Simplification and Expansiono f Simple Fractions

To amplify fractions

We will perform the same multiplication operation on the numerator and the denominator: the value of the fraction will be preserved.

You can expand as many times as you want and by any number.

To simplify fractions:

We will perform the same division operation on the numerator and the denominator: the value of the fraction will be preserved.

This can only be done with a number that is completely divisible by both the numerator and the denominator.

It is possible to simplify only until reaching a fraction in which it is not possible to find a number that divides without remainder both in the numerator and the denominator.

Suggested Topics to Practice in Advance

  1. A fraction as a divisor
  2. Numerator
  3. Denominator
  4. Fractions
  5. Part of a quantity
  6. Placing Fractions on the Number Line
  7. Common denominator

Practice Simplification and Expansion of Simple Fractions

Examples with solutions for Simplification and Expansion of Simple Fractions

Exercise #1

Simplify the following fraction:

11= \frac{1}{1}=

Video Solution

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 1:

1:11:1=11 \frac{1:1}{1:1}=\frac{1}{1}

Answer

11 \frac{1}{1}

Exercise #2

Simplify the following fraction:

124= \frac{12}{4}=

Video Solution

Step-by-Step Solution

Let's reduce as follows, divide the numerator by 4 and the denominator by 4:

12:44:4=31 \frac{12:4}{4:4}=\frac{3}{1}

Answer

31 \frac{3}{1}

Exercise #3

Simplify the following fraction:

128= \frac{12}{8}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

12:28:2=64 \frac{12:2}{8:2}=\frac{6}{4}

Answer

64 \frac{6}{4}

Exercise #4

Simplify the following fraction:

168= \frac{16}{8}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

16:28:2=84 \frac{16:2}{8:2}=\frac{8}{4}

Answer

84 \frac{8}{4}

Exercise #5

Simplify the following fraction:

210= \frac{2}{10}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 2 and the denominator by 2:

2:210:2=15 \frac{2:2}{10:2}=\frac{1}{5}

Answer

15 \frac{1}{5}

Exercise #6

Simplify the following fraction:

416= \frac{4}{16}=

Video Solution

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 4 and the denominator by 4:

4:416:4=14 \frac{4:4}{16:4}=\frac{1}{4}

Answer

14 \frac{1}{4}

Exercise #7

Simplify the following fraction by a factor of 1:

310= \frac{3}{10}=

Video Solution

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 1 and the denominator by 1:

3:110:1=310 \frac{3:1}{10:1}=\frac{3}{10}

Answer

310 \frac{3}{10}

Exercise #8

Simplify the following fraction by a factor of 3:

36= \frac{3}{6}=

Video Solution

Step-by-Step Solution

We will reduce as follows, divide the numerator by 3 and the denominator by 3:

3:36:3=12 \frac{3:3}{6:3}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #9

Simplify the following fraction by a factor of 4:

48= \frac{4}{8}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator by 4 and the denominator by 4:

4:48:4=12 \frac{4:4}{8:4}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #10

Simplify the following fraction by a factor of 5:

1510= \frac{15}{10}=

Video Solution

Step-by-Step Solution

Let's reduce as follows, we'll divide both the numerator and denominator by 5:

15:510:5=32 \frac{15:5}{10:5}=\frac{3}{2}

Answer

32 \frac{3}{2}

Exercise #11

Simplify the following fraction and specify the simplification factor:

1636 \frac{16}{36}

Video Solution

Step-by-Step Solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 36, gives us a result of 18.

Therefore:

16:236:2=818 \frac{16:2}{36:2}=\frac{8}{18}

Answer

818 \frac{8}{18} , factor of 2

Exercise #12

Simplify the following fraction and specify the simplification factor:

2050 \frac{20}{50}

Video Solution

Step-by-Step Solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 50, gives us a result of 10.

Therefore:

20:550:5=410 \frac{20:5}{50:5}=\frac{4}{10}

Answer

410 \frac{4}{10} , factor of 5

Exercise #13

Simplify the following fraction:

624 \frac{6}{24}

Video Solution

Step-by-Step Solution

Let's look at the denominator of the fraction. We'll try to find a number that, when divided by 24, gives us a result of 4:

6:624:6=14 \frac{6:6}{24:6}=\frac{1}{4}

Answer

14 \frac{1}{4}

Exercise #14

Simplify the following fraction:

816 \frac{8}{16}

Video Solution

Step-by-Step Solution

First look at the denominator of the fraction. Try to find a number that, when divided by 16, gives you a result of 4:

8:416:4=24 \frac{8:4}{16:4}=\frac{2}{4}

Answer

24 \frac{2}{4}

Exercise #15

Simplify the following fraction by a factor of 10:

10010= \frac{100}{10}=

Video Solution

Step-by-Step Solution

Let's simplify as follows, we'll divide both the numerator and denominator by 10:

100:1010:10=101 \frac{100:10}{10:10}=\frac{10}{1}

Answer

101 \frac{10}{1}

Topics learned in later sections

  1. How do you simplify fractions?