Operations with Fractions

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SSAT Upper Level Quantitative › Operations with Fractions

Questions 1 - 10

1

Solve,

$\frac{2}{13}+\frac{4}{13}=?$

$\frac{6}{13}$

$\frac{6}{26}$

$\frac{3}{13}$

$\frac{2}{13}$

Explanation

Since the denominators for the fractions are the same, keep the denominator and add the numerators.

$\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}$

2

$\frac{5}{6}\div \frac{1}{12}=?$

$\frac{5}{72}$

$\frac{1}{2}$

Explanation

Turn the second fraction upside down to find its reciprocal, and then multiply the first fraction by the reciprocal of the second fraction to divide the two fractions. When multiplying fractions, you can multiply across, finding the products of the numbers being multiplied in the numerator and in the denominator.

$\frac{5}{6}\div \frac{1}{12}=\frac{5}{6}\times\frac{12}{1}=\frac{60}{6}=10$

3

Multiply these fractions:

$\frac{1}{4}\cdot \frac{2}{5}$

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{1}{20}$

$\frac{2}{9}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{1}{4}\cdot \frac{2}{5}=\frac{1\cdot 2}{4\cdot 5}=\frac{2}{20}$

Then simplify the fraction accordingly:

$\frac{2\div 2}{20\div 2}=\frac{1}{10}$

4

Multiply these fractions:

$\frac{1}{4}\cdot \frac{2}{5}$

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{1}{20}$

$\frac{2}{9}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{1}{4}\cdot \frac{2}{5}=\frac{1\cdot 2}{4\cdot 5}=\frac{2}{20}$

Then simplify the fraction accordingly:

$\frac{2\div 2}{20\div 2}=\frac{1}{10}$

5

Solve,

$\frac{2}{13}+\frac{4}{13}=?$

$\frac{6}{13}$

$\frac{6}{26}$

$\frac{3}{13}$

$\frac{2}{13}$

Explanation

Since the denominators for the fractions are the same, keep the denominator and add the numerators.

$\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}$

6

$\frac{5}{6}\div \frac{1}{12}=?$

$\frac{5}{72}$

$\frac{1}{2}$

Explanation

Turn the second fraction upside down to find its reciprocal, and then multiply the first fraction by the reciprocal of the second fraction to divide the two fractions. When multiplying fractions, you can multiply across, finding the products of the numbers being multiplied in the numerator and in the denominator.

$\frac{5}{6}\div \frac{1}{12}=\frac{5}{6}\times\frac{12}{1}=\frac{60}{6}=10$

7

What is the result of this operation?

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

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{2}{7}$

Explanation

Since the denominators are exactly the same, we can just subtract the tops.

So

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

By reducing we get

$\frac{1}{2}$

8

What is the result of this operation?

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

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{1}{4}$

$\frac{2}{7}$

Explanation

Since the denominators are exactly the same, we can just subtract the tops.

So

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

By reducing we get

$\frac{1}{2}$

9

$\frac{4}{5}\div\frac{7}{8}=?$

$\frac{32}{35}$

$\frac{14}{27}$

$\frac{7}{20}$

$\frac{35}{32}$

Explanation

Turn the second fraction upside down to find its reciprocal, and then multiply the first fraction by the reciprocal of the second fraction to divide the two fractions. When multiplying fractions, you can multiply across, finding the products of the numbers being multiplied in the numerator and in the denominator.

$\frac{4}{5}\div\frac{7}{8}=\frac{4}{5}\times\frac{8}{7}=\frac{32}{35}$

10

Multiply these fractions:

$\frac{2}{3}\cdot \frac{1}{7}$

$\frac{2}{21}$

$\frac{2}{11}$

$\frac{3}{11}$

$\frac{2}{23}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{2}{3}\cdot \frac{1}{7}=\frac{2\cdot 1}{3\cdot 7}=\frac{2}{21}$

Since this fraction is in its simplest form, that is the final answer.

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