Simplify \(\frac{3}{9}\) to \(\frac{1}{3}\).
\[\frac{1}{3}+\frac{6}{10}+\frac{18}{90}\]
Simplify \(\frac{6}{10}\) to \(\frac{3}{5}\).
\[\frac{1}{3}+\frac{3}{5}+\frac{18}{90}\]
Simplify \(\frac{18}{90}\) to \(\frac{1}{5}\).
\[\frac{1}{3}+\frac{3}{5}+\frac{1}{5}\]
Find the Least Common Denominator (LCD) of \(\frac{1}{3},\frac{3}{5},\frac{1}{5}\). In other words, find the Least Common Multiple (LCM) of \(3,5,5\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 3
: 3, 6, 9, 12, 15, ...
Multiples of 5
: 5, 10, 15, ...
Multiples of 5
: 5, 10, 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 3
: 3
Prime Factors of 5
: 5
Prime Factors of 5
: 5
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.
\[\frac{1\times 5}{3\times 5}+\frac{3\times 3}{5\times 3}+\frac{1\times 3}{5\times 3}\]
Simplify. Denominators are now the same.
\[\frac{5}{15}+\frac{9}{15}+\frac{3}{15}\]
Join the denominators.
\[\frac{5+9+3}{15}\]
Simplify.
\[\frac{17}{15}\]
Convert to mixed fraction.
\[1\frac{2}{15}\]
Decimal Form: 1.133333
mixed(1,2/15)
