Question

simplify each fraction.
\frac{6}{21} =
\frac{8}{12} =
\frac{27}{45} =

Explanation:

Simplifying $\boldsymbol{\frac{6}{21}}$

Step1: Find GCD of 6 and 21

The factors of 6 are 1, 2, 3, 6. The factors of 21 are 1, 3, 7, 21. The greatest common divisor (GCD) is 3.

Step2: Divide numerator and denominator by GCD

Divide 6 by 3: $6\div3 = 2$. Divide 21 by 3: $21\div3 = 7$. So $\frac{6}{21}=\frac{2}{7}$.

Simplifying $\boldsymbol{\frac{8}{12}}$

Step1: Find GCD of 8 and 12

The factors of 8 are 1, 2, 4, 8. The factors of 12 are 1, 2, 3, 4, 6, 12. The GCD is 4.

Step2: Divide numerator and denominator by GCD

Divide 8 by 4: $8\div4 = 2$. Divide 12 by 4: $12\div4 = 3$. So $\frac{8}{12}=\frac{2}{3}$.

Simplifying $\boldsymbol{\frac{27}{45}}$

Step1: Find GCD of 27 and 45

The factors of 27 are 1, 3, 9, 27. The factors of 45 are 1, 3, 5, 9, 15, 45. The GCD is 9.

Step2: Divide numerator and denominator by GCD

Divide 27 by 9: $27\div9 = 3$. Divide 45 by 9: $45\div9 = 5$. So $\frac{27}{45}=\frac{3}{5}$.

Answer:

$\frac{6}{21}=\boldsymbol{\frac{2}{7}}$, $\frac{8}{12}=\boldsymbol{\frac{2}{3}}$, $\frac{27}{45}=\boldsymbol{\frac{3}{5}}$