1. Find the Least Common Denominator (LCD) of [tex] \frac{2}{5} , \frac{1}{2} [/tex]
Method 1: By Listing MultiplesList out all multiples of each denominator, and find the first common one.
5: 5,10
2: 2, 4, 6, 8,10
Method 2: By Prime FactorsList all prime factors of each denominator, and find the union of these primes.
5 : 5
2 : 2
Therefore, the LCD is 2 x 5 = 10
2. Make the denominators the same as the LCD
[tex] \frac{2 * 2}{5 * 2} + \frac{1 * 5}{2 * 5} [/tex]
3. Simplify. Denominators are now the same
[tex] \frac{4}{10} + \frac{5}{10} [/tex]
4. Join the denominators
[tex] \frac{4+5}{10} [/tex]
5. Simplify
[tex] \frac{9}{10} [/tex]
Done (Fact: Decimal Form 0.9)
