\[\frac{1}{2}+\frac{1}{7}+\frac{3}{28}\]

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Find the Least Common Denominator (LCD) of

\frac{1}{2},\frac{1}{7},\frac{3}{28}

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

2,7,28

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 2

: 2, 4, 6, ... , 24, 26, 28, ...

Multiples of 7

: 7, 14, 21, 28, ...

Multiples of 28

: 28, ...

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

LCM =

28

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 2

: 2

Prime Factors of 7

: 7

Prime Factors of 28

: 2, 2, 7

Find the union of these primes.

2,2,7

Multiply these numbers:

2\times 2\times 7=28

. This is the LCM.

LCM =

28

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LCD =

28

Make the denominators the same as the LCD.

\frac{1\times 14}{2\times 14}+\frac{1\times 4}{7\times 4}+\frac{3}{28}

Simplify. Denominators are now the same.

\frac{14}{28}+\frac{4}{28}+\frac{3}{28}

Join the denominators.

\frac{14+4+3}{28}

Simplify.

\frac{21}{28}

Simplify.

\frac{3}{4}

Done

Decimal Form: 0.75

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