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Reducing Fractions – Explanation & Examples

How to Simplify Fractions?

A fraction can have a numerator and denominator that are composite numbers. There are two methods of how to simplify such a fraction.

Below are the steps on how to reduce a fraction to the lowest possible terms:

  • The first step is to identify a common factor of the denominator and numerator.
  • The denominator and numerator are both divided by the common factor
  • The division operation is repeated until there are no more factors.
  • The fraction is said to be simplified if no more factors exit

Another method of simplifying a fraction include:

  • Finding the Greatest common factor (GCF) of both the numerator and denominator of a fraction.
  • Both the denominator and numerator are divided by the GCF.


Example 1

Simplify the following expression,

3 1/3 ÷ 5/3 – 1/10 of 2 ½ + 7/4

Solution
3 1/3 ÷ 5/3 – 1/10 of 2 ½ + 7/4
= (3 × 3 + 1)/3 ÷ 5/3 – 1/10 of (2 × 2 + 1)/2 + 7/4
= 10/3 ÷ 5/3 – 1/10 of 5/2 + 7/4

= 10/3 × 3/5 – ½ × ½ + 7/4

= 2/1 – ¼ + 7/4
= (2 × 4)/1 × 4) – (1 × 1)/4 × 1) + (7 × 1)/4 × 1)
= 8/4 – ¼ + 7/4

Now the denominators have a common number.
= (8 – 1 + 7)/4
= 14/4
= 7/2

Example 2

Solve and Simplify the answer : 45 of 3/5 ÷ 1 2/3 + 3 of 1/3 – 10

Solution
45 of 3/5 ÷ 1 2/3 + 3 of 1/3 – 10
= 45 of 3/5 ÷ (1 × 3 + 2)/3 + 3 of 1/3 – 10
= 45 of 3/5 ÷ 5/3 + 3 of 1/3 – 10
= 45 × 3/5 ÷ 5/3 + 3 × 1/3 – 10

= 9 × 3 × 3/5 + 3 × 1/3 – 10

= (27 × 3)/5 + 1 – 10
= 81/5 + 1 – 10
= (81 × 1)/(5 × 1) + (1 × 5)/(1 × 5) – (10 × 5)/(1 × 5)
= 81/5 + 5/5 – 50/5

Since the denominators are common for each of the fractions,
= (81 + 5 – 50)/5
= 36/5

= 7 1/5

Example 3

Simplify: {18 + (2 ½ + 4/5)} of 1/1000

Solution
= {18 + (5/2 + 4/5)} of 1/1000
= {18 + ((25 + 8)/10)} of 1/1000
= {18 + 33/10} of 1/1000
= {(180 + 33)/10} of 1/1000
= 213/10 of 1/1000
= 213/10 × 1/1000
= (213 × 1)/(10 × 1000)

= 213/10000
= 0.0213

Example 4

Simplify the following expression:

43 of 1/86 ÷ 1/14 × 2/7 + 9/4 – 1/4

Solution
43 of 1/86 ÷ 1/14 × 2/7 + 9/4 – 1/4
= 43 × 1/86 ÷ 1/14 × 2/7 + 9/4 – 1/4

= 2/1 + 9/4 – 1/4
= (2 × 4)/1 × 4) + (9 × 1)/4 × 1) – (1 × 1)/4 × 1)
= 8/4 + 9/4 – 1/4

Since the denominators are all the same for the fractions,
= (8 + 9 – 1)/4
= 16/4
= 4

Example 5

Simplify: 9/10 ÷ (3/5 + 2 1/10)

Solution
9/10 ÷ (3/5 + 2 1/10)
= 9/10 ÷ (3/5 + 21/10)
= 9/10 ÷ ((6 +21)/10)
= 9/10 ÷ 27/10
= 9/10 × 10/27
= 1/3

Example 6

Simplify: (7 ¼ – 6 1/4) of (2/5 + 3/15)

Solution
(7 ¼ – 6 1/4) of (2/5 + 3/15)
= (29/4 – 25/4) of (2/5 + 3/15)
= ((29 – 25)/4) × ((6 + 3)/15)
= 4/4 × 9/15

Reduce to the fraction to its lowest term

= 1 × 3/5
= 3/5

Practice Questions

1. A person is carrying 48 blue balls and 9 red balls.

a. Write, in simplified form, the fraction of the balls that are blue.

b. Write, in simplified form, the fraction of the blue balls to the red balls.

2. Sam has a piece of wood that 7/8 of a meter long. If he needs to cut into pieces of 1/32 of a meter long each, how many total pieces can Sam cut?

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