Simplify \(\frac{4}{6}\) to \(\frac{2}{3}\).
\[\frac{9}{5}+\frac{2}{3}+\frac{2}{3}\]
Find the Least Common Denominator (LCD) of \(\frac{9}{5},\frac{2}{3},\frac{2}{3}\). In other words, find the Least Common Multiple (LCM) of \(5,3,3\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 5
: 5, 10, 15, ...
Multiples of 3
: 3, 6, 9, 12, 15, ...
Multiples of 3
: 3, 6, 9, 12, 15, ...
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 3
: 3
Prime Factors of 3
: 3
Find the union of these primes.
\[3,5\]
Multiply these numbers: \(3\times 5=15\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{9\times 3}{5\times 3}+\frac{2\times 5}{3\times 5}+\frac{2\times 5}{3\times 5}\]
Simplify. Denominators are now the same.
\[\frac{27}{15}+\frac{10}{15}+\frac{10}{15}\]
Join the denominators.
\[\frac{27+10+10}{15}\]
Simplify.
\[\frac{47}{15}\]
Convert to mixed fraction.
\[3\frac{2}{15}\]
Decimal Form: 3.133333
mixed(3,2/15)
