## Answers to the Multiplying Fractions Practice Test

In the previous post, we have learned how to multiply fractions. We have learned that it is Below are the solutions and answers to the Practice Test on Multiplying Fractions.  If you have forgotten the methods of calculation, you can read How to Multiply Fractions.

The methods shown in some of the solutions below is only one among the many. I have mentioned some tips, but I don’t want to fill the solution with short cuts because there are times that when you forget the shortcut, you are not able to solve the problem. My advice if you want to pass the Civil Service Examination for Numerical Literacy is to master the basics, practice a lot, and develop your own shortcuts.

1. $\displaystyle \frac{2}{3} \times \frac{4}{5}$

Solution $\displaystyle \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5}= \frac{8}{15}$

2. $\displaystyle \frac{3}{4} \times \frac{5}{6}$

Solution $\displaystyle \frac{3}{4} \times \frac{5}{6} = \frac{3 \times 5}{4 \times 6} = \frac{15}{24}$

Now, reducing to lowest term we have $\displaystyle \frac{15 \div 3}{24 \div 3} = \frac{5}{8}$.

3. $\displaystyle \frac{3}{5} \times \frac{5}{7}$

Solution $\displaystyle \frac{3}{5} \times \frac{5}{7} = \frac{3 \times 5}{5 \times 7} = \frac{15}{35}$

Reducing to lowest terms, we have $\displaystyle \frac{15 \div 5}{35 \div 5} = \frac{3}{7}$.

Note: Notice that the numerator and the denominator of both fractions have 5’s. Since we are multiplying them, we can actually cancel 5 from the start of the calculation making the answer $\frac{3}{7}$.

4. $\displaystyle \frac{8}{16} \times \frac{2}{3}$

Solution

In computations, if some fractions can be reduced to the lowest term before starting the calculation, the better. In this case, $\frac{8}{16}$ can be reduced to $\frac{1}{2}$, so we just multiply $\frac{1}{2}$ and $\frac{2}{3}$. $\displaystyle \frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6}$.

Dividing both the numerator and the denominator by two reduces $\frac{2}{6}$ to $\frac{1}{3}$ which is the final answer.

5. $\displaystyle \frac{6}{15} \times \frac{1}{4}$

Solution

First, we reduce first $\frac{6}{15}$ to $\frac{2}{5}$ by dividing both the numerator and denominator by 3.  We then multiply the two fractions. $\displaystyle \frac{2}{5} \times \frac{1}{4} = \frac{2}{20}$.

We reduce to lowest terms by dividing both the numerator and the denominator by 2 which results to $\frac{1}{10}$.

6. $\displaystyle \frac{11}{12} \times \frac{5}{22}$

Solution

In this example, 11 and 22 are both multiples of 11.  Eleven is a numerator and 22 is a other one is in the denominator. This way, you can cancel them by dividing both sides by 11. This makes the first fraction $\frac{1}{12}$ and the second fraction $\frac{5}{2}$. That is, $\displaystyle \frac{11}{12} \times \frac{5}{22} = \frac{11 \div 11}{12} \times \frac{5}{22 \div 11} = \frac{1}{12} \times \frac{5}{2}$.

This gives the final product $\displaystyle \frac{5}{24}$.

7. $\displaystyle \frac{8}{15} \times 9$

Solution

When multiplying  whole numbers with fractions, just put 1 as the denominator of the whole numbers. $\displaystyle \frac{8}{15} \times \frac{9}{1} = \frac{72}{15}$

Dividing both the numerator and denominator by 3, we have $\frac{24}{5}$ or $4 \frac{4}{5}$ in mixed fraction form.

8. $\displaystyle \frac{2}{3} \times \frac{6}{5}$

Solution $\displaystyle \frac{2}{3} \times \frac{6}{5} = \frac{12}{15}$

Dividing the numerator and the denominator by 3, we have $\frac{4}{5}$.

9. $\displaystyle \frac{15}{4} \times \frac{3}{18}$

Solution $\displaystyle \frac{15}{4} \times \frac{3}{18} = \frac{45}{72}$

Dividing both the numerator and the denominator by 9 gives $\frac{5}{8}$ as the final answer.

10. $\displaystyle \frac{1}{8} \times 1 \frac{2}{9}$

Solution

First we convert $1 \frac{2}{9}$ to improper fraction. That is, $1 \displaystyle \frac{2}{9} = \frac{(9 \times 1) + 2}{9} = \frac{11}{9}$.

Then we multiply: $\displaystyle \frac{1 \times 11}{8 \times 9} = \frac{11}{72}$.

The correct answer is $\frac{11}{72}$.

11. $\displaystyle 1\frac{5}{9} \times 3 \frac{2}{7}$

Solution

In this example, we convert $3 \frac{2}{7}$ first to improper fraction. To convert, multiply the denominator by the whole number and then add the numerator to the product. This will be the numerator of the mixed fraction as shown in the following computation. $\displaystyle 3 \frac{2}{7} = \frac{7 \times 3 + 2}{7} = \frac{23}{7}$.

Now, converting $1 \frac{5}{9}$ to mixed fraction gives us \frac{14}{9}\$.

Multiplying the fractions, we have $\displaystyle \frac{14}{9} \times \frac{23}{7}$.

We can reduce the fraction to $\frac{2}{9} \times 23$ by dividing $14$ and $7$ by 7. Therefore, the final answer is $\frac{46}{9}$ or $5 \displaystyle \frac{1}{9}$

In the next post, we are going to learn how to convert mixed form to improper fraction.