3. How many fourths in 12 units?
4. How many fourths in 2 units?

5. How many fourths in 4 units?

6. How many fourths in 3 units? In 5 units?
7. How many halves in 1 unit? In 2 units?
8. How many halves in 1 units?

9. How many thirds in 1 unit? In 2 units? 10. How many thirds in 3 units? In 7 units? 11. How many thirds in 13 units? In 23 units? 12. How many sixths in 1 unit? In 2 units? Fractions like, 2, 1, 2, in which the value is less than one, are called proper fractions.

24 3

Fractions like, 4, 4, in which the value is equal to or greater than one, are called improper fractions. The numerator of a proper fraction is less than the denominator.

The numerator of an improper fraction is equal to or greater than the denominator.

Written Exercise

384. Copy and place in separate columns the

proper and improper fractions:

To Change a Whole Number to an Improper Fraction

385. 1. How many fourths in 3?

6. How many tenths in 3? In 10? In 15?

6. How many fourths in 4? In 101? In 121?

7. How many sixths in 5? In 65? In 16?

To Change a Mixed Number to an Improper Fraction

387. 1. How many fifths in 2g?

Oral Problems

389. 1. How many pieces of lace, each yd. long, can be cut from a piece 12 yd. long?

2. How many boxes, each holding doz., can be filled from a crate containing 6 doz. eggs ?

3. How many pecks of corn in a sack containing 21 bu.?

4. How many packages of tea, each containing lb., can be put up from a can containing 10 lb. ? 5. How many 10-cent pieces in $56?

To Reduce an Improper Fraction to a Whole Number or Mixed Number

390. 1. Reduce 24 to a whole number.

PROCESS BY CANCELATION

EXPLANATION. - Can

cel the common factor 4 from the numerator and denominator.

2. Reduce 159 to a whole number.

PROCESS BY DIVISION

A fraction is an indicated division. The numerator is the dividend, the denominator is the divisor.

IMPORTANT PRINCIPLE IN FRACTIONS

I

Dividing both terms of a fraction by the same number does not change the value of the fraction.

To Reduce a Fraction to Lower Terms

392. 1. Reduce 3g to lower terms.

PROCESS

1 3

EXPLANATION.

Cancel the com

36 X 3 mon factors in the numerator and the

48

=

=

8x8 4

1 4

denominator.

2. Reduce 48 to lower terms:

PROCESS

1 3 1

540 10 × 9 × 6

=

720 10 × 12×6

1 4 1

3

=

4

EXPLANATION.-Cancel the common factors from the numerator and denominator.

When all the common factors have been canceled from the numerator and the de

nominator, the fraction is in its lowest terms.

In practice the factor 1 is not written.