Mixed Number to Improper Fraction Calculator (and Back)

A mixed number to improper fraction calculator multiplies the whole number by the denominator, adds the numerator and keeps the denominator. For 2 3/4: 2 × 4 = 8, then 8 + 3 = 11, so 2 3/4 = 11/4. Going back, divide: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.

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How to use the converter

1. Choose a direction: Mixed → Improper, Improper → Mixed, or List for a whole set of homework answers at once.
2. Type the whole number, numerator and denominator (or the numerator and denominator of an improper fraction). Put a minus sign on the whole number for a negative mixed number.
3. Pick simplify to get lowest terms, or keep as calculated if your teacher wants the unsimplified form first.
4. Read the answer, the decimal value and the division check, look at the circles or fraction strips, and open Show steps for the full working.

Mixed numbers and improper fractions

A mixed number is a whole number and a proper fraction written together, such as 3 2/5, which means 3 + 2/5. An improper fraction has a numerator that is equal to or larger than its denominator, such as 17/5. Both name the same amount. Mixed numbers are easier to picture and estimate; improper fractions are easier to multiply and divide.

How to convert a mixed number to an improper fraction

For a mixed number w n/d (whole number w, numerator n, denominator d):

w n/d = (w × d + n)/d

1. Multiply the whole number by the denominator. This counts the pieces in the whole parts.
2. Add the numerator. This adds the extra pieces.
3. Write the total over the same denominator. The size of each piece does not change.

Why it works: in 3 2/5 each whole is 5 fifths, so 3 wholes are 15 fifths. Add the 2 fifths and you have 17 fifths, or 17/5.

How to convert an improper fraction to a mixed number

1. Divide the numerator by the denominator.
2. The quotient is the whole number.
3. The remainder goes over the original denominator. Simplify that fraction if you can.

For 23/6: 23 ÷ 6 = 3 remainder 5, because 6 × 3 = 18 and 23 − 18 = 5. So 23/6 = 3 5/6. Check: 3 × 6 + 5 = 23.

Worked examples

Example 1: 4 1/3 to an improper fraction

4 × 3 = 12, and 12 + 1 = 13. The denominator stays 3, so 4 1/3 = 13/3. As a decimal this is 4.333…, which is 13 ÷ 3.

Example 2: 26/8 to a mixed number

26 ÷ 8 = 3 remainder 2, so 26/8 = 3 2/8. The fraction part simplifies because GCF(2, 8) = 2: 3 2/8 = 3 1/4. You get the same answer if you simplify first: 26/8 = 13/4 = 3 1/4.

Example 3: a negative mixed number, −1 5/8

The minus sign applies to the whole amount: −1 5/8 means −(1 + 5/8). Convert 1 5/8 as usual (1 × 8 + 5 = 13) and put the sign back: −1 5/8 = −13/8. A common error is to work out −1 × 8 + 5 = −3 and write −3/8, which is far too small.

Example 4: a whole number as an improper fraction

Any whole number can be written over 1: 5 = 5/1. To use a particular denominator, multiply top and bottom by it: 5 = 20/4 = 15/3.

Quick reference table

Common mistakes to avoid

A fast check: the decimal of the improper fraction should lie between the whole number and the next whole number. 11/4 = 2.75 sits between 2 and 3, so 2 3/4 = 11/4 is reasonable.

When to use each form

• Multiplying and dividing fractions: change mixed numbers to improper fractions first. 1 1/2 × 2 2/3 = 3/2 × 8/3 = 4.
• Adding and subtracting: either form works; improper fractions avoid borrowing.
• Final answers and measurements: mixed numbers are easier to read, such as 2 3/4 cups or 5 3/8 inches.

Mixed Numbers and Improper Fractions practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

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

Multiply the whole number by the denominator, add the numerator and write the result over the original denominator. For 3 2/5: 3 × 5 + 2 = 17, so the answer is 17/5.

How do I convert an improper fraction into a mixed number?

Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator. For 23/6: 23 ÷ 6 = 3 remainder 5, so 23/6 = 3 5/6. Check by working back: 3 × 6 + 5 = 23.

Can a mixed number have an improper fraction in it?

Not in final form. The fraction part of a mixed number should be proper. If you get something like 2 7/4, rewrite 7/4 as 1 3/4 and add it to the whole number: 2 7/4 = 3 3/4. The calculator accepts 2 7/4 and shows the proper form.

How do you change an improper fraction to a mixed number on a calculator?

For 17/5, divide 17 by 5 to get 3.4. The whole number is 3. Multiply 3 × 5 = 15 and subtract from 17 to get the remainder 2, so 17/5 = 3 2/5.

How do you write a whole number as an improper fraction?

Put it over 1: 5 = 5/1. To match another fraction's denominator, multiply top and bottom by that number, such as 5 = 20/4.

Do I need to simplify the improper fraction?

Usually yes. 2 4/6 converts to 16/6, and GCF(16, 6) = 2 gives 8/3. Simplifying 4/6 to 2/3 before converting gives the same answer: 2 2/3 = 8/3.

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