1. Reduce 387 to a fraction.

38 = 38 x 9 ninths = 342 ninths.

342 ninths plus 7 ninths = 349 ninths.

=

The work may be expressed thus: 387-349 Ans.

33. Change 156 to a fraction whose denominator shall be 12.

LEAST COMMON DENOMINATOR

116. Fractions whose denominators are alike have a common denominator; e.g. 60 is a common denominator of 3

18, and 27.

60 60

117. Fractions having the smallest possible common denominator have their least common denominator; e.g. 6, 20, 2.0.

118. Oral

6

1. We have found that when we add fractions having different denominators, we must first change them to fractions having the same denominator. What shall we call that denominator?

2. Since the common denominator must contain all the given denominators, it must be what of those denominators? (A number that exactly contains two or more other numbers is what?)

3. The least common denominator, then, must be which multiple of the given denominators?

and to fractions having the least common

4. Reduce,, and

denominator.

119. Written

33,

Change, 18, and 17 to fractions having the least com mon denominator.

2×3×5×11=330 L. C. M. 330 ÷ 30 = 11

ADDITION OF FRACTIONS AND MIXED NUMBERS

120. A number is in its simplest form when it is in the form of an integer, or a proper fraction in its lowest terms, or a mixed number whose fractional part is in its lowest terms; e.g. 18, , and 5 are in simplest form; 26, 21, 46, and 88 are not. Answers should always be expressed in simplest form.

Why?

=

We add the integers and fractions separately, and then unite the

sums.

RULE. To add fractions, reduce them to their least common denominator, add the numerators, place the sum over the common denominator, and reduce the result to simplest form.

When there are integers or mixed numbers, add the integers and the fractions separately, and unite the results.

13. During a storm, a tree was broken off 173 feet from the ground. The piece broken off was 415 feet long. How tall was the tree before it was broken?

14. The subtrahend is 8933 and the remainder 4911. What can you find? Find it.

15. A rectangular field is 5095 feet long and 347 feet wide. How many feet of fence are required to inclose it?

SUBTRACTION OF FRACTIONS AND MIXED NUMBERS

122. Fractions must have a common denominator in order that one may be subtracted from the other.

In subtracting mixed numbers, if the fraction in the subtrahend is greater than that in the minuend, one integral unit of the minuend must be united with the fraction to form an improper fraction, before subtracting.