Fraction Calculator · Practical guide
How to Convert Mixed Numbers to Improper Fractions
Multiply the whole number by the denominator, add the numerator, and keep the same denominator — examples below.
At a glance
The Short Answer
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and put the result over the original denominator. So 2 3/5 = (2 × 5 + 3)/5 = 13/5. The calculator above works with improper fractions, so convert mixed numbers this way before entering them.
Interactive tool
Fraction Calculator
Enter your own values, then compare the result with the examples below.
Result
The Formula
For a mixed number W n/d:
W n/d = (W × d + n) / d
The whole number W represents W complete groups of d parts, and the extra n parts go on top.
Worked Examples
- 1 1/2 = (1 × 2 + 1)/2 = 3/2
- 2 3/5 = (2 × 5 + 3)/5 = 13/5
- 4 2/3 = (4 × 3 + 2)/3 = 14/3
- 7 1/8 = (7 × 8 + 1)/8 = 57/8
Going the Other Direction
To turn an improper fraction back into a mixed number, divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator. For example, 17 ÷ 12 = 1 remainder 5, so 17/12 = 1 5/12.
Why Bother Converting?
Improper fractions are much easier to calculate with. Adding, subtracting, multiplying, and dividing mixed numbers directly is error-prone, while improper fractions plug straight into the standard formulas — and straight into this calculator. Enter 3/2 instead of 1 1/2 and you will always get a clean simplified result with its decimal value.
A Quick Check
Your improper fraction should always be larger than the original fractional part: the numerator ends up bigger than the denominator. If 5 1/4 came out as 6/4, you forgot to multiply the whole number first — the right answer is 21/4.
Frequently Asked Questions
What is the difference between a mixed number and an improper fraction?
They are two ways to write the same value. A mixed number splits it into a whole part plus a proper fraction (1 5/12), while an improper fraction keeps everything in one fraction (17/12).
Can this calculator take mixed numbers directly?
It accepts numerators and denominators only, so convert mixed numbers to improper fractions first — for example, enter 1 1/2 as 3/2. The result still shows the decimal value.
How do I handle negative mixed numbers?
Convert the positive version, then apply the sign to the whole fraction: negative 2 3/5 = −13/5. Do not make only the numerator negative and leave the whole part positive.
Do improper fractions need simplifying after conversion?
Only if the original fraction was not in lowest terms. Since 3/5 is already reduced, 13/5 is too. If you convert 1 2/4, reduce 2/4 to 1/2 first, giving 3/2.