Fractions · Add & subtract · 6.7

Subtract mixed numbers.

Subtract mixed numbers part by part. If the top fraction is too small, borrow one whole (turn it into extra pieces) before subtracting.

01 / THE IDEA

See it work.

Watch the method

Subtract mixed numbers

3 1/4 − 1 3/4: borrow → 2 5/4 − 1 3/4 = 1 2/4 = 1 1/2.

1 / 2
314−1343\frac{1}{4} - 1\frac{3}{4}
1

Subtract the numerators

Same denominator — keep it, combine the tops.

13−74=64\frac{13 - 7}{4} = \frac{6}{4}
2

Simplify

Reduce to lowest terms.

1121\frac{1}{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a fraction like 3/4 or 1 1/2.

streak 0
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— / WHY IT WORKS

The idea underneath.

Borrowing

A whole is d/d. Borrow it into the fraction part so you can subtract.

Why it works

Break a whole into pieces to have enough to take away.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Subtract 3 1/4 - 2 3/4

1

Subtract the numerators

Same denominator — keep it, combine the tops. \frac{13 - 11}{4} = 2/4

2

Simplify

Reduce to lowest terms. 1/2

EX 2medium

Subtract 4 1/4 - 1 1/4

1

Subtract the numerators

Same denominator — keep it, combine the tops. \frac{17 - 5}{4} = 12/4

2

Simplify

Reduce to lowest terms. 3

EX 3hard

Subtract 4 1/4 - 2 1/4

1

Subtract the numerators

Same denominator — keep it, combine the tops. \frac{17 - 9}{4} = 8/4

2

Simplify

Reduce to lowest terms. 2

04 / COMMON TRAPS

Where students slip.

Trap

Subtracting and getting a negative fraction part.

Fix

Borrow a whole first.

Trap

Forgetting to reduce the whole count after borrowing.

Fix

The whole part drops by 1 when you borrow.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Subtract 3 1/4 - 2 3/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
C2

Subtract 4 1/4 - 2 3/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
C3

Subtract 4 1/4 - 2 3/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
C4

Subtract 3 1/4 - 2 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
Apply

Apply (4)

A1

Subtract 4 1/4 - 1 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
A2

Subtract 4 1/4 - 1 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
A3

Subtract 4 1/4 - 1 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
A4

Subtract 4 1/4 - 1 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
Extension

Extension (4)

E1

Subtract 4 1/4 - 2 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
E2

Subtract 4 1/4 - 1 3/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
E3

Subtract 5 1/4 - 1 3/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.
E4

Subtract 3 1/4 - 2 1/4

Need a hint?
  • Borrow a whole if needed.
  • Then subtract wholes and fractions.