# Solution to the Exercises on Reducing Fractions to Lowest Terms

Below are the complete solutions and answers to the exercises on reducing fractions to lowest terms. I will not give any tips or methods of shortcuts on doing this because teaching you shortcuts will give you problems in case you forget them. The best thing that you can do is to solve as many related problems as you can and develop shortcuts that work for you. Each person has his own preference in solving procedural problems such as these, so it is important that you discover what’s best for you.

For converting improper fractions to mixed form, I will discuss it in a separate post. Try to see the solutions below and see if you can use these solutions to develop your own method. Honestly, the three examples below on converting improper fractions to mixed form should be enough to teach you how to do it yourself. 🙂

Reducing Fractions to Lowest Terms

1. $\displaystyle \frac{12}{15}$

Solution

$\displaystyle \frac{12 \div 3}{15 \div 3} = \frac{4}{5}$

2. $\displaystyle \frac{18}{24}$

Solution

$\displaystyle \frac{18 \div 6 }{24 \div 6} = \frac{3}{4}$

3. $\displaystyle \frac{21}{49}$

Solution

$\displaystyle \frac{21 \div 7 }{49 \div 7} = \frac{3}{7}$

4. $\displaystyle \frac{56}{72}$

Solution

$\displaystyle \frac{56 \div 8 }{72 \div 8} = \frac{7}{9}$

5. $\displaystyle \frac{26}{65}$

Solution

$\displaystyle \frac{26 \div 13 }{65 \div 13} = \frac{2}{5}$

6. $\displaystyle \frac{18}{32}$

Solution

$\displaystyle \frac{18 \div 2 }{32 \div 2} = \frac{9}{16}$

7. $\displaystyle \frac{38}{95}$

Solution

$\displaystyle \frac{38 \div 19 }{95 \div 19} = \frac{2}{5}$

8. $\displaystyle \frac{32}{12}$

Solution

First, convert to lowest terms:
$\displaystyle \frac{32 \div 4 }{12 \div 4} = \frac{8}{3}$

Second, convert to mixed form. Eight divided by 3 is 2 remainder 3. So 2 becomes the whole number, 2 (the remainder) becomes the numerator and 8 becomes the denominator. Therefore, the answer is $2 \frac{2}{3}$.

9. $\displaystyle \frac{16}{84}$

Solution

$\displaystyle \frac{16 \div 4 }{84 \div 4} = \frac{4}{21}$

10. $\displaystyle \frac{39}{24}$

Solution

First, reduce to lowest terms.

$\displaystyle \frac{39 \div 3 }{24 \div 3} = \frac{13}{8}$

Second, convert the answer to mixed form. Thirteen divided by 8 is 1 remainder 5. So 1 becomes the whole number, 5 (the remainder) becomes the numerator of the fraction and 8 becomes the denominator. So the correct answer is $1 \frac{5}{8}$.

11. $\displaystyle \frac{15}{45}$

Solution

$\displaystyle \frac{15 \div 15 }{45 \div 15} = \frac{1}{3}$.

12. $\displaystyle \frac{51}{85}$

Solution

$\displaystyle \frac{51 \div 17 }{85 \div 17} = \frac{3}{5}$

13. $\displaystyle \frac{18}{54}$

Solution

$\displaystyle \frac{18 \div 18 }{54 \div 18} = \frac{1}{3}$

14. $\displaystyle \frac{35}{49}$

Solution

$\displaystyle \frac{35 \div 7}{49 \div 7} = \frac{5}{7}$

15. $\displaystyle \frac{74}{24}$

Solution

First, reduce to lowest terms.

$\displaystyle \frac{74 \div 2 }{24 \div 2} = \frac{37}{12}$

Second, divide 37 by 12. The answer is 3 remainder 1. Now, 3 becomes the whole number, 1 becomes the numerator of the fraction, and 12 becomes the denominator. So, the correct answer is $3 \frac{1}{12}$.

In the next post, we will be talking about multiplying and dividing fractions.

### 6 Responses

1. rooky says:

Sir, when I solved # 2 I got an answer ¼ lowest term of 18/24 correct me if I am wrong because I had two LCM. 1st LCM (2) 18/24 = 9/12; 2nd LCM (3) 9/12 = 1/4

2. Civil Service Reviewer says:

Hi Rooky,

Thank you for your question. In reducing fractions to lowest terms, you are not getting the LCM. You are actually getting the greatest common factor (GCF). You get the LCM if you want to add or subtract two (or more) fractions whose denominators are not equal.

In your solution, the GCF of 9 and 12 is 3. So, you must divide 9 by 3, which is equal to 3.

3. Supercute says:

Sir, i think no. 15 should be 3 1/6

4. Supercute says:

Here’s my computation:

74/24

3
_____
24 / 74
72
___________
r. 4

Convert it to mixed fraction:

4
3 ____
24

Convert to lowest term:

1
3 ___
6

• Civil Service Reviewer says:

Hello supercute,

The answer in the explanation is correct. Even if you convert it first to fraction, 74/24 becomes 3 and 2/24 or 3 and 1/12. 🙂

1. October 12, 2013

[…] Now that you know how to convert fractions to lowest terms, you might want to try the practice test and check your solution and answer. […]