Questions: Equivalent Fractions

Question 1

Which fraction is equivalent to 2/3?

• A. 3/4
• B. 4/6
• C. 4/5
• D. 5/6

Answer: (B)

Multiplying both the numerator and denominator of 2/3 by 2 gives 4/6. The fraction represents the same amount — the same portion of a whole — just cut into more pieces.

Question 2

You can make an equivalent fraction by adding the same number to both the numerator and denominator. For example, 1/3 = 2/4 because you add 1 to both.

• T. True
• F. False

Answer: False

Adding does not work — it changes the value of the fraction. 1/3 ≈ 0.333 but 2/4 = 0.5, which are different. You must multiply (or divide) both numerator and denominator by the same nonzero number to preserve the fraction's value.

Question 3

Why does multiplying both the numerator and denominator by the same number produce an equivalent fraction?

Model answer: Because multiplying by n/n is the same as multiplying by 1, which does not change the value of the fraction. You are splitting each existing piece into more equal parts, so the total amount represented stays the same.

For example, 2/3 × 4/4 = 8/12. Since 4/4 = 1, the value is unchanged. Visually: if you cut each third into 4 smaller pieces, you now have 12 pieces total and 8 of them — but the shaded region is exactly the same size.