A fraction is a part of a whole expressed as a figure placed on top of another figure. The one on top is called Numerator while the one below is called Denominator

E.g 2/3, 4/7, 5/9 etc.

There are essentially two types: proper and improper fraction.

A proper fraction has the numerator less than the denominator e.g. 2/3, 8/11, 5/7 while an improper fraction has the numerator greater than the denominator

e.g 5/3, 8/5, 13/6 etc, also we have a mixed number when consists of a whole number and fractions written together.

e.g 1 5/7, 2 1/6, 7 5/8 etc. solving problems involving fractions does not create any difficulty once you remember the word “BODMAS” and use it effectively.

The word “BODMAS” means

B = Bracket

O = Of

D = Division

M = Multiplication

A = Addition

S = Subtraction

Make sure you write down this important word on you book and know what each letter stands for.

Having known the basics of fraction, let solve some problems

**Solution To Simplification of Fraction**

**Example 1:**

Simplify ¾ (3 3/8 + 1 5/8)/2 1/8 – 1 ½

Solution

Using BODMAS, we start by removing the bracket

¾ (8×3+3/8 + 8×1+5/8)

8×2+1/8 – 2×1+1/2

¾(27/8 + 12/8)

17/8 – 3/2

Since the denominators in the bracket are the same, simply add the numerator

¾ x 27+13/8

= ¾ x 40/8

= 17/8 – 3/2

We are done with bracket, let now go into multiplication in the numerator

3×40/4×8 = 120/32

120/32

17/8 – 3/2

Let’s solve the denominator, the L.C.M of 8 and 2 is 8

120/32/17-12/8 = 120/32/5/8

How do I get 12?

2 into 8 is 4, 4 x3 = 12

120/32 x 8/5

= 24/4 = 6

N/B: When the sign is changed from division to multiplication sign, the second fraction is reverse i.e if it was 4/5, it will be 5/4

e.g 8/5 / 7/6 = 8/5 x 6/7

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**Example 2:**

Simplify ½ *of* ¼ / 1/3/1/6-3/4 – ½

**Solution**

Using BODMAS, we start with division, “of” means multiplication

½ x ¼ / 1/3 / 1/6-3/4-1/3 = 2 x ¼ / 1/3 / 1/6 – ¾ – 1/3 = 1/8 / 1/3 / 1/6-3/4-1/3

Up next is the division

Change the sign and reverse the second fraction.

1/8 x 3/1 = 3/8

3/8 / 1/6 – ¾ – ½

Let’s now tackle the denominator for the L.C.M of 2, 4 and 6 is 12

3/8 / 2×1-3×3-6×1/12 = 3/8/2-9-6/12

3/8/-13/12 = 3/8 x 12/-13

= 3×3/2x-13 = 9/26

The answer = 9/26

**Example 3:**

Simplify 1 ¼ + 1 1/2/ 5 1/8 – 3 ¾

**Solution**

Let’s start with changing the mixed from

4×1+1/4 + 2×1+1/2

8×5+1/8 – 4×3+3/4

4+1/4 – 2+1/3

40+1/8 – 12+3/4

5/4 + 3/2 / 41/8 – 15/4

We now start with addition the L.C.M of 2 and 4 is 4

5+2×3/4 / 41/8-15/4 = 11/4/41/8 – 15/4

The denominator is next, the L.C.M of 4 and 8 is 8

11/4/41-15×2/8 = 11/4 / 41-30/8 = 11/4/11/8

11/4 / 11/8

We change the division sign to multiplication sign

11/4 x 8/11 = 88/44 = 2

Therefore the answer is 2

**Example 4:**

Simplify 71/2 –(21/2 + 3) + 161/2

**Solution**

Using BODMAS, we start by eliminating the bracket. But first the change the mixed fractions

2×7+1/2 – (2×2+1/2 + 3) + 2×16+1/2

14+1/2 – (4+1/2 + 3) + 32 +1/2

15/2 – (5/2 + 3/2) + 33/2

15/2 – 5+6/2 + 33/2

15/2 = 11/2 + 33/2

Since the denominator is 2 all through, add and subtract the numerator

15-11+33/2 = 37/2

= 18 ½

**Example 5:**

Simplify 1 7/8 x 2 2/5 / 6 ¾ / ¾

**Solution**

Let’s start by changing the mixed fractions

8×1+7/8 x 3×2+2/5

4×6+3/4 / ¾

15/8 / ¾

Up next is division

15/8 x 12/5 / 27/4 x 4/3

We can now carry out

15/8 x 12/5 / 27/4 x 4/3 = 3×3/2 / 9

= 9/2 = 9/2 x 1/9

9/2×9 = 9/18 = ½

In conclusion, when you encounter problems that as to do with simplification of fractions, always remember “BODMAS”.

Your ability to use it effectively determines how accurate your answer will be. The rule remains the same, change the mixed fraction to a proper or improper fraction and then apply the use of BODMAS and simplify it accordingly.