Teaching Models

Add and Subtract Fractions

Comparison of Fractions
Which is greater, three-sevenths or 4/7? When comparing fractions with like denominators, it is enough to compare the numerators. Since 4 unit fractions of one-seventh is greater than 3 unit fractions of one-seventh, four-sevenths is greater than three-sevenths. Which is greater, 7/12 or 5/8? When comparing fractions with unlike denominators, it is usually necessary to find a common denominator. In the example, any common multiple of 12 and 8 will do. For simplicity, choose 12 × 8 = 96.

Since 60 > 56, five-eighths > seven-twelfths.
Now, seven-twelfths = 7 × eight-twelfths × 8 = fifty-six-ninety-sixths and five-eighths = 5 × 12/8 × 12 = sixty-ninety-sixths.

Should students want to use only the least common denominator, suggest they try it both ways and decide for themselves which method is quicker or easier.

Mixed Numbers
A fraction like five-sevenths is said to be proper because the numerator is less than the denominator. A fraction like 4/3 is said to be improper because the numerator is not less than the denominator. Whole numbers can also be written as improper fractions: 1 = five-fifths and 2 = four-halves. The improper fraction four-thirds can be written as the mixed number 1one-third.

Addition and Subtraction of Fractions
To add or subtract fractions with a common denominator, find the sum or difference of the numerators and keep the common denominator. Answers should be expressed in simplest form.

For example, in 3/4 + two-fourths, three unit fractions of one-fourth plus two unit fractions of one-fourth equals five unit fractions of one-fourth. So the answer is five-fourths, or 1 one-fourth. In three-fourthsone-fourth, one unit fraction of one-fourth is subtracted from three unit fractions of one-fourth giving a result of two unit fractions of one-fourth. So the answer is two-fourths, or one-half.

Teaching Model 20.2: Add and Subtract Mixed Numbers

Houghton Mifflin Math Grade 4