Find the Least Common Denominator (LCD) of \(\frac{11}{20},\frac{1}{2}\). In other words, find the Least Common Multiple (LCM) of \(20,2\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 20
: 20, ...
Multiples of 2
: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
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 20
: 2, 2, 5
Prime Factors of 2
: 2
Find the union of these primes.
\[2,2,5\]
Multiply these numbers: \(2\times 2\times 5=20\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{11}{20}-\frac{1\times 10}{2\times 10}\]
Simplify. Denominators are now the same.
\[\frac{11}{20}-\frac{10}{20}\]
Join the denominators.
\[\frac{11-10}{20}\]
Simplify.
\[\frac{1}{20}\]
Decimal Form: 0.05
1/20
