Mixed Numbers and Improper Fractions
Grade 4 · Math · Study Guide
Learn what mixed numbers and improper fractions are and how to convert between them.
A fraction where the numerator is bigger than the denominator is called an improper fraction. For example, 9/4 is improper because 9 is bigger than 4. Improper fractions are perfectly fine in math — they're just another way to show an amount greater than one whole.
A mixed number combines a whole number and a fraction. For example, 2 1/4 means 2 whole things plus 1/4 of another. You can picture this as 2 whole pizzas plus a quarter of another pizza.
To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator. So 9/4: 9 ÷ 4 = 2 remainder 1. That gives us 2 1/4.
To convert a mixed number back to an improper fraction, multiply the whole number by the denominator and add the numerator. That becomes your new numerator. So 3 2/5: (3 × 5) + 2 = 17. The improper fraction is 17/5. Both forms are correct — you pick the one that's most useful for a given situation.
| Improper Fraction | Mixed Number |
|---|---|
| 5/3 | 1 2/3 |
| 9/4 | 2 1/4 |
| 11/5 | 2 1/5 |
| 7/2 | 3 1/2 |
Key terms
- Improper fraction
- A fraction where the numerator is greater than or equal to the denominator.
- Mixed number
- A number made of a whole number and a fraction, like 2 3/4.
- Convert
- Change from one form to another, like from an improper fraction to a mixed number.
Flashcards
- Improper fraction
- Numerator is greater than or equal to denominator. Example: 9/4.
- Mixed number
- A whole number plus a fraction. Example: 2 1/4.
- Convert 9/4 to a mixed number
- 9 ÷ 4 = 2 R1 → 2 1/4
- Convert 3 2/5 to an improper fraction
- (3 × 5) + 2 = 17 → 17/5
- Convert 11/3 to a mixed number
- 11 ÷ 3 = 3 R2 → 3 2/3
- Convert 2 3/4 to an improper fraction
- (2 × 4) + 3 = 11 → 11/4
Practice questions
What mixed number is equal to 11/4?
- 2 1/4
- 2 3/4
- 3 1/4
- 3 3/4
Show answer
Answer: 2 3/4
11 ÷ 4 = 2 remainder 3. So 11/4 = 2 3/4.
5/5 equals 1 whole.
Show answer
Answer: True
Any fraction where numerator equals denominator equals 1. 5/5 = 1 whole.
To convert 3 2/7 to an improper fraction, you calculate (3 × 7) + 2 = ___ over 7.
Show answer
Answer: 23
(3 × 7) + 2 = 21 + 2 = 23. The improper fraction is 23/7.
Which is an improper fraction?
- 3/8
- 7/7
- 5/9
- 2/11
Show answer
Answer: 7/7
7/7 has numerator equal to denominator, so it's improper (equals 1 whole). The others all have smaller numerators.
7/3 as a mixed number is 2 and ___/3.
Show answer
Answer: 1
7 ÷ 3 = 2 remainder 1. So 7/3 = 2 1/3.
Fun facts
- Bakers use mixed numbers all the time — recipes often call for 2 1/2 cups of flour, not 5/2 cups!
- Improper fractions are actually considered 'more proper' in algebra — many equations are easier to solve with them.
Get a personalized course on Mixed Numbers and Improper Fractions built around your child.