\[\frac{1}{6}-\frac{4}{5}\]

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Find the Least Common Denominator (LCD) of

\frac{1}{6},\frac{4}{5}

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

6,5

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 6

: 6, 12, 18, 24, 30, ...

Multiples of 5

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

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

LCM =

30

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 6

: 2, 3

Prime Factors of 5

: 5

Find the union of these primes.

2,3,5

Multiply these numbers:

2\times 3\times 5=30

. This is the LCM.

LCM =

30

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LCD =

30

Make the denominators the same as the LCD.

\frac{1\times 5}{6\times 5}-\frac{4\times 6}{5\times 6}

Simplify. Denominators are now the same.

\frac{5}{30}-\frac{24}{30}

Join the denominators.

\frac{5-24}{30}

Simplify.

-\frac{19}{30}

Done

Decimal Form: -0.633333

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