Improper Fractions and Mixed Numbers

Two ways to write the same amount of pizza.

🧱 See It

Imagine 2 whole pizzas (each cut into 3 slices, all eaten) plus 1 more slice from a third pizza that's also cut into 3 slices.

Two full pizzas and one-third of another. Every pizza is cut into 3 equal slices.

✏️ Draw It

The exact same picture can be labelled two different ways — one way counts every filled slice, the other way counts whole pizzas first.

Count all filled slices → improper fraction

7 filled slices out of every 3 → 7/3

Group into wholes → mixed number

2 whole pizzas + 1/3 of a pizza → 2 1/3

7/3 and 2 1/3 are the same amount.

🔢 Write It

Improper fraction → mixed number: divide the top number by the bottom number.

7/3 = 7 ÷ 3 = 2 remainder 1 → 2 1/3

Mixed number → improper fraction: multiply the whole number by the bottom, then add the top.

2 1/3 → (2 × 3 + 1)/3 = 7/3

The bottom number (denominator) never changes size — it just tells you the slice size the whole way through.

💡 Worked Examples

Example 1 — Improper to Mixed: 11/4

  1. Divide the top by the bottom: 11 ÷ 4 = 2 remainder 3
  2. The whole-number part is the answer to the division: 2
  3. The remainder becomes the new top number, and the bottom number stays the same: 3/4
  4. Answer: 2 3/4

Example 2 — Mixed to Improper: 3 2/5

  1. Multiply the whole number by the bottom: 3 × 5 = 15
  2. Add the top number: 15 + 2 = 17
  3. Keep the same bottom number: 5
  4. Answer: 17/5

🧠 Quick Reference

Improper → Mixed: divide top by bottom; the remainder becomes the new top number, keep the same bottom number.
Mixed → Improper: multiply the whole number by the bottom, add the top, keep the same bottom number.
👪 For Parents & Tutors

BC Curriculum (Level 1 / Grade 6, Number): "Improper fractions and mixed numbers."

Why fraction bars come first: The bars are drawn before any division is attempted symbolically. That keeps the "amount" concrete, so the division step (7 ÷ 3) is just describing a picture that already makes sense, rather than an abstract procedure performed on digits with no anchor. If he can see the two full bars and the partial bar, "2 remainder 1" is just naming what's already in front of him.

Watch for: The most common trap is forgetting to keep the same denominator during conversion, or dropping the remainder entirely (writing 11/4 as just 2). If either happens, go back to drawing the fraction bars before re-attempting the symbolic steps — the picture makes both errors obvious immediately.

Comes up again: This resurfaces heavily in Level 3 (Grade 8) fraction operations, where adding, subtracting, multiplying, and dividing fractions routinely requires converting between improper and mixed forms mid-problem.