ţ, the fractional part of the answer.

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5. A girl's weight on June 15th was 941 lb., and on August 15th was 1024 lb. How much did she gain in two months ?

6. Alice bought 12 yd. of lace and used 8 yd. to trim a dress. How much of the lace had she left ?

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7. Find the sum of 23 lb., 63 lb., and 8} lb.
8. Find the sum of 3} yd., 63 yd., and 83 yd.

282. Oral Exercises.

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1. In the fractions , }, }, and , the unit of measure is : The 5 shows into how many equal parts the quantity is divided. It is called the denominator of the fractions. It names the equal parts. The 2, 3, 1, and 4 tell the number of equal parts taken, or the number of times the unit of measure is taken. The upper term is called the numerator of the fraction.

2. In 4, 6 is the denominator. It shows that the quantity is divided into 6 equal parts, or into sixths, and that the unit of measure is d. The numerator is 4. It tells the number of equal parts taken, or the number of times the unit of measure, t, is taken.

3. A fraction whose numerator is less than the denominator is called a proper fraction.

4. A fraction whose numerator is equal to or greater than the denominator is called an improper fraction.

5. Name the numerator, the denominator, and the unit of measure in the following. Tell which are proper fractions: , , }, }, }, , 4, §, 4.

: 6. Such numbers as 8, 7, 4, 25, etc., are called integers. When a number is composed of an integer and a fraction, it is called a mixed number. 8 is a mixed number. It is expressed in two units of measure. The 8 is expressed in ones, the sin fourths. It may all be changed to fourths. There are 4 in 1. In 8 there are 3 32 and i are 35.

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REDUCTION OF FRACTIONS 283. To change a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, add the numerator, and write the sum over the denominator of the fraction.

1. Change 6 to an improper fraction. MODEL: 5x6 = 30

To change the 6 to fifths, 30 + $ = 34

multiply it by 5. 5 times 6

is 30. 2. Change the following mixed numbers to improper fractions : 89, 94, 75, 93, 10.7, 153, 64.

3. Write ten mixed numbers and change them to improper fractions.

4. Change to improper fractions: 73, 63, 34, 43.

284. To change an improper fraction lo a mixed number, divide the numerator by the denominator. 1. Change 25 to a mixed number.

61 MODEL:

Divide 25 by 4. 2. Change the following improper fractions to mixed numbers: 4, 18, 6,5, *, 17, 18. 3. Change to mixed numbers: 13, 14, 145, 83.

. 4. Write ten improper fractions and change them to mixed numbers.

5. Find the sum of the following by adding the numerators together. Reduce the answer to a mixed number: 5, 16, 23, 14, 17. 7.

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1 = 4 1 = 1= 1 = 12 285. 1. Show in a similar way: }= , = s, } = 12. 2. Show in a similar way: 1=5, £= 12, 4 = 16 . 3. Change to 12ths : }, }, 1, 1. 4. Which is the larger, and how much, for

5 ? 5. The fractions , , , and ^ are alike in value.

1å They differ in form.

6. Can you add the following fractions as they stand: 1 ft., i ft., and ift.?

7. Can you add the following fractions as they stand: 1 ft., } ft., and i ft.?!

8. Can you add the fractions in Question 7 if they are changed to inches?

9. Can you add the following fractions : 1 ft., } doz., 1 gal.? Is there a common unit to which

a they can be changed ?

10. Multiply the numerator and the denominator of 1 by 4. The answer is — Has the value of the fraction been changed ?

11. Multiply the numerator and the denominator of } by 4. The answer is — Has the value of the fraction been changed ?

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