Simplify \(\frac{2}{1}\) to \(2\).
\[\frac{9}{25}+2-\frac{4}{5}\]
Find the Least Common Denominator (LCD) of \(\frac{9}{25},\frac{4}{5}\). In other words, find the Least Common Multiple (LCM) of \(25,5\).
Method 1: By Listing Multiples
List the multiples of each number.
Multiples of 25
: 25, ...
Multiples of 5
: 5, 10, 15, 20, 25, ...
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 25
: 5, 5
Prime Factors of 5
: 5
Find the union of these primes.
\[5,5\]
Multiply these numbers: \(5\times 5=25\). This is the LCM.
Make the denominators the same as the LCD.
\[\frac{9}{25}+2\times \frac{25}{25}-\frac{4\times 5}{5\times 5}\]
Simplify. Denominators are now the same.
\[\frac{9}{25}+\frac{50}{25}-\frac{20}{25}\]
Join the denominators.
\[\frac{9+50-20}{25}\]
Simplify.
\[\frac{39}{25}\]
Convert to mixed fraction.
\[1\frac{14}{25}\]
Decimal Form: 1.56
mixed(1,14/25)
