\[\frac{2}{9}+\frac{3}{15}\]

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Examples

Simplify

\frac{3}{15}

\frac{1}{5}

\frac{2}{9}+\frac{1}{5}

Find the Least Common Denominator (LCD) of

\frac{2}{9},\frac{1}{5}

. In other words, find the Least Common Multiple (LCM) of

9,5

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 9

: 9, 18, 27, 36, 45, ...

Multiples of 5

: 5, 10, 15, 20, 25, 30, 35, 40, 45, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM =

45

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 9

: 3, 3

Prime Factors of 5

: 5

Find the union of these primes.

3,3,5

Multiply these numbers:

3\times 3\times 5=45

. This is the LCM.

LCM =

45

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LCD =

45

Make the denominators the same as the LCD.

\frac{2\times 5}{9\times 5}+\frac{1\times 9}{5\times 9}

Simplify. Denominators are now the same.

\frac{10}{45}+\frac{9}{45}

Join the denominators.

\frac{10+9}{45}

Simplify.

\frac{19}{45}

Done

Decimal Form: 0.422222

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