Simplification and Expansion of Simple Fractions - Examples, Exercises and Solutions

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 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 #2

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 #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 by the factor 8:

1632= \frac{16}{32}=

Video Solution

Step-by-Step Solution

Let's reduce in the following way, divide the numerator by 8 and the denominator by 8:

16:832:8=24 \frac{16:8}{32:8}=\frac{2}{4}

Answer

24 \frac{2}{4}

Exercise #5

Simplify the following fraction by a factor of 6.

3618= \frac{36}{18}=

Video Solution

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 6 and the denominator by 6:

36:618:6=63 \frac{36:6}{18:6}=\frac{6}{3}

Answer

63 \frac{6}{3}

examples with solutions for simplification and expansion of simple fractions

Exercise #1

Simplify the following fraction by a factor of 7:

2870= \frac{28}{70}=

Video Solution

Step-by-Step Solution

We will reduce in the following way, divide the numerator by 7 and the denominator by 7:

28:770:7=410 \frac{28:7}{70:7}=\frac{4}{10}

Answer

410 \frac{4}{10}

Exercise #2

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}

Exercise #3

Simplify the following fraction by a factor of 1:

310= \frac{3}{10}=

Video Solution

Answer

310 \frac{3}{10}

Exercise #4

Simplify the following fraction:

210= \frac{2}{10}=

Video Solution

Answer

15 \frac{1}{5}

Exercise #5

Simplify the following fraction by a factor of 3:

36= \frac{3}{6}=

Video Solution

Answer

12 \frac{1}{2}

examples with solutions for simplification and expansion of simple fractions

Exercise #1

Simplify the following fraction:

11= \frac{1}{1}=

Video Solution

Answer

11 \frac{1}{1}

Exercise #2

Simplify the following fraction by a factor of 5:

1510= \frac{15}{10}=

Video Solution

Answer

32 \frac{3}{2}

Exercise #3

Simplify the following fraction:

124= \frac{12}{4}=

Video Solution

Answer

31 \frac{3}{1}

Exercise #4

Simplify the following fraction:

168= \frac{16}{8}=

Video Solution

Answer

84 \frac{8}{4}

Exercise #5

Enlarge the following fraction by the factor 8:

910= \frac{9}{10}=

Video Solution

Answer

7280 \frac{72}{80}

Topics learned in later sections

  1. How do you simplify fractions?