\[\frac{1}{8}+\frac{7}{12}\]

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Find the Least Common Denominator (LCD) of

\frac{1}{8},\frac{7}{12}

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

8,12

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 8

: 8, 16, 24, ...

Multiples of 12

: 12, 24, ...

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

LCM =

24

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 8

: 2, 2, 2

Prime Factors of 12

: 2, 2, 3

Find the union of these primes.

2,2,2,3

Multiply these numbers:

2\times 2\times 2\times 3=24

. This is the LCM.

LCM =

24

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LCD =

24

Make the denominators the same as the LCD.

\frac{1\times 3}{8\times 3}+\frac{7\times 2}{12\times 2}

Simplify. Denominators are now the same.

\frac{3}{24}+\frac{14}{24}

Join the denominators.

\frac{3+14}{24}

Simplify.

\frac{17}{24}

Done

Decimal Form: 0.708333

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