Find the Least Common Denominator (LCD) of \(\frac{21}{5},\frac{31}{10}\). In other words, find the Least Common Multiple (LCM) of \(5,10\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 5
: 5, 10, ...
Multiples of 10
: 10, ...
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 5
: 5
Prime Factors of 10
: 2, 5
Find the union of these primes.
\[2,5\]
Multiply these numbers: \(2\times 5=10\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{21\times 2}{5\times 2}-\frac{31}{10}\]
Simplify. Denominators are now the same.
\[\frac{42}{10}-\frac{31}{10}\]
Join the denominators.
\[\frac{42-31}{10}\]
Simplify.
\[\frac{11}{10}\]
Convert to mixed fraction.
\[1\frac{1}{10}\]
Decimal Form: 1.1
mixed(1,1/10)
