Number + Fraction Calculator

Convert whole numbers combined with fractions into improper fractions or mixed numbers. This calculator handles the addition of integers and fractional parts, automatically simplifying the result and showing it in multiple formats.

Calculate

Whole Number

Fraction Part

What This Calculator Does

This calculator converts expressions like "5 and 3/4" into both improper fraction form (23/4) and proper mixed number form (5 3/4), along with decimal and percentage equivalents.

The process multiplies the whole number by the denominator, adds the numerator, then places the result over the original denominator. The calculator then simplifies the fraction if possible and provides all common formats.

When You'd Use This

Recipe Conversions: Converting measurements like "2 and 1/2 cups" into improper fractions for scaling recipes up or down
Construction and Carpentry: Working with measurements like "3 and 3/8 inches" when calculating total lengths or making cuts
Academic Problems: Homework and test questions that require converting between mixed numbers and improper fractions
Time Calculations: Converting mixed hour measurements like "2 and 1/4 hours" into improper fractions for further calculations

Step-by-Step Method

Multiply Whole Number by Denominator

Take the whole number and multiply it by the denominator of the fraction. This converts the whole number into an equivalent fraction with the same denominator as the fractional part.

Example: For 5 3/4, multiply 5 × 4 = 20

Add the Numerator

Add the original numerator to the result from step 1. This gives you the total number of fractional parts.

Example: 20 + 3 = 23

Place Over Original Denominator

Put the sum from step 2 over the original denominator to get your improper fraction.

Example: 23/4

Simplify if Needed

Check if the numerator and denominator share any common factors. If they do, divide both by their greatest common divisor to simplify.

Example: 23/4 is already in simplest form (23 is prime)

Convert to Other Formats

Divide the numerator by the denominator to get the decimal form. Multiply the decimal by 100 to get the percentage.

Example: 23 ÷ 4 = 5.75 = 575%

Common Mistakes to Avoid

Forgetting to Multiply the Whole Number

A common error is adding the whole number directly to the numerator without first multiplying by the denominator. For example, incorrectly thinking 5 3/4 becomes 8/4 instead of the correct 23/4.

Adding Denominators

The denominator never changes in this operation. You're not adding two separate fractions; you're converting a whole number into fractional parts with the same denominator, then combining the numerators.

Skipping Simplification

Always check whether the final fraction can be simplified. Results depend on showing fractions in their simplest form unless explicitly stated otherwise.

Frequently Asked Questions

What if the whole number is zero?

If the whole number is zero, you simply have the original fraction. The calculation still works: 0 × denominator + numerator = numerator, giving you numerator/denominator.

Can this work with negative numbers?

Yes, the same method applies to negative mixed numbers. For example, -3 1/2 becomes -7/2 (multiply -3 × 2 = -6, then add 1 to get -5 for the total negative parts, but accounting for the sign gives -7/2).

What's the difference between an improper fraction and a mixed number?

An improper fraction has a numerator larger than or equal to its denominator (like 23/4), while a mixed number combines a whole number with a proper fraction (like 5 3/4). They represent the same value in different formats.

When should I use improper fractions instead of mixed numbers?

Improper fractions are often easier to work with when multiplying or dividing fractions. Mixed numbers are typically easier to understand for measurements and real-world quantities. Different contexts prefer different formats.

Does this calculator work for ratios too?

This calculator specifically handles whole numbers plus fractions. For ratio calculations, use the dedicated ratio simplifier tool, which handles ratio notation differently.