\[\frac{1}{5}-\frac{1}{4}+\frac{1}{20}\]

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Find the Least Common Denominator (LCD) of

\frac{1}{5},\frac{1}{4},\frac{1}{20}

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

5,4,20

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 5

: 5, 10, 15, 20, ...

Multiples of 4

: 4, 8, 12, 16, 20, ...

Multiples of 20

: 20, ...

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

LCM =

20

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 5

: 5

Prime Factors of 4

: 2, 2

Prime Factors of 20

: 2, 2, 5

Find the union of these primes.

2,2,5

Multiply these numbers:

2\times 2\times 5=20

. This is the LCM.

LCM =

20

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LCD =

20

Make the denominators the same as the LCD.

\frac{1\times 4}{5\times 4}-\frac{1\times 5}{4\times 5}+\frac{1}{20}

Simplify. Denominators are now the same.

\frac{4}{20}-\frac{5}{20}+\frac{1}{20}

Join the denominators.

\frac{4-5+1}{20}

Simplify.

0

Done

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