How to subtract fractions

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ISEE Middle Level Quantitative Reasoning › How to subtract fractions

Questions 1 - 10

Subtract:

$\frac{9}{9}-\frac{5}{9}=$

$\frac{4}{9}$

$1\frac{3}{9}$

Explanation

Subtract the numerators and leave the denominators the same:

$\frac{9}{9}-\frac{5}{9}=\frac{4}{9}$

Answer: $\frac{4}{9}$

$x = \frac{1}{2} + \frac{1}{3}$

$y = \frac{1}{2} + \frac{2}{3}$

Which is the greater quantity?

(a)

(b) $-\frac{1}{2}$

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

Subtract both sides of the two equations:

$x = \frac{1}{2} + \frac{1}{3}$

$y = \frac{1}{2} + \frac{2}{3}$

$x - y = \frac{1}{2} + \frac{1}{3}- \left ( \frac{1}{2} + \frac{2}{3} \right )$

$x - y = \frac{1}{2} + \frac{1}{3}-\frac{1}{2} - \frac{2}{3}$

$x - y = \frac{1}{2} -\frac{1}{2}+ \frac{1}{3} - \frac{2}{3}$

$x - y = - \frac{1}{3}$

Since $\frac{1}{3} < \frac{1}{2}$ , then $x-y = -\frac{1}{3} > - \frac{1}{2}$

Solve:

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

$\frac{1}{14}$

$\frac{3}{5}$

$-\frac{3}{5}$

$-\frac{1}{14}$

$\frac{1}{7}$

Explanation

The lowest common denominator of 2 and 7 is 14.

$\frac{1}{2}=\frac{7}{14}$

$\frac{3}{7}=\frac{6}{14}$

$\frac{7}{14}-\frac{6}{14}=\frac{1}{14}$

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

Subtract:

$\frac{90}{91}-\frac{47}{91}=$

$\frac{43}{91}$

$\frac{34}{91}$

$\frac{47}{91}$

Explanation

Subtract the numerators and leave the denominators the same:

$\frac{90}{91}-\frac{47}{91}=\frac{43}{91}$

Answer: $\frac{43}{91}$

Subtract:

$\frac{25}{88}-\frac{16}{88}=$

$\frac{9}{88}$

$\frac{34}{88}$

$\frac{41}{88}$

Explanation

To solve, subtract the numerators and leave the denominators the same:

$\frac{25}{63}-\frac{16}{88}=\frac{9}{88}$

Answer: $\frac{9}{88}$

A baker used $\frac{1}{3}$ of a package of sprinkles and $\frac{2}{3}$ of a package of icing when decorating a cake. How much more icing than sprinkles did the baker use?

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{3}{3}$

$\frac{4}{3}$

$\frac{5}{3}$

Explanation

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

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

1 3

Subtract the following fractions:

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

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{3}{4}$

Explanation

Subtract the following fractions:

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

To solve this problem, we need to find a common denominator. 6 will work, because both 6 and 3 fit evenly into 6.

We need to change "two-thirds" into sixths. to do so, multiply the top and bottom of the term by 2. Then subtract by taking 5-4 and keeping the denominator.

$\frac{5}{6}-\frac{2*2}{3*2}=\frac{5}{6}-\frac{4}{6}=\frac{1}{6}$

So our answer becomes:

$\frac{1}{6}$

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.

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