Improper Fraction to Mixed Number Calculator

Convert improper fractions to mixed numbers with step-by-step solutions

Convert Improper Fraction

Numerator (top number)

The top number of the fraction

Denominator (bottom number)

The bottom number of the fraction (cannot be zero)

Input Fraction

8 / 5

This is an improper fraction (numerator ≥ denominator)

Results

Mixed Number

1 3/5

8/5 = 1 3/5

Whole Number

Fractional Part

3/5

Division Result

1 R 3

Verification:

1 × 5 + 3 = 8 = 8 ✓

Step-by-Step Solution

1.Given improper fraction: 8/5

2.Step 1: Divide the numerator by the denominator

3.8 ÷ 5 = 1 remainder 3

4.Step 2: The quotient (1) becomes the whole number part

5.Step 3: The remainder (3) becomes the new numerator

6.Step 4: The denominator stays the same (5)

7.Final result: 8/5 = 1 3/5

Common Examples

Example 1

7/3 = 2 1/3

7 ÷ 3 = 2 remainder 1

Example 2

13/4 = 3 1/4

13 ÷ 4 = 3 remainder 1

Example 3

22/6 = 3 2/3

22 ÷ 6 = 3 remainder 4 → 4/6 = 2/3

Example 4

15/5 = 3

15 ÷ 5 = 3 remainder 0

Key Concepts

Improper Fraction

Numerator ≥ denominator (top-heavy)

Mixed Number

Whole number + proper fraction

Division Method

Quotient becomes whole part

Remainder

Becomes new numerator

Conversion Steps

Divide numerator by denominator

Quotient = whole number part

Remainder = new numerator

Denominator stays the same

Simplify if possible

Tips & Notes

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Only works with improper fractions

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Negative fractions are handled correctly

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Fractional part is automatically simplified

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Result can be verified by conversion back

Understanding Improper Fractions and Mixed Numbers

What is an Improper Fraction?

An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). This means the fraction represents a value of 1 or greater.

Examples of Improper Fractions

• 7/3 (seven thirds)
• 13/4 (thirteen fourths)
• 22/6 (twenty-two sixths)
• 15/5 (fifteen fifths)

Real-World Examples

🍰10 slices when each cake has 6 slices = 10/6
🍫8 rows when each bar has 5 rows = 8/5
🍊21 segments when each orange has 8 = 21/8

What is a Mixed Number?

A mixed number combines a whole number with a proper fraction. It's another way to express an improper fraction that makes it easier to understand the actual quantity.

Conversion Process

Step 1: Division

Divide the numerator by the denominator to find the quotient and remainder

Step 2: Whole Number

The quotient becomes the whole number part of the mixed number

Step 3: Fraction

The remainder becomes the numerator, denominator stays the same

Detailed Example

Convert 22/6 to a mixed number:

Step 1: Divide 22 ÷ 6 = 3 remainder 4

Step 2: The whole number part is 3

Step 3: The fractional part is 4/6

Step 4: Simplify 4/6 = 2/3

Result: 22/6 = 3 2/3

Verification: 3 × 6 + 4 = 18 + 4 = 22 ✓

Special Cases

No Remainder

When the division is exact:

15/5 = 3 (no fractional part)

Negative Fractions

Negative sign applies to whole result:

-7/3 = -2 1/3

Related Calculators

Mixed Number to Improper Fraction

Convert mixed numbers back to improper fractions

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