Simplify \(\frac{4}{8}\) to \(\frac{1}{2}\).
\[\frac{7}{8}+\frac{1}{2}+\frac{1}{2}\]
Find the Least Common Denominator (LCD) of \(\frac{7}{8},\frac{1}{2},\frac{1}{2}\). In other words, find the Least Common Multiple (LCM) of \(8,2,2\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 8
: 8, ...
Multiples of 2
: 2, 4, 6, 8, ...
Multiples of 2
: 2, 4, 6, 8, ...
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 8
: 2, 2, 2
Prime Factors of 2
: 2
Prime Factors of 2
: 2
Find the union of these primes.
\[2,2,2\]
Multiply these numbers: \(2\times 2\times 2=8\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{7}{8}+\frac{1\times 4}{2\times 4}+\frac{1\times 4}{2\times 4}\]
Simplify. Denominators are now the same.
\[\frac{7}{8}+\frac{4}{8}+\frac{4}{8}\]
Join the denominators.
\[\frac{7+4+4}{8}\]
Simplify.
\[\frac{15}{8}\]
Convert to mixed fraction.
\[1\frac{7}{8}\]
Decimal Form: 1.875
mixed(1,7/8)
