__Objectives:__

At the end of the lesson, students should be able to:

- Add fractions with the same denominator.
- Add fractions with different denominators.
- Add mixed fractions.

**When adding fractions, with the same denominator, simply add the numerators and maintain the denominator.**

__Example 1__

^{5/}_{9 }+ ^{2/}_{9 }

**Solution**

^{5/}_{9 }+ ^{2/}_{9 } Since the denominators are the same, add only the numerators and maintain the denominator: 5 + 2 = 7

^{5/}_{9} + ^{2/}_{9} = ^{7/}_{9}

**When the denominators are different, find the LCM of the denominators**.

__Example 2__

^{5/}_{8 }+ ^{6/}_{11}

__Solution__

^{5}^{/}_{8 }+ ^{6/}_{11}

The L.C.M (Least Common Multiple) of the denominators (8 and 11) is 88.

Divide the L.C.M by each denominator and multiply by the respective numerator as follows:

88 ÷ 8 = 11, 11 × 5 = 55

88 ÷ 11 = 8, 8 × 6 = 48

These results in 2 new fractions with a common denominator:

since the denominators are the same, the fractions can now be added simply. 55 + 48 = **103**

__Example 3__

__Solution__

When adding mixed fractions, first add the whole numbers (4 + 6 = 10) then find the LCM of the denominators. L.C.M of 3 and 7 is 21. Divide the L.C.M by each denominator and multiply by the respective numerator as follows:

21 ÷ 3 = 7, 7 × 1 = 7

21 ÷ 7 = 3, 3 × 2 = 6

Lesson Content

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