Simplify.
\[\frac{2}{3}-\frac{7}{12}\]
Find the Least Common Denominator (LCD) of \(\frac{2}{3},\frac{7}{12}\). In other words, find the Least Common Multiple (LCM) of \(3,12\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 3
: 3, 6, 9, 12, ...
Multiples of 12
: 12, ...
Find the smallest number that is shared by all rows above. This is the LCM.
Method 2: By Prime Factors
List the prime factors of each number.
Prime Factors of 3
: 3
Prime Factors of 12
: 2, 2, 3
Find the union of these primes.
\[2,2,3\]
Multiply these numbers: \(2\times 2\times 3=12\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{2\times 4}{3\times 4}-\frac{7}{12}\]
Simplify. Denominators are now the same.
\[\frac{8}{12}-\frac{7}{12}\]
Join the denominators.
\[\frac{8-7}{12}\]
Simplify.
\[\frac{1}{12}\]
Decimal Form: 0.083333
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