How do you convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. That result becomes the new numerator; the denominator stays the same. Example: 2 3/5 -> (2×5)+3 = 13 -> 13/5.

Why do we convert mixed numbers to improper fractions?

Improper fractions are easier to use in multiplication and division. When multiplying or dividing mixed numbers, converting to improper fractions first makes the calculation straightforward.

What if the fractional part of a mixed number is 0?

If the fractional part is 0, the mixed number is just a whole number. For example, 5 0/3 = (5×3+0)/3 = 15/3 = 5.

Grade 4-6 conversion tool

Mixed Number to Improper Fraction Calculator

Convert any mixed number to an improper fraction instantly. See the full multiplication steps, a visual fraction bar, and practice problems. Free, no login needed.

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Need the reverse?Improper Fraction -> Mixed Number

Calculator

Convert mixed number to improper fraction

Enter a mixed number

WholeNumeratorDenominator

Result

2 3/5 = 13/5

Improper fraction = (whole × denominator + numerator) / denominator

Step-by-step solution

Step 1: Multiply whole number × denominator: 2 × 5 = 10.
Step 2: Add the numerator: 10 + 3 = 13.
Step 3: Keep the same denominator: new fraction = 13/5.
Step 4: Simplify if needed: GCF(13, 5) = 1 -> already in simplest form.

Visual

Visualize the conversion

Each row is one whole. Count all colored pieces to get the improper fraction.

1 whole = 5/5 = 5 pieces

3/5 remaining

Total pieces: 2 × 5 + 3 = 13. Total = 13/5.

How it works

How to convert a mixed number to an improper fraction

3 steps - works for any mixed number

Multiply

Multiply whole × denominator.

2 × 5 = 10

Add

Add the numerator.

10 + 3 = 13

Keep

Keep the same denominator.

13/5

Memory trick

Multiply and Add: whole times bottom, then plus top. The denominator never changes.

Examples

Worked examples

1 3/4

Basic: 1×4+3=7.

3 2/6

Simplify the result: 20/6 -> 10/3.

5 0/3

The fractional part is 0, so this is exactly 5.

Practice

Practice problems

Convert 2 1/3 to an improper fraction

Convert 4 3/8 to an improper fraction

Convert 3 4/6 to an improper fraction

Improper Fraction -> Mixed Number

Reverse this conversion and check your understanding.

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