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Basic Arithmetic : Division with Fractions

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Example Questions

Example Question #1 : Division With Fractions

Solve the following:

$\frac{4}{5}\div4$

Possible Answers:

$\frac{1}{5}$

$\frac{2}{5}$

$\frac{4}{5}$

$\frac{24}{5}$

$\frac{16}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

The correct answer is $\frac{1}{5}$ and can be found by using reciprocals as shown below:

$\frac{4}{5}\div\frac{4}{1} = \frac{4}{5}\ast \frac{1}{4} = \frac{4}{20}=\frac{1}{5}$

The first step is to identify that 4 can be written as 4 divided by 1. You can then take the first fraction and multiple it by the reciprocal of the second fraction, which can be found by switching the numerator and denominator. From there, you solve and simplify until you get to the final answer.

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Example Question #2 : Division With Fractions

Evaluate the following division problem and express the resulting fraction in its simplest form.

$\frac{16}{3}\div \frac{5}{12}$

Possible Answers:

$\frac{64}{5}$

$\frac{20}{9}$

$\frac{192}{8}$

$\frac{192}{15}$

$\frac{80}{36}$

Correct answer:

$\frac{64}{5}$

Explanation:

In order to divide two fractions you simply find the inverse of either fraction, and multiply that by the other fraction.

To find the inverse of a fraction, you just switch the numerator and the denominator.

The inverse of $\frac{5}{12}$ is $\frac{12}{5}$ .

So to divide:

$\frac{16}{3}\div \frac{5}{12}$

We turn it into the following multiplication problem:

$\frac{16}{3}\times\frac{12}{5}$

We multiply the numerators by each other and the denominators by each other to carry out the multiplication:

$\frac{16\times 12}{3\times 5}=\frac{192}{15}$

Both 192 and 15 are divisible by 3, so we divide 192 by 3 and 15 by 3 and are left with:

$\frac{64}{5}$

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Example Question #3 : Division With Fractions

Determine the answer as an improper fraction:

$\frac{16}{8} \div \frac{3}{4}=$

Possible Answers:

$\frac{3}{8}$

$\frac{13}{8}$

$\frac{6}{4}$

$\frac{8}{3}$

Correct answer:

$\frac{8}{3}$

Explanation:

1. Invert the second fraction:

$\frac{3}{4}\rightarrow \frac{4}{3}$

2. Multiply the two fractions:

$\frac{16}{8}\times \frac{4}{3}=\frac{64}{24}$

3. Reduce the improper fraction:

$\frac{64}{24}=\frac{8}{8}\times \frac{8}{3}$

So the improper fraction can be reduced to $\frac{8}{3}$ .

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Example Question #2 : Division With Fractions

Please choose the best answer for the question below.

What is 6/7 divided by 2/5 ?

Possible Answers:

35/12

7/15

15/7

30/17

12/35

Correct answer:

15/7

Explanation:

To divide fractions, simply invert the second fraction and multiply. So, 6/7 divided by 2/5 becomes:

$6/7 \cdot 5/2 = 30/14$

reduce to find the correct answer:

15/7 .

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Example Question #4 : Division With Fractions

Simplify $\frac{5}{3}\div\frac{7}{6}$ .

Possible Answers:

$\frac{35}{18}$

$\frac{30}{21}$

$\frac{21}{3}$

$\frac{3}{10}$

$\frac{10}{7}$

Correct answer:

$\frac{10}{7}$

Explanation:

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

$\frac{5}{3}\div\frac{7}{6}=\frac{5}{3}\cdot\frac{6}{7}$ .

Then, we multiply the numerators followed by the denomenators:

$\frac{5\cdot6}{3\cdot7}=\frac{30}{21}$ .

Lastly, the fraction must be simplified by a factor of 3:

$\frac{30}{21}=\frac{10}{7}$ , which gives us our final answer.

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Example Question #5 : Division With Fractions

Evaluate: $\frac{7}{6}\div 2\frac{3}{8}$

Possible Answers:

$\frac{17}{41}$

$\frac{28}{57}$

$\frac{133}{48}$

$\frac{48}{133}$

$\frac{57}{28}$

Correct answer:

$\frac{28}{57}$

Explanation:

Change all the fractions to improper fractions.

$\frac{7}{6}\div 2\frac{3}{8}=\frac{7}{6}\div \frac{19}{8}$

Convert the division sign to a multiplication sign, but flip the second term. Simplify.

$\frac{7}{6}\times \frac{8}{19}= \frac{7}{3}\times \frac{4}{19}= \frac{28}{57}$

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Example Question #6 : Division With Fractions

Divide and simplify:

$\frac{2}{11}\div \frac{9}{22}$ .

Possible Answers:

$\frac{4}{9}$

$\frac{2}{11}$

$\frac{11}{}9$

$\frac{18}{222}$

$\frac{1}{9}$

Correct answer:

$\frac{4}{9}$

Explanation:

Multiplying fractions is a two-step process. First, you must flip the second fraction (make it its reciprocal) and then set up the equation as a multiplication problem:

$\frac{2}{11}\cdot \frac{22}{}9$ .

Then, cross-reduce: 11 goes into both 11 and 22, so you can take that out so it looks like:

$\frac{2}{1}\cdot \frac{2}{9}$ .

Then, multiply straight across so that you get $\frac{4}{}9$ .

You can't simplify any further, so that's your answer!

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Example Question #5 : Division With Fractions

Divide these fractions:

$\frac{15}{30}\div15$

Possible Answers:

$\frac{1}{30}$

$\frac{2}{15}$

$\frac{1}{15}$

$\frac{1}{10}$

Correct answer:

$\frac{1}{30}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{15}{30}\div15=\frac{15}{30}*\frac{1}{15}=\frac{15*1}{30*15}$

Simplify the fraction to get the final answer:

$\frac{15*1}{30*15}=\frac{1}{30}$

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Example Question #6 : Division With Fractions

Divide these fractions:

$\frac{8}{56}\div \frac{1}{8}$

Possible Answers:

$\frac{1}{7}$

$1\frac{2}{7}$

$1\frac{1}{7}$

$1\frac{6}{7}$

Correct answer:

$1\frac{1}{7}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{8}{56}\div \frac{1}{8}=\frac{8}{56}*{8}=\frac{8*8}{56}=\frac{64}{56}$

Simplify the fraction to get the final answer:

$\frac{64}{56}\div \frac{8}{8}=\frac{8}{7}=1\frac{1}{7}$

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Example Question #7 : Division With Fractions

Divide these fractions:

$\frac{36}{16}\div \frac{3}{2}$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{2}$

$1\frac{1}{3}$

$1\frac{1}{2}$

Correct answer:

$1\frac{1}{2}$

Explanation:

When dividing fractions, first we need to flip the second fraction. Then multiply the numerators together and multiply the denominators together:

$\frac{36}{16}\div \frac{3}{2}=\frac{36}{16}* \frac{2}{3}=\frac{36*2}{16*3}=\frac{72}{48}$

Simplify the fraction to get the final answer:

$\frac{72}{48}\div \frac{12}{12}=\frac{6}{4}\div \frac{2}{2}=\frac{3}{2}=1\frac{1}{2}$

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Basic Arithmetic : Division with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #1 : Division With Fractions

Example Question #2 : Division With Fractions

Example Question #3 : Division With Fractions

Example Question #2 : Division With Fractions

Example Question #4 : Division With Fractions

Example Question #5 : Division With Fractions

Example Question #6 : Division With Fractions

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