Division with Fractions - Basic Math

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Question

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

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Answer

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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Question

Solve the following:

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

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Answer

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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Question

Please choose the best answer for the question below.

What is divided by ?

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Answer

To divide fractions, simply invert the second fraction and multiply. So, divided by becomes:

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

reduce to find the correct answer:

.

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Question

Determine the answer as an improper fraction:

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

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Answer

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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Question

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

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

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Answer

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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Question

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

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Answer

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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Question

Divide and simplify:

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

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Answer

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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Question

Divide these fractions:

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

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Answer

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}$=\frac{151}{3015}$

Simplify the fraction to get the final answer:

$\frac{151}{30*15}$=\frac{1}{30}$

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Question

Divide these fractions:

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

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Answer

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}${8}=\frac{88}{56}$=\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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Question

Divide these fractions:

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

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Answer

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{362}{163}$=\frac{72}{48}$

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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Question

Divide these fractions:

$$\frac{12}{54}$\div6$

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Answer

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

$\frac{12}{54}$\div6=\frac{12}{54}$$\frac{1}{6}$=\frac{121}{54*6}$=\frac{12}{324}$

Simplify the fraction to get the final answer:

$\frac{12}{324}$\div $\frac{12}{12}$=\frac{1}{27}$

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Question

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

Tap to reveal answer

Answer

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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Question

Solve the following:

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

Tap to reveal answer

Answer

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.

← Didn't Know|Knew It →

Question

Please choose the best answer for the question below.

What is divided by ?

Tap to reveal answer

Answer

To divide fractions, simply invert the second fraction and multiply. So, divided by becomes:

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

reduce to find the correct answer:

.

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Question

Determine the answer as an improper fraction:

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

Tap to reveal answer

Answer

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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Question

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

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

Tap to reveal answer

Answer

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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Question

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

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Answer

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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Question

Divide and simplify:

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

Tap to reveal answer

Answer

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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Question

Divide these fractions:

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

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Answer

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}$=\frac{151}{3015}$

Simplify the fraction to get the final answer:

$\frac{151}{30*15}$=\frac{1}{30}$

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Question

Divide these fractions:

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

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Answer

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}${8}=\frac{88}{56}$=\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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