SSAT Middle Level Quantitative - How to subtract fractions

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?

$\frac{2}{8}$

$\frac{3}{8}$

$\frac{4}{8}$

$\frac{5}{8}$

$\frac{6}{8}$

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

Evaluate:

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

$4 \frac{7}{15 }$

$4 \frac{1}{2 }$

$4 \frac{1}{3 }$

$4 \frac{8}{15 }$

$4 \frac{3}{5 }$

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:

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

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

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

$21\frac{3}{13}$

$22\frac{3}{13}$

$23\frac{3}{13}$

$21\frac{7}{13}$

$22\frac{7}{13}$

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

3 8

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.

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

3 6

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.

$7 \frac{1}{2}$ hours is how many more minutes than $3 \frac{3}{4}$ hours?

Explanation

This question requires you to subtract fractions as well as convert hours to minutes.

Subtracting $3\frac{3}{4}$ hours $\left ( \frac{15}{4} \right )$ from $7\frac{1}{2}$ hours $\left ( \frac{15}{2}\ or\ \frac{30}{4} \right )$

you get $3\frac{3}{4}$ hours $\left ( \frac{15}{4} \right )$ .

3 hours is 180 minutes $\left ( 3\cdot 60 \right )$

and $\frac{3}{4}$ of an hour is 45 minutes $\left ( \frac{3}{4}\cdot 60 \right )$ .

Thus the answer is

$180+45=225\ minutes$

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

$20\frac{1}{4}$

$19\frac{1}{4}$

$19\frac{2}{4}$

$20\frac{2}{4}$

$52\frac{6}{4}$

Explanation

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

$\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$

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

Give the result in simplest form:

$\frac{17}{40} - \frac{1}{40} + \frac{19}{40}$

$\frac{7}{8}$

$\frac{37}{40}$

$-\frac{3}{40}$

$\frac{3}{40}$

$\frac{7}{24}$

Explanation

$\frac{17}{40} - \frac{1}{40} + \frac{19}{40}$

$=\frac{17-1+19}{40}$

$=\frac{16+19}{40}$

$=\frac{35}{40} = \frac{35\div 5}{40\div 5} = \frac{7}{8}$

Solve:

$\frac{7}{8}-\frac{3}{16}$

$\frac{11}{16}$

$\frac{4}{16}$

$\frac{4}{8}$

$\frac{1}{4}$

$\frac{13}{16}$

Explanation

$\frac{7}{8}-\frac{3}{16}$

In order to solve this problem, we first have to find common denominators.

$\frac{7}{8}\times\frac{2}{2}=\frac{14}{16}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{14}{16}-\frac{3}{16}=\frac{11}{16}$

Select the fraction model that shows the difference of $\frac{7}{8}-\frac{3}{8}$

4 8

5 8

3 8

4 6

5 6

Explanation

$\frac{7}{8}-\frac{3}{8}=\frac{4}{8}$

The fraction model is broken up into eight pieces and four 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.

How to subtract fractions

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