# GCSE Fractions, Decimals, Percentages

Maths for GCSE Preparation

__Fractions, Decimals, Percentages__

__Fractions:-__

It can be defined as a small part or proportion or amount of some quantity. It has two parts numerator and denominator.

*Fraction = Numerator / denominator*

E.g.: 1/8, 5/4,etc

__Addition and Subtraction of Fractions:-__

**Case1****:** If denominators are the same:

Add/subtract the numerators and put that answer over that denominator, and then further simplification can be done if required.

E.g. Consider two fraction sets (1/6, 2/6), (1/4, 1/4)

1/6 +2/6 = (1+2)/6 = 3/6 = 1/2 (after simplification).

1/4 + 1/4 = (1+1)/4 = 2/4 = 1/2 (after simplification).

**Case2:** If denominators are different:

**LCM Method:**

If denominators of given fractions are different, then we need to make the denominators of the fractions as the same value before we add them. For that, there is a procedure i.e.,

- Find the LCM of denominators
- Now, change the denominator of the fraction as the LCM you got in the first step
- Then, proceed with the addition or subtraction of fractions

E.g.:

- Add (1/6) and (1/12)

Solution:

Here both denominators are different. Hence by the LCM method,

- LCM of 6 and 12 is 12
- (1/6) is changed as (2/12) i.e., the denominator of fraction needs to be changed as LCM obtained in the first step. The denominator of (1/12) is already 12, so no need to change. Now the denominators of both fractions are equal.e.,12
- Add two fractions

(2/12) + (1/12) = (2+1)/12 = 3/12 =1/4

Hence (1/6) + (1/12) = 1/4

**Common Method:**

Instead of the LCM method, we can directly cross multiply the numerator and denominators of the fractions to obtain the solution. LCM method is preferable to the common method.

*Fraction = ((num1 x den2) + (num2 x den1)) / (den1 x den2)*.

E.g. (i) Add two fractions (1/6, 1/12) (ii) Subtract two fractions (1/3, 1/4)

Solution:

- 1/6 + 1/12 = ((12 x1) + (6 x 1)) / (12 x6) = 18/6×12 = 1/4
- 1/3 — 1/4 = ((4 x1) – (3 x 1)) / (3 x4) = 1/12

**Multiplying and dividing fractions:**

**Multiplication:**

Similarly, for multiplication, we need to multiply numerators and denominators separately.

*Fraction = (num1 x num2) / (den1 xden2)*

E.g.: 1/3 x 1/4 = (1 x 1) / (3 x 4) = 1/12

**Division:**

*Fraction = (num1 x den2) / (den1 x num2)*

E.g.: (1/3) / (1/4) = (1 x 4) / (1 x 3) = 4/3

**Decimals:**

A fraction is said to be a decimal when its denominator is a power of ten.

E.g. (i) 1/2 can be written as 5/10 (denominator is a power of ten) = 0.5

(ii) 3/4 can be written as 75/100 = 0.75

**Adding and Subtracting decimals:**

To add/subtract two decimals, the decimal points must coincide.

E.g.: (i) Add 1.472 and 23.2752

Solution:

(ii)Subtract 10.37 and 6

Solution:

10.37 – 6 = 4.37

**Multiplying and dividing decimals:**

The decimals can be multiplied or divided directly or by converting them into fractions.

E.g.: (i) 0.5 x 0.2 = 1/2 x 1/5 = 1/10 = 0.1

(ii) 0.2 / 0.5 = (1/5) / (1/2) = 4/10 = 0.4

**Fraction to Decimal conversion:**

Fractions can be converted to decimals by making denominators in the order of power of 10s.

Another method is to use the division method to get the decimals.

E.g. Convert ½, ¼ into decimal

Solution:

Multiply numerator and denominator by 5 to get a fraction 5/10; this can be written as 0.5

Similarly, 1/4 can be written as 25/100 = 0.25

**Decimal to Fraction conversion:**

Decimal can be converted to a fraction by multiplying and dividing it with multiples of ten.

E.g.: Convert 0.25 and 0.334 as fraction

Solution:

0.25 can be converted to fraction multiplying and dividing it with 100

0.25 = (0.25 x 100) / 100 = 25/100 = 1/4

0.334= (0.334 x 1000) / 1000 = 334/ 1000 = 167/500

**Percentage to decimal conversion:**

To convert a percentage to a decimal, it must be divided by 100.

E.g.: Convert 25% and 37% to decimal

Solution:

25%= 25/100 = 0.25

37% = 37/100 = 0.37

**Fraction to Percentage conversion:**

To convert fraction to a percentage, it must be multiplied by 100.

E.g.: Convert ¼ and ½ to percentage

Solution:

1/4 = 0.25 x 100 = 25%

1/2 = 0.5 x 100 = 50%