Simplify \(\frac{3}{6}\) to \(\frac{1}{2}\).
\[\frac{1}{3}-\frac{1}{2}\]
Find the Least Common Denominator (LCD) of \(\frac{1}{3},\frac{1}{2}\). In other words, find the Least Common Multiple (LCM) of \(3,2\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 3
: 3, 6, ...
Multiples of 2
: 2, 4, 6, ...
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 2
: 2
Find the union of these primes.
\[2,3\]
Multiply these numbers: \(2\times 3=6\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{1\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}\]
Simplify. Denominators are now the same.
\[\frac{2}{6}-\frac{3}{6}\]
Join the denominators.
\[\frac{2-3}{6}\]
Simplify.
\[-\frac{1}{6}\]
Decimal Form: -0.166667
-1/6
