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# Reducing Fractions â€“ 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 }Ã· 5/3 – 1/10 of 2 Â½ + 7/4

__Solution__

3 ^{1}/_{3} Ã· 5/3 – 1/10 of 2 Â½ + 7/4

= (3 Ã— 3 + 1)/3 Ã· 5/3 â€“ 1/10 of (2 Ã— 2 + 1)/2 + 7/4

= 10/3 Ã· 5/3 – 1/10 of 5/2 + 7/4

= 10/3 Ã— 3/5 â€“ Â½ Ã— Â½ + 7/4

= 2/1 – Â¼ + 7/4

= (2 Ã— 4)/1 Ã— 4) – (1 Ã— 1)/4 Ã— 1) + (7 Ã— 1)/4 Ã— 1)

= 8/4 – Â¼ + 7/4

Now the denominators have a common number.

= (8 â€“ 1 + 7)/4

= 14/4

= 7/2

*Example 2*

Solve and Simplify the answer : 45 of 3/5 Ã· 1 2/3 + 3 of 1/3 â€“ 10

__Solution__

45 of 3/5 Ã· 1 2/3 + 3 of 1/3 â€“ 10

= 45 of 3/5 Ã· (1 Ã— 3 + 2)/3 + 3 of 1/3 â€“ 10

= 45 of 3/5 Ã· 5/3 + 3 of 1/3 â€“ 10

= 45 Ã— 3/5 Ã· 5/3 + 3 Ã— 1/3 â€“ 10

= 9 Ã— 3 Ã— 3/5 + 3 Ã— 1/3 â€“ 10

= (27 Ã— 3)/5 + 1 â€“ 10

= 81/5 + 1 â€“ 10

= (81 Ã— 1)/(5 Ã— 1) + (1 Ã— 5)/(1 Ã— 5) â€“ (10 Ã— 5)/(1 Ã— 5)

= 81/5 + 5/5 â€“ 50/5

Since the denominators are common for each of the fractions,

= (81 + 5 â€“ 50)/5

= 36/5

= 7 ^{1}/_{5}

*Example 3*

Simplify: {18 + (2 Â½ + 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 Ã— 1/1000

= (213 Ã— 1)/(10 Ã— 1000)

= 213/10000

= 0.0213

*Example 4*

Simplify the following expression:

43 of 1/86 Ã· 1/14 Ã— 2/7 + 9/4 â€“ 1/4

__Solution__

43 of 1/86 Ã· 1/14 Ã— 2/7 + 9/4 â€“ 1/4

= 43 Ã— 1/86 Ã· 1/14 Ã— 2/7 + 9/4 â€“ 1/4

= 2/1 + 9/4 â€“ 1/4

= (2 Ã— 4)/1 Ã— 4) + (9 Ã— 1)/4 Ã— 1) – (1 Ã— 1)/4 Ã— 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 Ã· (3/5 + 2 ^{1}/_{10})

__Solution__

9/10 Ã· (3/5 + 2 1/10)

= 9/10 Ã· (3/5 + 21/10)

= 9/10 Ã· ((6 +21)/10)

= 9/10 Ã· 27/10

= 9/10 Ã— 10/27

= 1/3

*Example 6*

Simplify:Â (7 Â¼ – 6 1/4) of (2/5 + 3/15)

__Solution__

(7 Â¼ – 6 1/4) of (2/5 + 3/15)

= (29/4 â€“ 25/4) of (2/5 + 3/15)

= ((29 â€“ 25)/4) Ã— ((6 + 3)/15)

= 4/4 Ã— 9/15

Reduce to the fraction to its lowest term

= 1 Ã— 3/5

= 3/5