Improper Fractions Worksheets

In Sheet type, pick the direction and number size, from a shaded 11/4 to 12 2/5 = 62/5, then press Print.

Sheet type

Problems

Answer key

12 problems. Improper to mixed, numerators to 20. Sheet B1N658, with its answer key.

Improper to mixed, numerators to 20

Name Date Score / 12

Write each improper fraction as a mixed number: divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator.

1. = ________
2. = ________
3. = ________
4. = ________
5. = ________
6. = ________
7. = ________
8. = ________
9. = ________
10. = ________
11. = ________
12. = ________

Sheet B1N658 · Made at homeroomtools.com

Answer key. Improper to mixed, numerators to 20

1. = (5 ÷ 2 = 2 remainder 1)
2. = (13 ÷ 6 = 2 remainder 1)
3. = (3 ÷ 2 = 1 remainder 1)
4. = (20 ÷ 3 = 6 remainder 2)
5. = (17 ÷ 5 = 3 remainder 2)
6. = (19 ÷ 3 = 6 remainder 1)
7. = (10 ÷ 3 = 3 remainder 1)
8. = (19 ÷ 5 = 3 remainder 4)
9. = (11 ÷ 4 = 2 remainder 3)
10. = (16 ÷ 3 = 5 remainder 1)
11. = (9 ÷ 4 = 2 remainder 1)
12. = (11 ÷ 6 = 1 remainder 5)

Sheet B1N658 · Made at homeroomtools.com

Next step Reduce the fraction part to lowest terms Make a whole-number worksheet

How it works

Make improper fractions worksheets that run in either direction. The page opens on improper to mixed with numerators to 20. Sheet type has pictures, larger numbers and the way back, such as 12 2/5 = 62/5. Make a new sheet changes the numbers.

Read the full guide

A name the standards never use

The word improper appears nowhere in the Common Core, nor in the Texas standards for kindergarten to grade 8. A fraction is improper whenever its numerator is not smaller than its denominator, so 4/4 counts. Some books say top-heavy fraction.

Two methods, one trade

To turn 11/4 into a mixed number, divide: 11 ÷ 4 is 2 with 3 left over, so 11/4 = 2 3/4. To go back, multiply the whole number by the denominator and add the numerator: 2 × 4 + 3 = 11. Both rest on trading wholes for fourths: 2 3/4 = 8/4 + 3/4 = 11/4.

Start with Name the shaded amount two ways. A pupil who counts 11 fourths accepts that 11/4 is 2 3/4.
Give Improper to mixed, some answers whole before a quiz. About a quarter of its fractions divide exactly.
Rename a mixed number for subtraction, 3 1/4 = 2 5/4, is the sheet to print the day before borrowing.

Questions and answers

Is an improper fraction a wrong answer?

No. Improper only means the numerator is equal to or larger than the denominator, so the value is 1 or more. 11/4 is as correct as 2 3/4 and easier to multiply with. A mixed number is easier to picture.

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

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator and the denominator stays. For 17/5, 17 ÷ 5 is 3 with 2 left over, so 17/5 = 3 2/5. With nothing left over, 12/4 = 3.

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

Multiply the whole number by the denominator, add the numerator and keep the denominator. For 12 2/5, 12 × 5 + 2 = 62, so 12 2/5 = 62/5. The key prints that line of working beside each answer. To leave the key off, clear Answer key.

What grade learns improper fractions?

Grade 4, under other names. Common Core 4.NF.3c has pupils replace a mixed number with an equivalent fraction. Texas 4.3(A) has them write a/b as a sum of fractions 1/b, including when a > b.

All 15 sheet types

What an improper fraction is 3

Improper fractions on a number line On a line from 0 to 3 cut into fourths, the dot 9 marks along is 9/4. It sits one mark past 2, so 9/4 = 2 1/4. Pupils name each dot both ways, which ties the counting name to the mixed number.
Name the shaded amount two ways Two full circles and 3 of the 4 parts of another are shaded. Counting fourths gives 11/4, and counting wholes first gives 2 3/4, so 11/4 = 2 3/4. Pupils write both names under each picture.
Which two whole numbers is it between? 17/5 lies between 3 and 4, because 15/5 = 3 and 20/5 = 4. No conversion is asked for, only the two neighbors. Common Core 5.NF.3 puts the same question about a division answer.

Show all 15 sheet types (12 more)

Improper fraction to mixed number 5

Improper to mixed, larger numerators 47/6 = 7 5/6, because 6 × 7 = 42 and 47 − 42 = 5. Numerators run to 100 and denominators to 12, so the sheet doubles as division practice with remainders.
Improper to mixed, numerators to 20 7/4 = 1 3/4. Four fourths make one whole and 3 fourths are left over. Denominators are 2, 3, 4, 5, 6 and 8, numerators stop at 20, and no answer needs reducing.
Improper to mixed, reduce as well 14/4 = 3 2/4 = 3 1/2. Convert first or reduce first, 14/4 = 7/2 = 3 1/2, and the answer is the same. Every fraction on the sheet has a common factor to divide out.
Improper to mixed, some answers whole 12/4 = 3 and 13/4 = 3 1/4. About a quarter of the fractions divide exactly, so pupils learn that no remainder means no fraction part, and that writing 3 0/4 is never needed.
Tenths and hundredths past 1 23/10 = 2 3/10 and 137/100 = 1 37/100. These are 2.3 and 1.37 in fraction form, so the split between whole and part lands where the decimal point will go. Answers stay in tenths and hundredths: 250/100 = 2 50/100 on the key.

Mixed number to improper fraction 4

Mixed to improper, larger wholes 12 2/5 = 62/5, since 12 × 5 + 2 = 62. Whole parts run from 5 to 20, the size that turns up when mixed numbers are multiplied or divided in grades 5 and 6.
Mixed to improper, missing number A mixed number made of 3 and some fifths equals 17/5. Since 3 × 5 = 15 and 17 − 15 = 2, the missing numerator is 2, and 3 2/5 = 17/5. The blank may be the whole number, either numerator or the denominator.
Mixed to improper, multiply and add 2 3/4 = 11/4. Multiply the whole number by the denominator and add the numerator: 2 × 4 + 3 = 11. The denominator stays 4. The key prints that line of working for every problem.
Mixed to improper, wholes written as fractions 2 3/4 = 8/4 + 3/4 = 11/4. Writing the 2 as 8/4 first shows where multiply and add comes from. Common Core 4.NF.3c calls this replacing a mixed number with an equivalent fraction.

Both directions 1

Improper and mixed, direction shuffled Half the problems run one way, 17/5 = 3 2/5, and half the other, 4 1/3 = 13/3. Pupils have to see which form they were handed before they start.

Using it, mistakes and review 2

Add, then write the sum as a mixed number 5/8 + 7/8 = 12/8 = 1 4/8 = 1 1/2. The adding is easy on purpose, so the work is in the last two steps. Every sum on the sheet passes 1.
Rename a mixed number for subtraction 3 1/4 = 2 5/4. One whole is traded for 4/4, which is what makes 3 1/4 − 1 3/4 possible: 2 5/4 − 1 3/4 = 1 2/4 = 1 1/2. The sheet asks only for the renaming, never the subtraction.

How this list was compiled: Own list of sheet types. Every worked example was checked with exact fraction arithmetic. Definitions and methods (proper and improper, top-heavy, mixed number, both conversions) were checked against https://en.wikipedia.org/wiki/Fraction. Standards were read in the full texts in September 2026: Common Core State Standards for Mathematics, https://learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf (4.NF.3b, 4.NF.3c, 5.NF.3); Texas Essential Knowledge and Skills, 19 TAC chapter 111, https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf (2.3(C), 4.3(A), 4.3(E)) and https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111b.pdf (6.2(E)). The word improper appears in none of the three files. Licence: own work