Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
\[\frac{1}{2}+\frac{6}{8}\]
Simplify \(\frac{6}{8}\) to \(\frac{3}{4}\).
\[\frac{1}{2}+\frac{3}{4}\]
Find the Least Common Denominator (LCD) of \(\frac{1}{2},\frac{3}{4}\). In other words, find the Least Common Multiple (LCM) of \(2,4\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 2
: 2, 4, ...
Multiples of 4
: 4, ...
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 4
: 2, 2
Find the union of these primes.
\[2,2\]
Multiply these numbers: \(2\times 2=4\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{1\times 2}{2\times 2}+\frac{3}{4}\]
Simplify. Denominators are now the same.
\[\frac{2}{4}+\frac{3}{4}\]
Join the denominators.
\[\frac{2+3}{4}\]
Simplify.
\[\frac{5}{4}\]
Convert to mixed fraction.
\[1\frac{1}{4}\]
Decimal Form: 1.25
mixed(1,1/4)
