Question

#13 what is the gcf of 16 and 54?
#14 find the unknown value in the pair of equivalent fractions.
\\(\frac{1}{8} = \frac{?}{4}\\)

Explanation:

For Question #13:

Step1: Factorize 16 and 54

Prime factors of \( 16 = 2 \times 2 \times 2 \times 2 \)
Prime factors of \( 54 = 2 \times 3 \times 3 \times 3 \)

Step2: Identify common factors

The common prime factor is \( 2 \). So, the GCF of \( 16 \) and \( 54 \) is \( 2 \).

Step1: Set up the proportion

We have \( \frac{1}{8} = \frac{?}{4} \). Let the unknown value be \( x \), so \( \frac{1}{8} = \frac{x}{4} \).

Step2: Cross - multiply

Cross - multiplying gives \( 8x = 1\times4 \), which simplifies to \( 8x = 4 \).

Step3: Solve for \( x \)

Divide both sides by \( 8 \): \( x=\frac{4}{8}=\frac{1}{2} \).

Answer:

2

For Question #14: