\[\frac{7}{8}+\frac{3}{5}\]

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Find the Least Common Denominator (LCD) of

\frac{7}{8},\frac{3}{5}

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

8,5

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 8

: 8, 16, 24, 32, 40, ...

Multiples of 5

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

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

LCM =

40

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 8

: 2, 2, 2

Prime Factors of 5

: 5

Find the union of these primes.

2,2,2,5

Multiply these numbers:

2\times 2\times 2\times 5=40

. This is the LCM.

LCM =

40

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LCD =

40

Make the denominators the same as the LCD.

\frac{7\times 5}{8\times 5}+\frac{3\times 8}{5\times 8}

Simplify. Denominators are now the same.

\frac{35}{40}+\frac{24}{40}

Join the denominators.

\frac{35+24}{40}

Simplify.

\frac{59}{40}

Convert to mixed fraction.

1\frac{19}{40}

Done

Decimal Form: 1.475

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