Question

13 \\(\frac{42}{63}=\underline{\quad\quad}=\\)\
15 \\(\frac{60}{75}=\underline{\quad\quad}=\\)\
17 \\(\frac{36}{84}=\underline{\quad\quad}=\\)\
simplifying fractions·mathantics

Explanation:

Problem 13: Simplify $\boldsymbol{\frac{42}{63}}$

Step1: Find GCD of 42 and 63

The greatest common divisor (GCD) of 42 and 63. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. Factors of 63: 1, 3, 7, 9, 21, 63. GCD is 21.

Step2: Divide numerator and denominator by GCD

$\frac{42\div21}{63\div21} = \frac{2}{3}$

Step1: Find GCD of 60 and 75

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. Factors of 75: 1, 3, 5, 15, 25, 75. GCD is 15.

Step2: Divide numerator and denominator by GCD

$\frac{60\div15}{75\div15} = \frac{4}{5}$

Step1: Find GCD of 36 and 84

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. GCD is 12.

Step2: Divide numerator and denominator by GCD

$\frac{36\div12}{84\div12} = \frac{3}{7}$

Answer:

$\frac{2}{3}$

Problem 15: Simplify $\boldsymbol{\frac{60}{75}}$