# Solutions and Answers to Subtraction of Fractions Practice Test

Below are the complete solutions and answers to the Practice Test on Subtraction of Fractions. If you do not know how to do it or you have forgotten the methods, please read  How to Subtract Fractions.

Practice Test on Subtraction of Fractions

1. $\frac{13}{17} - \frac{2}{17}$.

Solution

The given fractions are similar, so we just subtract the numerators and copy the denominator. $\displaystyle \frac{13}{17} - \frac{2}{17} = \frac{11}{17}$.

Answer: $\frac{11}{17}$.

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2. $\frac{8}{15} - \frac{4}{15}$.

This is similar to number 1. They are similar fractions. $\displaystyle \frac{8}{15} - \frac{4}{15} = \frac{4}{15}$.

Answer: $\frac{4}{15}$

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3. $\frac{5}{8} - \frac{1}{2}$

As we have mentioned in How to Add Fractions and How to Subtract Fractions, we need to make the dissimilar fractions similar in order to perform addition and subtraction. In this case, we need to make their denominators the same. We need to make $\frac{1}{2}$ as $\frac{n}{8}$, and clearly $n = 4$. So, $\displaystyle \frac{5}{8} - \frac{4}{8} = \frac{1}{8}$

Answer: $\frac{1}{8}$

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4. $\frac{4}{5} - \frac{1}{3}$

First, we find the Least Common Multiple (LCM) of 3 and 5 by listing:

Common Multiples of 3: 3, 6, 9, 12, 15, 18, …

Common Multiples of 5: 5, 10, 15, 20, 25

So, the LCM of 3 and 5 is 15.

Next, we convert the given to fractions whose denominator is 15. $\frac{4}{5} = \frac{x}{15}$ which means that $x = (15 \div 5) \times 4 = 12$. $\frac{1}{3} = \frac{y}{15}$ which means that $y = (15 \div 3) \times 1 = 5$.

So, $\frac{4}{5} = \frac{12}{15}$ and $\frac{1}{3} = \frac{5}{15}$.

Performing the subtraction, we have $\displaystyle \frac{12}{15} - \frac{5}{15} = \frac{7}{15}$.

Answer: $\frac{7}{15}$

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5. $2 \frac{3}{5} - \frac{1}{4}$

First, we get the LCM of 4 and 5 which is 20 (try listing as shown in the previous question.

Second, we we convert the mixed fraction to improper fraction. That is, $2 \frac{3}{5} = \frac{5 \times 2 + 3}{5} = \frac{13}{5}$.

Third, we get the equivalent fractions of $\frac{13}{5}$ and $\frac{1}{4}$ whose denominator is 20. Clearly, $\frac{1}{4} = \frac{5}{20}$, so we are only left with $\frac{13}{5}$. $\frac{13}{5} = \frac{n}{20}$

We solve for n: $(20 \div 5) \times 13 = 52$. This means that $\frac{13}{5} = \frac{52}{20}$.

Performing the subtraction, we have $\displaystyle \frac{52}{20} - \frac{5}{20} = \frac{47}{20}$.

Converting this improper fraction to mixed form, we have $2 \frac{7}{20}$ as the answer.

Answer: $2 \frac{7}{20}$.

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6. $4 \frac{5}{6} - 2 \frac{1}{6}$

This is one of the cases where you can separate the whole number and the fraction in subtraction. I will discuss about this later.  Here, we just subtract the whole numbers $4 - 2 = 2$ and then subtract the fraction $\frac{5}{6} - \frac{1}{6} = \frac{4}{6}$. So, the answer is $2 \frac{4}{6}$ or $2 \frac{2}{3}$ when reduced to lowest terms.

Answer: $2 \frac{2}{3}$.

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7. $4 \frac{3}{4} - 2 \frac{1}{3}$

First, we get the LCM of 4 and 3, which is clearly 12 (try listing as shown in No. 4).

Second, we convert the mixed fractions into improper fractions. $4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}$ $2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3}$

Now, we convert the given fractions to fractions whose denominator is 12. $\frac{19}{4} = \frac{m}{12}$, $m = (12 \div 4) \times 19 = 57$. $\frac{7}{3} = \frac{n}{12}$, $n = (12 \div 3) \times 7 = 28$.

This means that $\frac{19}{4} = \frac{57}{12}$ and $\frac{7}{3} = \frac{28}{12}$.

Now, subtracting the two fractions, we have $\displaystyle \frac{57}{12} - \frac{28}{12} = \frac{29}{12}$.

Converting the improper fraction to mixed form, we have $2\frac{5}{12}$.

Answer: $2 \frac{5}{12}$.

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8. $\frac{6}{13} - \frac{3}{10}$

The Least Common Multiple of 10 and 13 is 130. Converting both fractions and and subtracting, we have $\displaystyle \frac{60}{130} - \frac{39}{130} = \frac{21}{130}$.

Answer: $\frac{21}{130}$.

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9. $4 \frac{8}{15} - 2 \frac{3}{5}$

The Least Common Multiple of 15 and 5 is 15.

Now, converting the mixed fractions to improper fractions gives us $\frac{68}{15}$ and $\frac{13}{5}$.

We only need to convert $\frac{13}{5}$ to $\frac{n}{15}$ since the denominator of the other fraction is already $15$. Now, $\frac{13}{5} = \frac{39}{15}$. Subtracting the two fractions, we have $\displaystyle \frac{68}{15} - \frac{39}{15} = \frac{29}{15}$.

Converting the improper fraction to mixed number, we have $\frac{29}{15} = 1 \frac{14}{15}$.

Answer: $1 \frac{14}{15}$.

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10. $8 \frac{1}{3} - 4$

In this case, we just subtract the whole numbers which leaves an answer of $4 \frac{1}{3}$.

Answer: $4 \frac{1}{3}$

So far, we have finished all the operations on fractions. In the next posts, we will be discussing operations on decimals and number series (or number patterns). 