Question

fractions quiz

1. simplify the fractions:

a) \\(\frac{9}{12}\\)
b) \\(\frac{4}{16}\\)
c) \\(\frac{8}{10}\\)
d) \\(\frac{18}{27}\\)

Explanation:

Part (a)

Step1: Find GCD of 9 and 12

The factors of 9 are \(1, 3, 9\) and the factors of 12 are \(1, 2, 3, 4, 6, 12\). The greatest common divisor (GCD) is 3.

Step2: Divide numerator and denominator by GCD

Divide 9 and 12 by 3: \(\frac{9\div3}{12\div3}=\frac{3}{4}\)

Step1: Find GCD of 4 and 16

The factors of 4 are \(1, 2, 4\) and the factors of 16 are \(1, 2, 4, 8, 16\). The GCD is 4.

Step2: Divide numerator and denominator by GCD

Divide 4 and 16 by 4: \(\frac{4\div4}{16\div4}=\frac{1}{4}\)

Step1: Find GCD of 8 and 10

The factors of 8 are \(1, 2, 4, 8\) and the factors of 10 are \(1, 2, 5, 10\). The GCD is 2.

Step2: Divide numerator and denominator by GCD

Divide 8 and 10 by 2: \(\frac{8\div2}{10\div2}=\frac{4}{5}\)

Answer:

\(\frac{3}{4}\)

Part (b)