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Basic Arithmetic : Operations with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

Example Question #1 : Multiplying And Dividing Fractions

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

Possible Answers:

$\frac{3}{10}$

$\frac{30}{21}$

$\frac{35}{18}$

$\frac{21}{3}$

$\frac{10}{7}$

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:

$\frac{1}{10}$

$\frac{2}{15}$

$\frac{1}{15}$

$\frac{1}{30}$

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 #4 : Division With Fractions

Divide these fractions:

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

Possible Answers:

$\frac{1}{7}$

$1\frac{2}{7}$

$1\frac{6}{7}$

$1\frac{1}{7}$

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 #22 : Operations With Fractions

Divide these fractions:

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

Possible Answers:

$\frac{1}{3}$

$1\frac{1}{2}$

$\frac{1}{2}$

$1\frac{1}{3}$

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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Example Question #21 : Operations With Fractions

Divide these fractions:

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

Possible Answers:

$\frac{2}{27}$

$\frac{1}{28}$

$1\frac{1}{27}$

$\frac{1}{27}$

Correct answer:

$\frac{1}{27}$

Explanation:

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

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

Simplify the fraction to get the final answer:

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

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Example Question #1 : Addition With Fractions

Solve the following expression:

$\frac{1}{2}+\frac{1}{6}$

Possible Answers:

$\frac{2}{5}$

$\frac{1}{3}$

$\frac{1}{5}$

$\frac{1}{4}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

The correct answer is $\frac{2}{3}$ .

In order to start solving this problem, we need to get each term to have a common denominator.

The common denominator between 2 and 6 is 6. We can rewrite the expression and solve using the following method:

$\frac{1}{2}+\frac{1}{6} = \frac{3}{6}+\frac{1}{6} = \frac{4}{6} = \frac{2}{3}$

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Example Question #2 : Addition With Fractions

Determine the answer as a mixed number:

$\frac{3}{4} + \frac{5}{6} =$

Possible Answers:

$\frac{19}{12}$

$\frac{11}{12}$

$1\frac{3}{4}$

$1\frac{7}{12}$

Correct answer:

$1\frac{7}{12}$

Explanation:

1. Find the least common denominator:

The lowest number that both 4 and 6 can go into is 12 meaning that it is the least common denominator.

2. Use the new least common denominator to create two equivalent fractions with a denominator of 12.

$(\frac{3}{4})(\frac{3}{3})=\frac{9}{12}$

$(\frac{5}{6})(\frac{2}{2})=\frac{10}{12}$

3. Add the two fractions together.

$\frac{9}{12}+\frac{10}{12}=\frac{19}{12}$

4. Convert the fraction to a mixed number:

$\frac{19}{12}=1 \frac{7}{12}$

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Example Question #3 : Addition With Fractions

Evaluate:

$-\frac{6}{5}+\frac{5}{6}$

Possible Answers:

$-\frac{11}{30}$

$-\frac{61}{30}$

$-\frac{1}{30}$

Correct answer:

$-\frac{11}{30}$

Explanation:

In fractions, to add or subtract the numerator, the denominators must be equal.

Find the least common denominator, multiply the top and bottom with what was multiplied on the denominator, and simplify.

$-\frac{6}{5}+\frac{5}{6} = -\frac{6\cdot6}{5\cdot6}+\frac{5\cdot5}{6\cdot5}=-\frac{36}{30}+\frac{25}{30}$

= $-\frac{11}{30}$

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Basic Arithmetic : Operations with Fractions

Study concepts, example questions & explanations for Basic Arithmetic

All Basic Arithmetic Resources

Example Questions

Example Question #1 : Multiplying And Dividing Fractions

Example Question #5 : Division With Fractions

Example Question #6 : Division With Fractions

Example Question #5 : Division With Fractions

Example Question #4 : Division With Fractions

Example Question #22 : Operations With Fractions

Example Question #21 : Operations With Fractions

Example Question #1 : Addition With Fractions

Example Question #2 : Addition With Fractions

Example Question #3 : Addition With Fractions

All Basic Arithmetic Resources

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