Question

which of the following fractions is equivalent to 12/16? 4/3 6/8 20/32 2/6

Explanation:

Step1: Simplify $\frac{12}{16}$

Divide numerator and denominator by their greatest common divisor, which is 4. So $\frac{12\div4}{16\div4}=\frac{3}{4}$? Wait, no, wait, let's check each option. Wait, maybe I made a mistake. Wait, let's simplify each option.

Wait, first, simplify $\frac{12}{16}$: divide numerator and denominator by 4, we get $\frac{12\div4}{16\div4}=\frac{3}{4}$? No, wait 12 divided by 4 is 3, 16 divided by 4 is 4? Wait no, 12 and 16 have GCD 4? Wait 12 factors: 2×2×3, 16: 2×2×2×2. So GCD is 4. So 12/16 = 3/4? Wait no, 12÷4=3, 16÷4=4? Wait no, 12/16 = 3/4? Wait no, 12 divided by 4 is 3, 16 divided by 4 is 4? Wait, no, 12/16 = 3/4? Wait, but let's check the options.

Option 1: 4/3. That's greater than 1, 12/16 is less than 1, so no.

Option 2: 6/8. Simplify 6/8: divide numerator and denominator by 2, get 3/4. Wait, 12/16 simplified is 3/4? Wait, 12÷4=3, 16÷4=4? Wait, 12/16 = 3/4? Wait, no, 12 divided by 4 is 3, 16 divided by 4 is 4? Wait, 12/16 = 3/4? Wait, but 6/8: 6÷2=3, 8÷2=4, so 6/8=3/4. So 12/16 and 6/8 are equivalent? Wait, let's check by cross-multiplication. 12×8=96, 16×6=96. So yes, 12/16 = 6/8.

Wait, maybe my initial simplification was wrong. Let's do it again. 12/16: divide numerator and denominator by 2, get 6/8. Oh! Right, because 12÷2=6, 16÷2=8. So 12/16 = 6/8. So that's a simpler way. So step 1: divide numerator and denominator of 12/16 by 2, get 6/8. So 6/8 is equivalent.

Step2: Check other options

• 4/3: cross-multiply with 12/16: 4×16=64, 3×12=36. Not equal.
• 20/32: simplify 20/32: divide by 4, get 5/8. 12/16 is 3/4 (or 6/8), 5/8 is not equal to 6/8.
• 2/6: simplify to 1/3. Not equal to 6/8 or 12/16.

So the equivalent fraction is 6/8.

Answer:

B. 6/8 (assuming the options are labeled, but in the given, the second option is 6/8)