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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?*