  Fractions

Addition of fractions with the same denominator

Let us understand the addition of fractions having the same denominator by the following example.

Example:

2 / 8
and
3 / 8
.Draw a circle and divide it into 8 equal parts as shown below. Fraction that represents red coloured part of the circle is
2 / 8

Fraction that represents blue coloured part of the circle is
3 / 8

Fraction that represents total coloured part of the circle is
5 / 8

so,
2 / 8
+
3 / 8
=
5 / 8

To add the fractions with the same denominator, add the numerators and keep the denominator as it is.

Addition of fractions with different denominator

Let us understand the addition of fractions having different denominators by the following example.

Example:

2 / 8
and
3 / 6
.Draw two circles to represent these fractions as shown below. Fraction that represents the red coloured part of the circle is
2 / 8

Fraction that represents the blue coloured part of the circle is
3 / 6

Fraction that represents total coloured part of both the circles is
2 / 8
+
3 / 6

Since denominators (size of each part) are different, we cannot add numerators directly.

So, we need to make denominators equal.

LCM of 6 and 8 = 24

Divide both the circles in 24 equal parts. Fraction that represents the red coloured part of the circle is
2 / 8
=
2x3 / 8x3
=
6 / 24

Fraction that represents the blue coloured part of the circle is
3 / 6
=
3x4 / 6x4
=
12 / 24

Fraction that represents the total-coloured part of both the circles is
6 / 24
+
12 / 24
=
18 / 24

To add or subtract fractions, we need to make the denominators equal by using LCM of the denominators, and then add or subtract the numerators.

Subtraction of fractions with the same denominator

Let us understand the subtraction of fractions having the same denominator by the following example.

Example:

Suppose we need to subtract
2 / 8
from
3 / 8
.Draw two circles to represent these fractions as shown below. Fraction that represents the red coloured part of the circle is
2 / 8

Fraction that represents the blue coloured part of the circle is
3 / 8

There is one blue coloured part more than the red coloured parts.
3 / 8
-
2 / 8
=
1 / 8

To subtract the fractions with the same denominator, subtract the numerators and keep the denominator as it is.

Subtraction of fractions with the different denominator

Let us understand the subtraction of fractions having different denominators by the following example.

Example:

Suppose we need to subtract
2 / 8
from
3 / 6
.Draw two circles to represent these fractions.Since denominators (size of each part) are different, we cannot subtract numerators directly.

So, we need to make denominators equal.

LCM of 6 and 8 = 24

Divide both the circles in 24 equal parts. Fraction that represents the red coloured part of the circle is
2 / 8
=
2x3 / 8x3
=
6 / 24

Fraction that represents the blue coloured part of the circle is
3 / 6
=
3x4 / 6x4
=
12 / 24

Now,
12 / 24
-
6 / 24
=
6 / 24

There are six more blue parts than red coloured parts.

To add or subtract fractions, we need to make the denominators equal by using LCM of the denominators, and then add or subtract the numerators.

Rule for addition/ subtraction of fractions:

• Step 1: Check whether denominators are the same or not. If not, make the denominators the same by finding the LCM of denominators.
• Step 2: After making denominators the same, do the addition/subtraction of numerators.
• Step 3: Retain the same denominator.

Misconception:

A common misconception in the addition/subtraction of fractions is adding/subtracting different denominators. When adding or subtracting fractions, very first important rule is to make common denominators. Did you know?  • -