Mixed Number to Improper Fraction

Convert mixed numbers to improper fractions in 3 simple steps. See the full solution with each step explained.

Enter a mixed number to convert it to an improper fraction. See every step of the process — multiply, add, and write over the denominator.

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help_outlineHow to Useexpand_more

Enter the three parts of your mixed number — whole, numerator, and denominator — and the calculator converts it to an improper fraction instantly, showing every step.

3-step method:

  1. Multiply the denominator by the whole number
  2. Add the numerator to that result
  3. Write the total over the original denominator

Negative mixed numbers:

Click the +/− button to toggle the sign. The calculator applies the sign to the final improper fraction.

infoWhat is Mixed Number to Improper Fraction?expand_more

A mixed number has a whole number part plus a fractional part, such as 3 5/9. An improper fraction has a numerator greater than or equal to its denominator, such as 32/9. Both represent the exact same value.

Mixed Number

Whole number + fraction

3 5/9  |  2 3/4  |  1 7/8

Improper Fraction

Numerator ≥ denominator

32/9  |  11/4  |  15/8

Why convert?

Multiplying and dividing fractions is simpler in improper form. Adding and subtracting is often easier to compare in mixed number form. Converting between the two is a fundamental fraction skill.

functionsFormulaexpand_more

One-step formula:

Improper numerator = (denominator × whole) + numerator

The denominator stays the same.

Worked example — 3 5/9:

Step 1: Multiply denominator × whole number

9 × 3 = 27

Step 2: Add the numerator

27 + 5 = 32

Step 3: Write over the denominator

32/9

Result: 3 5/9 = 32/9

Worked example — 2 3/4:

Step 1: 4 × 2 = 8

Step 2: 8 + 3 = 11

Step 3: 11/4

Result: 2 3/4 = 11/4

lightbulbExamplesexpand_more

Example 1

3 5/9 = 32/9

(9×3)+5 = 32

Example 2

2 3/4 = 11/4

(4×2)+3 = 11

Example 3

1 7/8 = 15/8

(8×1)+7 = 15

Example 4

5 2/3 = 17/3

(3×5)+2 = 17

Negative

−2 1/2 = −5/2

(2×2)+1 = 5, then negate

Larger numbers

10 4/7 = 74/7

(7×10)+4 = 74

quizFAQexpand_more
What is an improper fraction?expand_more
An improper fraction has a numerator greater than or equal to its denominator, such as 7/4 or 9/9. It represents a value of one or more. They are called 'improper' by convention, but are perfectly valid in calculations.
Does converting change the value of the number?expand_more
No. 3 5/9 and 32/9 represent exactly the same quantity — they are just written differently. Converting between forms is like renaming a number, not changing it.
Why convert a mixed number to an improper fraction?expand_more
Arithmetic operations like multiplication and division are simpler on improper fractions. For example, multiplying 2 1/2 × 3 1/3 is easier as 5/2 × 10/3 = 50/6 = 25/3 = 8 1/3.
How do I convert back to a mixed number?expand_more
Divide the numerator by the denominator. The quotient is the whole number and the remainder becomes the new numerator. For example, 32 ÷ 9 = 3 remainder 5, so 32/9 = 3 5/9.
What if the numerator of my fraction is 0?expand_more
If the fractional part is 0, the mixed number is just a whole number. For example, 5 0/3 = (3×5+0)/3 = 15/3 = 5. The result simplifies to a whole number.
Can the numerator be equal to or larger than the denominator in a mixed number?expand_more
No — that would not be a valid mixed number. For a proper mixed number, the numerator must be less than the denominator. If your fraction part is 4/4 or 6/4, you should simplify or carry over to the whole number first.