Questions: Subtracting Fractions with Like Denominators

Question 1

A student computes 7/9 − 3/9 and gets 4/0. What error did they make?

• A. They subtracted the numerators incorrectly — it should be 10/0
• B. They subtracted the denominators when they should have kept the denominator as 9
• C. They should have found a common denominator before subtracting
• D. Fractions with the same denominator cannot be subtracted

Answer: (B)

The denominator names the unit — 'ninths' — and units don't change when you remove some of them. 7 ninths minus 3 ninths = 4 ninths (7/9 − 3/9 = 4/9). The denominator stays 9 because the size of each piece is unchanged; you simply have fewer of them. Subtracting the denominators (9 − 9 = 0) produces the nonsensical 4/0, which is undefined. This is the most common error in fraction subtraction.

Question 2

A student has 2 3/5 cups of flour and uses 1 1/5 cups. How much flour is left?

• A. 1 2/5 cups
• B. 1 2/0 cups
• C. 3 4/10 cups
• D. 1 1/5 cups

Answer: (A)

Subtract the fraction parts: 3/5 − 1/5 = 2/5 (subtract only numerators, keep denominator). Subtract the whole number parts: 2 − 1 = 1. Result: 1 2/5. This works because the fraction being subtracted (1/5) is smaller than the fraction being subtracted from (3/5), so no regrouping is needed. The denominator (5) never changes — it names the unit 'fifths' throughout.

Question 3

When you subtract 4/7 − 2/7, the denominator stays 7 because the size of each seventh-piece has not changed — only the number of pieces has changed.

• T. True
• F. False

Answer: True

Exactly right. The denominator (7) names the unit: 'sevenths.' When you remove 2 sevenths from 4 sevenths, you have 2 sevenths left. The unit name doesn't change — you're still dealing with sevenths. This is identical to saying '4 apples minus 2 apples equals 2 apples.' You'd never change the word 'apples' in that sentence, and you don't change 'sevenths' either.

Question 4

5/8 − 2/8 = 3/6 because you subtract both the numerators (5−2=3) and the denominators (8−2=6).

• T. True
• F. False

Answer: False

This is the classic fraction subtraction error. The correct answer is 3/8, not 3/6. The denominator 8 stays unchanged — you never subtract denominators when the fractions share the same denominator. Only the numerators are subtracted: 5 − 2 = 3, leaving 3/8. Subtracting the denominators changes the size of the pieces (from eighths to sixths), which is not what's happening mathematically.

Question 5

When subtracting fractions with the same denominator, why do you only subtract the numerators and leave the denominator unchanged?

Model answer: The denominator names the unit (the size of each piece). When you subtract, you're removing some pieces of that size from a collection of pieces of that size — the unit doesn't change, only the count does. Subtracting the denominators would change the unit, which makes no sense: taking 2 eighths away from 5 eighths leaves 3 eighths, not 3 sixths.

Think of it like subtracting 'apples.' 5 apples minus 2 apples = 3 apples — you never change the word 'apples.' Eighths work the same way. The denominator is not a quantity being operated on; it's a description of what kind of pieces you have. This insight carries forward into all fraction arithmetic.