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Basic Arithmetic : Operations with Fractions

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Example Questions

Example Question #1 : Fractions

Multiply:

$\frac{5}{6}\times\frac{12}{25}=?$

Possible Answers:

$\frac{60}{100}$

$\frac{2}{5}$

$\frac{1}{75}$

Correct answer:

$\frac{2}{5}$

Explanation:

Multiply the numerators together, then multiply the denominators together.

$\frac{5}{6}\times\frac{12}{25}=\frac{5 \times 12}{6\times25}=\frac{60}{150}$

To simplfy we can pull out a from the numerator and denominator, thus canceling them. The following answer is the result:

$=\frac{30\cdot2}{30\cdot5}=\frac{2}{5}$

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Example Question #2 : Fractions

In a classroom of 36, $\frac{1}{3}$ of the students are girls. If $\frac{1}{6}$ of the girls enjoy eating strawberries, and $\frac{1}{3}$ of the boys also enjoy eating strawberries, how many total students in the class enjoy eating strawberries?

Possible Answers:

Correct answer:

Explanation:

First, find out how many girls and boys are in the class.

Multiply 36 by $\frac{1}{3}$ to find the number of girls.

$36\times \frac{1}{3}=12$

Then, subtract the number of girls from the total number of students in the class to find the number of boys.

36-12=24

Now, we can figure out how many girls enjoy eating strawberries. Multiply the total number of girls by the fraction of girls who enjoy eating strawberries.

$12\times\frac{1}{6}=2$

Now, do the same with the boys.

$24\times\frac{1}{3}=8$

Add these two numbers together to get the total number of students who enjoy eating strawberries.

2+8=10

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Example Question #2 : Operations With Fractions

Solve and simplify.

$\frac{3}{4} \times \frac{4}{6}$

Possible Answers:

$\frac{7}{10}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{7}{24}$

$\frac{12}{10}$

Correct answer:

$\frac{1}{2}$

Explanation:

When multiplying fractions, you simply multiply the numerators and then multiply the denominators. Then simplify the fraction.

$\frac{3}{4} \times \frac{4}{6}=\frac{3\cdot 4}{4 \cdot 6}$

$=\frac{12}{24}=\frac{1\cdot 12}{2 \cdot 12}=\frac{1}{2}$

(Note: by dividing both our numerator and our denominator by , gives us our final answer of $\frac{1}{2}$ .

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Example Question #2 : Multiplication With Fractions

Evaluate the following:

$-\frac{4}{5}\cdot\left ( \frac{1}{2} \right )^{2}$

Possible Answers:

$-\frac{16}{5}$

$-\frac{1}{5}$

$-\frac{11}{20}$

$-\frac{17}{20}$

Correct answer:

$-\frac{1}{5}$

Explanation:

This problem involves order of operations.

The correct order is: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

Rewrite the exponent and cancel out the 4 on the numerator and denominator.

$-\frac{4}{5}\cdot\frac{1}{4}= -\frac{1}{5}$

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Example Question #2 : Fractions

Please choose the best answer for the question below.

$\frac{1}{2} \times\frac{36}{55}=$

Possible Answers:

36/115

36/22

18/55

36/105

9/25

Correct answer:

18/55

Explanation:

To do this problem, simply multiply through (i.e. numerator by numerator and denominator by denominator):

$1/2 \cdot 36/55 = 36/110$

And then reduce to find your answer--both and 110 are divisible by two.

36/110 = 18/55

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Example Question #1 : Fractions

Multiply these fractions:

$\frac{7}{9}*\frac{1}{14}$

Possible Answers:

$\frac{1}{9}$

$\frac{2}{9}$

$\frac{1}{18}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{18}$

Explanation:

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{7}{9}*\frac{1}{14}=\frac{7*1}{9*14}=\frac{7}{126}$

Simply the fraction to get the final answer:

$\frac{7}{126}\div \frac{7}{7}=\frac{1}{18}$

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Example Question #1 : Operations With Fractions

Multiply these fractions:

$\frac{5}{12}*\frac{3}{7}$

Possible Answers:

$\frac{3}{14}$

$\frac{5}{28}$

$\frac{1}{4}$

$\frac{5}{27}$

Correct answer:

$\frac{5}{28}$

Explanation:

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{5}{12}*\frac{3}{7}=\frac{5*3}{12*7}=\frac{15}{84}$

Simply the fraction to get the final answer:

$\frac{15}{84}\div \frac{3}{3}=\frac{5}{28}$

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Example Question #1 : Operations With Fractions

Multiply these fractions:

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

Possible Answers:

$\frac{2}{9}$

$\frac{7}{9}$

$\frac{5}{9}$

$\frac{4}{9}$

Correct answer:

$\frac{5}{9}$

Explanation:

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{2}{3}*\frac{5}{6}=\frac{2*5}{3*6}=\frac{10}{18}$

Simply the fraction to get the final answer:

$\frac{10}{18}\div \frac{2}{2}=\frac{5}{9}$

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Example Question #2 : Multiplication With Fractions

Multiply these fractions:

$\frac{1}{2}*\frac{2}{3}$

Possible Answers:

$\frac{1}{6}$

$\frac{1}{3}$

$1\frac{1}{2}$

$1\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{1}{2}*\frac{2}{3}=\frac{1*2}{2*3}=\frac{2}{6}$

Simply the fraction to get the final answer:

$\frac{2}{6}\div \frac{2}{2}=\frac{1}{3}$

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Example Question #3 : Fractions

Multiply these fractions:

$\frac{5}{7}*\frac{1}{3}$

Possible Answers:

$\frac{6}{21}$

$\frac{4}{21}$

$\frac{1}{3}$

$\frac{5}{21}$

Correct answer:

$\frac{5}{21}$

Explanation:

When multiplying fractions, all we have to do is multiply the numerators together and multiply the denominators together:

$\frac{5}{7}*\frac{1}{3}=\frac{5*1}{7*3}=\frac{5}{21}$

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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 : Fractions

Example Question #2 : Fractions

Example Question #2 : Operations With Fractions

Example Question #2 : Multiplication With Fractions

Example Question #2 : Fractions

Example Question #1 : Fractions

Example Question #1 : Operations With Fractions

Example Question #1 : Operations With Fractions

Example Question #2 : Multiplication With Fractions

Example Question #3 : Fractions

All Basic Arithmetic Resources

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