Which of the following fractions are equivalent to 4/16? Select all that apply.

Steps to Solve

1. Simplify the original fraction To find fractions equivalent to $\frac{4}{16}$, we first simplify it. Dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:

$$ \frac{4 \div 4}{16 \div 4} = \frac{1}{4} $$

2. Check each fraction for equivalence We need to simplify each of the given fractions to see if they equal $\frac{1}{4}$.

• Check $\frac{4}{12}$: Divide both the numerator and denominator by their GCD, which is 4: $$ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \quad (\text{not equivalent}) $$

• Check $\frac{2}{4}$: Divide both the numerator and denominator by their GCD, which is 2: $$ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \quad (\text{not equivalent}) $$

• Check $\frac{2}{8}$: Divide both the numerator and denominator by their GCD, which is 2: $$ \frac{2 \div 2}{8 \div 2} = \frac{1}{4} \quad (\text{equivalent}) $$

• Check $\frac{1}{4}$: This fraction is already in its simplest form and is clearly: $$ \frac{1}{4} \quad (\text{equivalent}) $$

• Check $\frac{16}{32}$: Divide both the numerator and denominator by their GCD, which is 16: $$ \frac{16 \div 16}{32 \div 16} = \frac{1}{2} \quad (\text{not equivalent}) $$

3. Identify equivalent fractions The equivalent fractions to $\frac{4}{16}$ are those that simplified to $\frac{1}{4}$. We found:

• $\frac{2}{8}$
• $\frac{1}{4}$