How to subtract fractions

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SSAT Middle Level Quantitative › How to subtract fractions

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Evaluate:

$8 \frac{4}{5} - 4 \frac{1}{3}$

$4 \frac{7}{15 }$

CORRECT

$4 \frac{1}{2 }$

$4 \frac{1}{3 }$

$4 \frac{8}{15 }$

$4 \frac{3}{5 }$

Explanation

Rewrite as the difference of improper fractions:

$8 \frac{4}{5} - 4 \frac{1}{3} = \frac{8 \times 5 + 4}{5} - \frac{4 \times 3 + 1}{3} = \frac{44}{5} - \frac{13}{3}$

Rewrite with a common denominator, then subtract numerators:

$\frac{44}{5} - \frac{13}{3} = \frac{44\times 3}{5 \times 3} - \frac{5 \times13}{5 \times3} = \frac{132}{15 } - \frac{65}{15 } = \frac{67}{15 }$

Rewrite as a mixed number:

$67\div 15 = 4 \textrm{ R } 7$

$\frac{67}{15 } = 4 \frac{7}{15 }$

A baker used $\frac{4}{8}$ of a package of sprinkles and $\frac{6}{8}$ of a package of icing when decorating a cake. How much more icing than sprinkles did the baker use?

$\frac{2}{8}$

CORRECT

$\frac{3}{8}$

$\frac{4}{8}$

$\frac{5}{8}$

$\frac{6}{8}$

Explanation

The phrase, "how much more" tells as that we want to find the difference, so we subtract.

$\frac{6}{8}-\frac{4}{8}=\frac{2}{8}$

2 8

Select the fraction model that shows the difference of $\frac{6}{8}-\frac{3}{8}$

3 8

CORRECT

3 6

3 4

4 8

5 8

Explanation

$\frac{6}{8}-\frac{3}{8}=\frac{3}{8}$

The fraction model is broken up into eight pieces and three of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

$29\frac{5}{13}-8\frac{2}{13}$

$21\frac{3}{13}$

CORRECT

$22\frac{3}{13}$

$23\frac{3}{13}$

$21\frac{7}{13}$

$22\frac{7}{13}$

Explanation

When we subtract mixed numbers, we subtract whole numbers by whole numbers and fractions by fractions.

$\frac{5}{13}-\frac{2}{13}=\frac{3}{13}$

Remember, when we are subtracting fractions we must have common denominators and we only subtract the numerators.

Select the fraction model that shows the difference of $\frac{5}{6}-\frac{2}{6}$

3 6

CORRECT

2 6

3 4

2 4

2 3

Explanation

$\frac{5}{6}-\frac{2}{6}=\frac{3}{6}$

The fraction model is broken up into six pieces and three of the pieces are shaded in. The numerator of the fraction tells us how many pieces should be shaded in, and the denominator tells us how many pieces the whole should be split up into.

$36\frac{3}{4}-16\frac{2}{4}$