Fraction division exercises

Fractionsare quotients between two whole numbers and the division of fractions It is a basic operation in which you divide a fraction by another fraction or by a whole number.

To divide fractions, use the following procedure:

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1º) The first fraction is conserved and the terms of the second are inverted, that is, numerator and denominator change places.

2º) Swap the division sign for the multiplication sign.

3º) resolves to multiplication between fractions.

$\dpi{120} \mathrm{\frac{a}{b}: \frac{c}{d} \frac{a}{b}\cdot \frac{d}{c} \frac{a\cdot d }{b\cdot c}}$

The results of the operation can be simplified or cancellation technique can be used before calculating the multiplication.

See below for a list of fraction division exercises, all solved step by step!

Fraction division exercises

Question 1. Calculate divisions and simplify:

The) $\dpi{120} \frac{5}{6}:\frac{1}{6}$

B) $\dpi{120} \frac{5}{7}:\frac{2}{3}$

w) $\dpi{120} \frac{2}{9}:10$

Question 2. Carry out the operations:

The) $\dpi{120} \frac{9}{12}:\frac{3}{4}$

B) $\dpi{120} \frac{1}{2}:\bigg(\frac{2}{3}\cdot \frac{5}{2} \bigg)$

w) $\dpi{120} \bigg(\frac{5}{11}:\frac{2}{11}\bigg)\cdot \frac{5}{8}$

Question 3. Solve:

$\dpi{120} \frac{9}{10} - \frac{2}{5}:\bigg( \frac{1}{2}+\frac{1}{6}\bigg)$

Question 4. Calculate:

$\dpi{120} 1\frac{3}{5}:2\frac{1}{3}$

Question 5. Calculate and simplify:

$\dpi{150} \large \frac{\frac{5}{12}}{\frac{10}{36}}$

Question 6. Calculate:

$\dpi{120} \bigg (3\cdot \frac{1}{2}\bigg):\bigg (8: \frac{2}{3}\bigg)$

Question 7. Calculate:

$\dpi{200} \large \frac{\frac{\frac{3}{5}}{\frac{3}{2}}} {\frac{\frac{7}{8}}{\frac{ 3}{4}}}$

Resolution of question 1

The) $\dpi{120} \frac{5}{6}:\frac{1}{6}$

We must invert the terms of the second fraction of the operation and change the division sign for a multiplication sign:

$\dpi{120} \frac{5}{6}:\frac{1}{6} \frac{5}{6}\cdot \frac{6}{1} \frac{5}{\cancel{6 }}\cdot \frac{\cancel{6}}{1} 5$

B) $\dpi{120} \frac{5}{7}:\frac{2}{3}$

We must invert the terms of the second fraction of the operation and change the division sign for a multiplication sign:

$\dpi{120} \frac{5}{7}:\frac{2}{3} \frac{5}{7}\cdot \frac{3}{2} \frac{15}{14}$

w) $\dpi{120} \frac{2}{9}:10$

The number 10 is the same as $\dpi{120} \frac{10}{1}$ , so when we invert it becomes $\dpi{120} \frac{1}{10}$ :

$\dpi{120} \frac{2}{9}:10 \frac{2}{9}\cdot \frac{1}{10} \frac{\cancel{2}^1}{9}\cdot \ frac{1}{\cancel{10}^5} \frac{1}{45}$

Resolution of question 2

The) $\dpi{120} \frac{9}{12}:\frac{3}{4}$

We must invert the terms of the second fraction of the operation and change the division sign for a multiplication sign:

$\dpi{120} \frac{9}{12}:\frac{3}{4} \frac{9}{12}\cdot \frac{4}{3} \frac{\cancel{9}^3 }{\cancel{12}^4}\cdot \frac{4}{3} 1$

B) $\dpi{120} \frac{1}{2}:\bigg(\frac{2}{3}\cdot \frac{5}{2} \bigg)$

First, we solve the multiplication operation between parentheses. Then we calculate the division.

$\dpi{120} \frac{1}{2}:\bigg(\frac{\cancel{2}}{3}\cdot \frac{5}{\cancel{2}} \bigg) \frac{1 }{2}:\frac{5}{3} \frac{1}{2}\cdot \frac{3}{5} \frac{3}{10}$

w) $\dpi{120} \bigg(\frac{5}{11}:\frac{2}{11}\bigg)\cdot \frac{5}{8}$

First, we solve the division operation between parentheses. Then we calculate the multiplication.

$\dpi{120} \bigg(\frac{5}{11}:\frac{2}{11}\bigg)\cdot \frac{5}{8} \bigg(\frac{5}{\cancel{ 11}}\cdot \frac{\cancel{11}}{2}\bigg)\cdot \frac{5}{8} \frac{5}{2}\cdot \frac{5}{8}\frac {25}{16}$

Resolution of question 3

$\dpi{120} \frac{9}{10} - \frac{2}{5}:\bigg( \frac{1}{2}+\frac{1}{6}\bigg)$

To solve numerical expressions with fractions, we follow the same order of performing operations in numerical expressions with integers.

First, we solve the operation between parentheses:

$\dpi{120} \frac{9}{10} - \frac{2}{5}:\bigg( \frac{1}{2}+\frac{1}{6}\bigg) \frac{9 }{10} - \frac{2}{5}:\frac{2}{3}$

Now, there are no more parentheses. We solve the division:

$\dpi{120} \frac{9}{10} - \frac{\cancel{2}}{5}\cdot \frac{3}{\cancel{2}} \frac{9}{10} - \ fraction{3}{5}$

Finally, we solve the subtraction:

$\dpi{120} \frac{9}{10} - \frac{3}{5} \frac{3}{10}$

Resolution of question 4

$\dpi{120} 1\frac{3}{5}:2\frac{1}{3}$

In this operation, we have mixed fractions, which are formed by an integer part and a fractional part.

Let's solve each term separately by turning the mixed fraction into improper fraction.

$\dpi{120} 1\frac{3}{5} 1 + \frac{3}{5} \frac{8}{5}$

$\dpi{120} 2\frac{1}{3} 2 + \frac{1}{3} \frac{7}{3}$

So, we have to:

$\dpi{120} 1\frac{3}{5}:2\frac{1}{3} \frac{8}{5}:\frac{7}{3}$

All that remains is to solve the division:

$\dpi{120} \frac{8}{5}:\frac{7}{3} \frac{8}{5}\cdot \frac{3}{7} \frac{24}{35}$

Resolution of question 5

$\dpi{150} \large \frac{\frac{5}{12}}{\frac{10}{36}}$

A fraction is a quotient, that is, a division of the numerator by the denominator. So, we can rewrite the above fraction as follows:

$\dpi{120} \frac{5}{12}:\frac{10}{36}$

Now, we solve the division:

$\dpi{120} \frac{5}{12}:\frac{10}{36} \frac{5}{12}\cdot \frac{36}{10} \frac{\cancel{5}}{ 12}\cdot \frac{18}{\cancel{5}} \frac{18}{12} \frac{3}{2}$

Resolution of question 6

$\dpi{120} \bigg (3\cdot \frac{1}{2}\bigg):\bigg (8: \frac{2}{3}\bigg)$

First, we solve the operations between parentheses:

$\dpi{120} 3\cdot \frac{1}{2} \frac{3}{2}$

$\dpi{120} 8:\frac{2}{3} 8\cdot \frac{3}{2} \frac{24}{2} 12$

Therefore:

$\dpi{120} \bigg (3\cdot \frac{1}{2}\bigg):\bigg (8: \frac{2}{3}\bigg) \frac{3}{2}:12$

So, it only remains to solve the last division:

$\dpi{120} \frac{3}{2}:12 \frac{3}{2}\cdot \frac{1}{12} \frac{3}{24} \frac{1}{8}$

Resolution of question 7

$\dpi{200} \large \frac{\frac{\frac{3}{5}}{\frac{3}{2}}} {\frac{\frac{7}{8}}{\frac{ 3}{4}}}$

We can rewrite the above fraction as follows:

$\dpi{200} \frac{\frac{3}{5}}{\frac{3}{2}}: \frac{\frac{7}{8}}{\frac{3}{4}}$

Now we solve each term separately:

$\dpi{200} \frac{\frac{3}{5}}{\frac{3}{2}}$ $\dpi{120} \frac{3}{5}:\frac{3}{2}\frac{\cancel{3}}{5}\cdot \frac{2}{\cancel{3}} \frac {2}{5}$

$\dpi{200} \frac{\frac{7}{8}}{\frac{3}{4}}$ $\dpi{120} \frac{7}{8}:\frac{3}{4}\frac{7}{8}\cdot \frac{4}{3} \frac{28}{24} \frac {7}{6}$

Therefore, we must solve the following division:

$\dpi{120} \frac{2}{5}:\frac{7}{6}$

Let's solve:

$\dpi{120} \frac{2}{5}:\frac{7}{6} \frac{2}{5}\cdot \frac{6}{7} \frac{12}{35}$

Soon:

$\dpi{200} \large \frac{\frac{\frac{3}{5}}{\frac{3}{2}}} {\frac{\frac{7}{8}}{\frac{ 3}{4}}}$ $\dpi{120} \frac{12}{35}$

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Fraction division exercises

Fraction division exercises

Resolution of question 1

Resolution of question 2

Resolution of question 3

Resolution of question 4

Resolution of question 5

Resolution of question 6

Resolution of question 7

$\dpi{200} \frac{\frac{3}{5}}{\frac{3}{2}}$ $\dpi{120} \frac{3}{5}:\frac{3}{2}\frac{\cancel{3}}{5}\cdot \frac{2}{\cancel{3}} \frac {2}{5}$

$\dpi{200} \frac{\frac{7}{8}}{\frac{3}{4}}$ $\dpi{120} \frac{7}{8}:\frac{3}{4}\frac{7}{8}\cdot \frac{4}{3} \frac{28}{24} \frac {7}{6}$

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