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question 65
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reduce the following to its lowest terms
\\( \frac{39}{42} = \frac{x}{y} \\)
solve for x in the above question;
solve for y in the above question:
question 66
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reduce the following to its lowest terms
\\( \frac{56}{84} = \frac{x}{y} \\)
solve for x in the above question;
solve for y in the above question:

Explanation:

Question 65

Step1: Find GCD of 39 and 42

The GCD of 39 and 42 is 3.

Step2: Divide numerator and denominator by GCD

Divide 39 by 3: $39 \div 3 = 13$
Divide 42 by 3: $42 \div 3 = 14$
So, $\frac{39}{42} = \frac{13}{14}$, thus $x = 13$ and $y = 14$.

Step1: Find GCD of 56 and 84

The GCD of 56 and 84 is 28.

Step2: Divide numerator and denominator by GCD

Divide 56 by 28: $56 \div 28 = 2$
Divide 84 by 28: $84 \div 28 = 3$
So, $\frac{56}{84} = \frac{2}{3}$, thus $x = 2$ and $y = 3$.

Answer:

For $x$: 13
For $y$: 14

Question 66