Find the Least Common Denominator (LCD) of \(\frac{1}{2},\frac{12}{5}\). In other words, find the Least Common Multiple (LCM) of \(2,5\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 2
: 2, 4, 6, 8, 10, ...
Multiples of 5
: 5, 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 2
: 2
Prime Factors of 5
: 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.
\[-\frac{1\times 5}{2\times 5}+\frac{12\times 2}{5\times 2}-5\times \frac{10}{10}\]
Simplify. Denominators are now the same.
\[-\frac{5}{10}+\frac{24}{10}-\frac{50}{10}\]
Join the denominators.
\[\frac{-5+24-50}{10}\]
Simplify.
\[-\frac{31}{10}\]
Convert to mixed fraction.
\[-3\frac{1}{10}\]
Decimal Form: -3.1
-mixed(3,1/10)
