Questions: Adding and Subtracting Fractions with Like Denominators (5th Grade)

Question 1

What is 4 1/3 − 1 2/3?

• A. 3 1/3, because 4 − 1 = 3 and 1 − 2 = 1 (keeping the smaller numerator)
• B. 2 2/3, by first regrouping 4 1/3 as 3 4/3, then subtracting (3−1) + (4/3−2/3)
• C. 3 −1/3, because you subtract the fractions and whole numbers separately without regrouping
• D. 5 3/3, by combining the fractional parts

Answer: (B)

The correct answer is 2 2/3. Since 1/3 < 2/3, you cannot subtract without regrouping. Convert 4 1/3 to 3 4/3 (borrow one whole from the 4 and add 3/3 to the 1/3). Then: (3 − 1) + (4/3 − 2/3) = 2 + 2/3 = 2 2/3. Option C (3 −1/3) reveals the missing step — getting a negative fraction signals that regrouping was required but skipped.

Question 2

A student computes 5 1/4 − 2 3/4 by subtracting whole numbers (5 − 2 = 3) and fractions (1/4 − 3/4 = −2/4) and writes the answer as 3 −2/4. What should the student have done first?

• A. Added the fractions instead of subtracting, then adjusted the sign
• B. Subtracted the fractions before subtracting the whole numbers
• C. Regrouped 5 1/4 as 4 5/4 before subtracting, because 1/4 < 3/4
• D. Converted both numbers to decimals before subtracting

Answer: (C)

Because 1/4 < 3/4, you cannot subtract the fractional parts directly without going negative. The fix is to regroup first: borrow one whole from the 5, converting 5 1/4 to 4 5/4 (4 + 4/4 + 1/4 = 4 + 5/4). Now subtract: (4 − 2) + (5/4 − 3/4) = 2 + 2/4 = 2 1/2. This is identical in logic to borrowing in whole-number subtraction — the new unit borrowed is just expressed in fractional form.

Question 3

When adding mixed numbers with like denominators results in an improper fraction, you must convert it and add the extra whole to the whole-number sum.

• T. True
• F. False

Answer: True

True. For example, 3 2/5 + 2 4/5: the fraction sum is 2/5 + 4/5 = 6/5, which is improper (greater than one whole). Convert 6/5 = 1 1/5, then add the extra whole to the whole-number sum: 5 + 1 1/5 = 6 1/5. Skipping this step — writing the answer as 5 6/5 — leaves an improper fraction in the fractional part, which is not standard mixed-number form.

Question 4

To subtract 3 1/5 − 1 4/5, you can compute 3 − 1 = 2 and 1/5 − 4/5 = −3/5, giving the answer 2 −3/5.

• T. True
• F. False

Answer: False

False. Getting a negative fraction is a signal that regrouping was required but not done. The correct first step is to regroup 3 1/5 as 2 6/5 (borrow one whole: 3 = 2 + 5/5, then 5/5 + 1/5 = 6/5). Now subtract: (2 − 1) + (6/5 − 4/5) = 1 + 2/5 = 1 2/5. A mixed number with a negative fraction is not a valid answer — it is evidence of a missing step.

Question 5

Explain why regrouping is necessary when subtracting 4 1/3 − 1 2/3, and describe what the regrouped form of 4 1/3 looks like.

Model answer: Regrouping is necessary because the fractional part being subtracted (2/3) is larger than the fractional part you have (1/3). You cannot subtract 2/3 from 1/3 without going negative. To regroup, borrow one whole from the 4: 4 1/3 becomes 3 + 1 1/3 = 3 + 3/3 + 1/3 = 3 4/3. Now you have enough thirds to subtract.

Regrouping in fraction subtraction mirrors whole-number borrowing: instead of converting 1 ten into 10 ones, you convert 1 whole into fractional parts matching the denominator. For thirds, 1 whole = 3/3. Adding that to the existing 1/3 gives 4/3 — now 4/3 − 2/3 = 2/3 is straightforward. The concept is identical to 42 − 17 requiring borrowing from the tens column; the only difference is that the borrowed unit is denominated in thirds, not tens.