Skip to main content
CalcChef

Mixed Number Calculator

Add, subtract, multiply or divide two mixed numbers. The answer comes as a mixed number, an improper fraction and a decimal, with each step written out. How it works

Use the Mixed Number Calculator

Mixed number 1
Mixed number 2

Whole numbers only, up to 30 digits per box. Put a minus sign on the whole part: -1 1/2 means -(1 + 1/2), and -0 1/2 is minus one half. Enter 0 for a missing whole part or numerator, and 1 as the denominator of a whole number.

Result
4 1/4

1 1/2 + 2 3/4 = 4 1/4

Improper fraction
17/4
Decimal
4.25Exact: the decimal ends.

Working, step by step

  1. Step 1. Convert each mixed number to an improper fraction: whole × denominator + numerator, over the denominator. A minus sign on the whole part makes the whole mixed number negative.
  2. Number 1: 1 1/2 = (1 × 2 + 1) / 2 = 3/2
  3. Number 2: 2 3/4 = (2 × 4 + 3) / 4 = 11/4
  4. Step 2. Find a common denominator: the least common multiple of 2 and 4 is 4.
  5. 3/2 = 6/4 and 11/4 = 11/4.
  6. Step 3. Add the numerators: 6 + 11 = 17, so the result is 17/4.
  7. Step 4. Reduce: the greatest common divisor of 17 and 4 is 1, so 17/4 is already in lowest terms.
  8. Step 5. Convert back to a mixed number: 17 ÷ 4 = 4 remainder 1, so 17/4 = 4 1/4.

About the Mixed Number Calculator

1 1/2 + 2 3/4 = 4 1/4, which is 17/4 as an improper fraction and 4.25 as a decimal. This mixed number calculator adds, subtracts, multiplies or divides two mixed numbers and writes out each step: the improper fractions, the common denominator, the reduction and the conversion back.

Mixed number arithmetic: worked answers

CalculationMixed numberImproper fractionDecimal
1 1/2 + 2 3/44 1/417/44.25
2 1/3 + 1 1/63 1/27/23.5
2 2/3 + 1 3/44 5/1253/124.41(6)
3 3/4 + 2 1/26 1/425/46.25
3 1/4 − 1 2/31 7/1219/121.58(3)
4 1/2 − 1 3/42 3/411/42.75
10 1/2 − 3 3/46 3/427/46.75
1 1/2 × 2 2/3444
2 1/4 × 3 1/37 1/215/27.5
1 1/2 × 1 1/22 1/49/42.25
3 1/2 ÷ 1 1/42 4/514/52.8
6 1/4 ÷ 2 1/22 1/25/22.5
1 3/4 ÷ 2 1/33/43/40.75

Digits in brackets repeat forever: 1.58(3) is 1.58333… A whole-number answer is written without a denominator in the improper-fraction column.

Mixed numbers as improper fractions and decimals

Mixed numberImproper fractionDecimal
1 1/23/21.5
1 1/34/31.(3)
1 7/815/81.875
2 1/715/72.(142857)
2 2/38/32.(6)
2 3/411/42.75
3 5/829/83.625
4 5/629/64.8(3)
5 1/1681/165.0625

To convert one number in the tool, add 0 to it: enter 0, 0 and 1 as the second mixed number.

How to use this tool

  1. Type each mixed number in its three boxes: whole part, numerator and denominator. For a plain fraction enter 0 as the whole part, and for a whole number enter 0 over 1 as the fraction.
  2. Choose add, subtract, multiply or divide.
  3. Read the answer as a mixed number, an improper fraction and a decimal, then follow the numbered working under it.

Frequently asked questions

How do you add mixed numbers?
Convert both to improper fractions, rewrite them over a common denominator, add the numerators and convert back. 2 2/3 + 1 3/4 is 8/3 + 7/4 = 32/12 + 21/12 = 53/12, which is 4 5/12.
How do you multiply mixed numbers?
Convert to improper fractions and multiply straight across; no common denominator is needed. 2 1/4 × 3 1/3 is 9/4 × 10/3 = 90/12, which reduces to 15/2, or 7 1/2.
How do you divide mixed numbers?
Convert to improper fractions and multiply by the reciprocal of the second one. 3 1/2 ÷ 1 1/4 is 7/2 × 4/5 = 28/10, which reduces to 14/5, or 2 4/5.
How do I convert a mixed number to an improper fraction?
Multiply the whole part by the denominator and add the numerator. 3 5/8 is (3 × 8 + 5)/8 = 29/8, or 3.625. The tool shows this conversion as step 1 of every calculation.
How do I enter a negative mixed number?
Put the minus sign on the whole part. -1 1/2 is read as -(1 + 1/2), not as -1 + 1/2, so -1 1/2 × 2 = -3. For a negative fraction with no whole part, type -0 as the whole part: -0 1/2 is minus one half.
How do I subtract a mixed number from a whole number?
Enter the whole number with a numerator of 0 and a denominator of 1. 5 − 2 3/8 is 40/8 − 19/8 = 21/8, which is 2 5/8, or 2.625.

Adding measurements and scaling recipes

Fraction homework where the answer has to be a mixed number in lowest terms, with working to check each line against. Adding measurements in inches or cups: 3 3/4 + 2 1/2 = 6 1/4. Scaling a recipe or a cut list: 2 1/4 × 3 1/3 = 7 1/2, and 6 1/4 ÷ 2 1/2 = 2 1/2.

Improper fractions, then back to a mixed number

Each mixed number is first turned into an improper fraction:

whole a/b = (whole × b + a)/b

Then the operation is done on the two fractions.

  • Add or subtract: rewrite both over the least common multiple of the denominators, then add or subtract the numerators.

  • Multiply: multiply the numerators and multiply the denominators.

  • Divide: multiply by the reciprocal of the second fraction.

The result is reduced by the greatest common divisor and converted back: dividing the numerator by the denominator gives the whole part, and the remainder is the new numerator.

Worked example, 1 1/2 + 2 3/4: the improper fractions are 3/2 and 11/4. Over the common denominator 4 they are 6/4 and 11/4, which add up to 17/4. 17 ÷ 4 is 4 remainder 1, so the answer is 4 1/4, or 4.25.

Each box takes a whole number of up to 30 digits and the arithmetic is exact. A decimal that repeats is shown with the repeating digits in brackets, such as 1.58(3), and rounded to 10 places beside it.

Related Tools

View all tools
Math

Decimal to Fraction

Convert a decimal to a fraction in lowest terms and see the working: 0.75 = 3/4, 2.75 = 11/4 or 2 3/4, and 0.333… (3 repeating) = 1/3.

Math

Fraction Calculator

Add, subtract, multiply or divide two fractions or mixed numbers. Exact answer in lowest terms, with mixed number, decimal and the steps.

Math

Prime Number Checker

Type a whole number below 3.3 × 10^24 to see whether it is prime. A composite gets its smallest prime factor, and the five primes on either side are listed.

Math

Arithmetic Sequence Calculator

Arithmetic sequence nth term aₙ = a₁ + (n − 1)d and sum Sₙ of the first n terms, with the first 20 terms listed and the position of any value.

Math

Basic Calculator

Basic calculator for + − × ÷ in the standard order of operations (2 + 3 × 4 = 14), with % and memory keys, ^ for powers and the result as a fraction.

Math

Derivative Calculator

Enter f(x) and a point x = a to get f′(a), f(a), the tangent line and its graph, plus the formula for f′(x). Flags corners, jumps and vertical tangents.