Simplify \(\frac{6}{12}\) to \(\frac{1}{2}\).
\[\frac{10}{11}-\frac{1}{2}\]
Find the Least Common Denominator (LCD) of \(\frac{10}{11},\frac{1}{2}\). In other words, find the Least Common Multiple (LCM) of \(11,2\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 11
: 11, 22, ...
Multiples of 2
: 2, 4, 6, ... , 18, 20, 22, ...
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 11
: 11
Prime Factors of 2
: 2
Find the union of these primes.
\[2,11\]
Multiply these numbers: \(2\times 11=22\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{10\times 2}{11\times 2}-\frac{1\times 11}{2\times 11}\]
Simplify. Denominators are now the same.
\[\frac{20}{22}-\frac{11}{22}\]
Join the denominators.
\[\frac{20-11}{22}\]
Simplify.
\[\frac{9}{22}\]
Decimal Form: 0.409091
9/22
