- Add and Subtract Fractions
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- Add or Subtract Fractions With the Same Denominator
- Add or Subtract Fractions With the Same Denominator and Simplification
- Finding the LCD of Two Fractions
- Addition or Subtraction of Unit Fractions
- Addition or Subtraction of Fractions With Different Denominators
- Add or Subtract Fractions With Different Denominators Advanced
- Word Problem Involving Add or Subtract Fractions With Different Denominators
- Fractional Part of a Circle

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# Addition or Subtraction of Unit Fractions

A unit fraction is a fraction where the numerator is always one and the denominator is a positive integer. Addition or subtraction of unit fractions can be of two types; one, where the denominators are same; two, where the denominators are different.

When the unit fractions have like denominators, we add the numerators and put the result over the common denominator to get the answer.

When the unit fractions have unlike or different denominators, we first find the LCD of the fractions. Then we rewrite all unit fractions to equivalent fractions using the LCD as the denominator. Now that all denominators are alike, we add the numerators and put the result over the common denominator to get the answer.

When the unit fractions have like denominators, we subtract the numerators and put the result over the common denominator to get the answer.

When the unit fractions have unlike or different denominators, we first find the LCD of the fractions. Then we rewrite all unit fractions to equivalent fractions using the LCD as the denominator. Now that all denominators are alike, we subtract the numerators and put the result over the common denominator to get the answer.

Add $\frac{1}{3}$ + $\frac{1}{9}$

### Solution

**Step 1:**

Add $\frac{1}{3}$ + $\frac{1}{9}$

Here the denominators are different. As 9 is a multiple of 3, the LCD is 9 itself.

**Step 2:**

Rewriting

$\frac{1}{3}$ + $\frac{1}{9}$ = $\frac{(1×3)}{(3×3)}$ + $\frac{1}{9}$ = $\frac{3}{9}$ + $\frac{1}{9}$

**Step 3:**

As the denominators have become equal

$\frac{3}{9}$ + $\frac{1}{9}$ = $\frac{(3+1)}{9}$ = $\frac{4}{9}$

**Step 4:**

So, $\frac{1}{3}$ + $\frac{1}{9}$ = $\frac{4}{9}$

Subtract $\frac{1}{9}$ − $\frac{1}{12}$

### Solution

**Step 1:**

Subtract $\frac{1}{9}$ − $\frac{1}{12}$

Here the denominators are different. The LCD of the fractions is 36.

**Step 2:**

Rewriting

$\frac{1}{9}$ − $\frac{1}{12}$ = $\frac{(1×4)}{(9×4)}$ − $\frac{(1×3)}{(12×3)}$ = $\frac{4}{36}$ − $\frac{3}{36}$

**Step 3:**

As the denominators have become equal

$\frac{4}{36}$ − $\frac{3}{36}$ = $\frac{(4−3)}{36}$ = $\frac{1}{36}$

**Step 4:**

So, $\frac{1}{9}$ − $\frac{1}{12}$ = $\frac{1}{36}$