2. 18 to 16ths; 32 to 12ths; 35 to 40ths; 45 to 9ths. 3. 164 to 3ds.

MODEL. 1 = }; 164 = 164 × }

=

432; 492 + 2 = 494 Ans.

4. 22 to 4ths; 163 to 8ths; 25 to 7ths; 485 to 18ths. In practice we multiply the whole number by the denominator of the fraction, and add to the product the numerator of the fraction, and write the denominator of the fraction under the sum.

5. Change 21 to an improper fraction.

11

6. Change 268 to an improper fraction.
7. Change 285 to a mixed number.
H=1, hence 285 as many 1's as 11 is con-
tained times in 235, which is 21.

Change to whole or mixed numbers:
8. 263, 564, $105, 279 rd., 873 ft.
9. Change and to 36ths.

36

Both terms of each fraction are multiplied by that number which will raise the denominators of the given fractions to the required denominator. (Lesson 25, 8th.)

=, hence 18 = as many 's as 4 is contained times in 16, which is 4, therefore 18 = 1.

Both terms of the fraction are divided by that number which will reduce the denominator of the given fraction to the required denominator.

The value of a fraction is not changed if both numerator and denominator are divided by the same number. (Lesson 26, 6th.)

A fraction is in its lowest terms when the numerator and denominator are prime to each other.

40

80

25

7. Change to lowest terms: 4, 3, 48, 12%, 188, 120,

75 48 105 75 160 400 64' 135' 120°

LESSON 40

When the denominators of several fractions are similar, they are said to have a Common Denominator. Thus, and have a common denominator.

The smallest common denominator which several fractions may have is called their Least Common Denominator. The least common denominator which,, and may have is 12.

10. Change, 2, 18 to their least common denominator.

Least common denominator is 36. Both terms of each fraction are multiplied by that number which will raise the denominators of the given fractions to the required denominator.

To find the number by which we multiply, we divide the required denominator by the denominators of the several fractions.

Change to their L. C. D.:

OPERATION

5

5 × 6

30

6

6 x 6

36

7

7 x 3

21

=

12

12 × 3

36

13 × 2

26

13

18 x 2

The least common denominator of several fractions is

their Least Common Multiple.

GRAD. ARITH. V. —4

Therefore when the L. C. D. of several fractions cannot be easily found by inspection it may be found as follows:

1. Change, to their L. C. D.

MODEL. 9 = 3 x 3

2 x 2 x 3 x 3 x 5 = 180 L. C. M. of the denominators, which is the L. C. D. to which the fractions may be reduced.

11. When is a fraction said to be in its lowest terms?

12. How do you reduce a fraction to its lowest terms? 13. Change 5 to an improper fraction. Give analysis.

14. In practice, how do we change a mixed number to an improper fraction?

15. How many 4ths of a yard in 93 yards?

16. Change to 5 equivalent fractions.

17. Name several denominators to which 6ths and 8ths may be reduced.

17. A boy rode of a mile and walked of a mile. How far did he go?

18. How much silk are 31 yards and 4 yards?

MODEL. 3 yards + 4 yards = 7 yards.yard + yard = 7 yards,

or 11 yards. 7 yards + 1 yards = 84 yards.

19. How many gallons are 31 gallons and
20. How many inches are 31 in. and 2 in. ?
21. Add by 11 from to 15.

22. A farmer sold & dozen eggs to one man,
another, and dozen to another.
he sell?

gallon?

dozen to

How many dozen did

23. How many pounds are 53 lb. and 45 lb. ? 24. What is the sum of $3, $, and $?