An improper fraction has a numerator that is greater than or equal to its denominator.
Learn the definition, see real examples, use the visual strip model, and jump into the calculator when you are ready to convert.
frac74visual idea
numerator 7 > denominator 4
The top number is large enough to make at least one complete whole.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Because the numerator is at least as large as the denominator, the value is 1 or greater.
The fraction 7/4 means 7 pieces where each piece is 1/4 of a whole. Every 4 pieces make one whole, so 7 pieces equals 1 3/4.
frac74frac53frac99frac125| Type | Definition | Examples | Value |
|---|---|---|---|
| Proper fraction | numerator < denominator | 1/2, 3/4 | Between 0 and 1 |
| Mixed number | whole + proper fraction | 1 3/4, 2 1/2 | Greater than 1 |
| Improper fraction | numerator >= denominator | 7/4, 9/9 | 1 or greater |
10/6
10 slices, each pizza cut into 6.
8/5
8 rows, each bar has 5 rows.
7/2
7 half-inches = 3 and a half inches.
9/4
9 quarter-cups = 2 and a quarter cups.
Between 1 and 2 on the number line.
Between 1 and 2, closer to 2.
Between 2 and 3, closer to 2.
visual tool
Enter an improper fraction and see how complete wholes and leftovers appear.
7/4 = 1 3/4
1 whole (4/4)
3/4 remaining
compare
The key difference is the size of the numerator
Proper fractions stay before 1. Improper fractions start at 1 or move to the right of 1.
3 steps
Step 1
Divide numerator by denominator
7 ÷ 4 = 1 remainder 3
Step 2
Whole number = quotient
whole = 1
Step 3
Fraction = remainder / denominator
3/4
frac74=1frac341. Is 5/3 a proper or improper fraction?
2. Which fractions are improper? A) 2/5 B) 7/7 C) 4/9 D) 11/8
3. Convert 9/4 to a mixed number
The everyday form of many improper fractions.
Use the conversion method from this page.
Convert in the reverse direction.
Plot improper fractions greater than 1.
See wholes and leftover pieces.
Calculate with improper fractions.