Question

topic: reducing fractions
reduce the following fractions to lowest form. then explain the mathematics that makes it possible to rewrite the fraction in its new form. (improper fractions should not be written as mixed numbers.) if a fraction can’t be reduced, explain why.

1. $\frac{12}{15}$ explanation:
2. $\frac{26}{11}$ explanation:
3. $\frac{51}{17}$ explanation:
4. $\frac{6}{13}$ explanation:
5. $\frac{114}{27}$ explanation:
6. $\frac{-14529}{14529}$ explanation:

Explanation:

Problem 14: $\boldsymbol{\frac{12}{15}}$

Step1: Find GCD of 12 and 15

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 15: 1, 3, 5, 15
GCD(12,15) = 3

Step2: Divide numerator and denominator by GCD

$\frac{12\div3}{15\div3} = \frac{4}{5}$

Step1: Check GCD of 26 and 11

11 is prime. Factors of 26: 1, 2, 13, 26.
GCD(26,11) = 1

Step2: Since GCD is 1, fraction is reduced

$\frac{26}{11}$ (can’t be reduced as GCD is 1)

Step1: Find GCD of 51 and 17

17 is prime. 51 ÷ 17 = 3, so GCD(51,17) = 17

Step2: Divide numerator and denominator by GCD

$\frac{51\div17}{17\div17} = \frac{3}{1} = 3$

Answer:

$\frac{4}{5}$

Problem 15: $\boldsymbol{\frac{26}{11}}$