Question

simplify each fraction.
\\(\frac{9}{27}\\)
\\(\frac{8}{36}\\)
\\(\frac{7}{27}\\)

Explanation:

Simplify $\boldsymbol{\frac{9}{27}}$

Step1: Find GCD of 9 and 27

The greatest common divisor (GCD) of 9 and 27 is 9, since $9 = 9\times1$ and $27 = 9\times3$.

Step2: Divide numerator and denominator by GCD

Divide both the numerator and the denominator by 9: $\frac{9\div9}{27\div9}=\frac{1}{3}$

Simplify $\boldsymbol{\frac{8}{36}}$

Step1: Find GCD of 8 and 36

The factors of 8 are 1, 2, 4, 8; the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The GCD of 8 and 36 is 4.

Step2: Divide numerator and denominator by GCD

Divide both by 4: $\frac{8\div4}{36\div4}=\frac{2}{9}$

Simplify $\boldsymbol{\frac{7}{27}}$

Step1: Check GCD of 7 and 27

The factors of 7 are 1, 7; the factors of 27 are 1, 3, 9, 27. The GCD of 7 and 27 is 1.

Step2: Since GCD is 1, the fraction is already in simplest form. So $\frac{7}{27}$ remains as $\frac{7}{27}$.

Answer:

s:

• $\frac{9}{27}$ simplifies to $\frac{1}{3}$
• $\frac{8}{36}$ simplifies to $\frac{2}{9}$
• $\frac{7}{27}$ simplifies to $\frac{7}{27}$