Preston-Stevens Elementary Arithmetic by DeForest A. Preston Edward Lawrence Stevens

Author:DeForest A. Preston , Edward Lawrence Stevens
Language: eng
Format: epub, pdf
Publisher: Macmillan
Published: 1910-03-25T05:00:00+00:00

2. Which is the larger, ^ or f? (Sketch.)

3. Which is the larger, |^ or f ? (Sketch.)

4. Which is the larger, | or ^ ? (Sketch.)

If you made sketches as required above, or folded paper and compared the parts, you found that

Study the examples given and see if this statement is true:

Both numerator and denominator may be multiplied by the same number without changing the value of the fraction.

Dividing both numerator and denominator of f by 4, we have |. Did we change the value of the fraction ?

Dividing both numerator and denominator of f by 3, we have ^. Dividing both numerator and denominator of f by 3, we have ^. Does it change the value of a fraction to divide both numerator and denominator by the same number ?

Changing fraction to higher or lower terms.

Note to Teacher, It is better not to use the common term, <' reduction/' as reduction suggests change of value. To reduce anything, such as a debt, we make it less.

103. 1. Change | to a fraction of the same value, having a denominator of 12. (Multiply both numerator and denominator by 4.) How can you tell whether to multiply by 4 or 5 ?

2. Change f to 14ths. What number shall we use to multiply the numerator and denominator ?

3. Change ^ to 25ths.

4. Change | to 24ths.

5. Change f to 28ths.

6. Change ^ to smaller terms. (The numerator and the denominator are called terms of a fraction.)

7. Change \^ to smaller terms.

8. Change ^ to smaller terms.

9. Change ^^ to smaller terms.

In such cases, where the numbers are large, we make use of several small divisors, dividing by 2, 2, 2, 2, etc., until the terms get small enough for us to see what single divisor we can use to complete the change.

10. Change |^| to smaller terms.

ADDITION OF FRACTIONS

In adding fractions, if the denominators are alike, we add the numerators. Adding two thirds and one third is like adding $ 2 and $ 1. f and ^ make |, just as $2 and $1 make $3. If the denominators are not alike, we must change the terms of the fractions until they are alike before we can add. To add ^ and ^ we change the terms, so that ^ becomes f and ^- becomes f. Then we add ^ and ^ and have |- Ans.

104. 1. Add f and |.

ji=l^ Am. 2. Add f and ^.

i=ia

3. Find the sum of f and |^.

4. Find the sum of f and f.

5. Find the sum of |- and f.

161

|- 6. Find the sum of IQ^ and 24^.

f We add the whole numbers and the frac-

f tions separately. A convenient form of

arrangement is shown.

7. Find the sum of 67| lb. and 241 lb.

8. What is the sum of 67^ bu. and 45|^ bu.?

9. Add24|; 16i; 42J; 15; 25f.

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