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

Steps to Solve

1. Simplify the original fraction
   First, we need to simplify the fraction ( \frac{4}{16} ).
   Divide 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 option for equivalence
   Now we will check each of the options to see if they simplify to ( \frac{1}{4} ).

3. Evaluate ( \frac{4}{12} )
   To simplify ( \frac{4}{12} ), divide both the numerator and the denominator by their GCD, which is 4:
   $$ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} $$
   (Does not equal ( \frac{1}{4} ))

4. Evaluate ( \frac{2}{4} )
   To simplify ( \frac{2}{4} ), divide both the numerator and the denominator by their GCD, which is 2:
   $$ \frac{2 \div 2}{4 \div 2} = \frac{1}{2} $$
   (Does not equal ( \frac{1}{4} ))

5. Evaluate ( \frac{2}{8} )
   To simplify ( \frac{2}{8} ), divide both the numerator and the denominator by their GCD, which is 2:
   $$ \frac{2 \div 2}{8 \div 2} = \frac{1}{4} $$
   (Equals ( \frac{1}{4} ))

6. Evaluate ( \frac{1}{4} )
   The fraction is already simplified to ( \frac{1}{4} ).
   (Equals ( \frac{1}{4} ))

7. Evaluate ( \frac{16}{32} )
   To simplify ( \frac{16}{32} ), divide both the numerator and the denominator by their GCD, which is 16:
   $$ \frac{16 \div 16}{32 \div 16} = \frac{1}{2} $$
   (Does not equal ( \frac{1}{4} ))