Mixed Numbers & Improper Fractions

Math Level 6 • Lesson 6 • A gentle step-by-step lesson

Today's goal: You will learn how a mixed number and an improper fraction can mean the same amount, then use that skill to solve the worksheet problems.

1. First: What is a mixed number?

A mixed number has a whole number plus a fraction.

2 + 34 = 234

Think: 2 whole pies + 3 fourths of another pie.

2. What is an improper fraction?

An improper fraction has a numerator that is greater than its denominator. It represents at least one whole.

114 = 234

Why? Four fourths make one whole. So 8 fourths make 2 wholes, with 3 fourths left.

3. The big trick: Mixed → Improper

Remember this order: Multiply → Add → Keep the denominator.

234

Multiply the whole number by the denominator: 2 × 4 = 8

Add the numerator: 8 + 3 = 11

Keep the denominator: 4

234 = 114

4. Try the four worksheet conversions

Do each one on paper before opening the answer.

#1 2½

2 × 2 + 1 = 5 → 52

#2 1⅓

1 × 3 + 1 = 4 → 43

#3 3¼

3 × 4 + 1 = 13 → 134

#4 2¼

2 × 4 + 1 = 9 → 94

5. Reading the shaded-circle pictures

For pictures, first ask: “How many pieces make one whole?” That number becomes the denominator.

Then count every shaded piece across all the circles. That total is the numerator.

4 wholes + 38 = 358

So the picture in #6 is read as 4⅜, or 35/8.

6. Adding & subtracting mixed numbers

Like denominators? Add or subtract the fractions first, then add or subtract the whole numbers.

638 + 418

Fractions: 3/8 + 1/8 = 4/8

Wholes: 6 + 4 = 10

Put them together: 10 4/8

Reduce 4/8 to 1/2: 10½

Important: Always check whether the final fraction can be reduced.

7. Your worksheet #9–11

#9 8 6/10 − 5 4/10

6/10 − 4/10 = 2/10, and 8 − 5 = 3. So 3 2/10 = 3⅕.

#10 9 6/15 + 3 4/15

6/15 + 4/15 = 10/15, and 9 + 3 = 12. So 12 10/15 = 12⅔.

#11 7 11/20 + 3 5/20

11/20 + 5/20 = 16/20, and 7 + 3 = 10. So 10 16/20 = 10⅘.

8. Mixed Review: Prime Factors

A prime number has exactly two factors: 1 and itself.

Use a factor tree until every branch ends in a prime number.

#12: 36

36 = 6 × 6 = (2 × 3)(2 × 3)

So 36 = 2 × 2 × 3 × 3 = 2² × 3²

#13: 48

48 = 6 × 8 = (2 × 3)(2 × 2 × 2)

So 48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

⭐ One-minute memory card

Mixed → improper: Multiply, Add, Keep the denominator.
Picture → improper: denominator = pieces per whole; numerator = shaded pieces total.
Add/subtract mixed numbers: fractions first, wholes second.
Final step: Reduce the fraction if possible.
Factor tree: keep splitting until every number is prime.

Quick Check

Convert 3⅖ to an improper fraction.

3 × 5 + 2 = 17 → 17/5

Convert 14/3 to a mixed number.

14 ÷ 3 = 4 remainder 2 → 4⅔

What should you do with 10/15 at the end?

Reduce it: 10/15 ÷ 5 = 2/3.