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GRADE 6 · MATHEMATICS

Mixed Numbers and Improper Fractions

Fractions can be written in different forms. Learn what proper fractions, improper fractions and mixed numbers mean, how to convert between them, and how to check that your answers represent the same amount.

Learning time: approximately 25–30 minutes · Beginner level

What You Will Learn

1. Proper Fractions

A proper fraction has a numerator smaller than its denominator. Its value is less than one whole.

34is less than 1 whole

Three quarters means three out of four equal parts of one whole.

Examples include 1/2, 3/5 and 7/10.

2. Improper Fractions

An improper fraction has a numerator that is equal to or greater than its denominator. Its value is one whole or more.

Remember: “Improper” is a name for this fraction form. It does not mean the fraction is mathematically wrong.

3. Mixed Numbers

A mixed number contains a whole number and a proper fraction. For example, 1 3/4 means one whole and three quarters.

1 whole+34= 1 3/4

One complete object plus three quarters of another same-sized object.

Mixed numbers are useful when describing measurements, recipes and quantities that are more than one whole.

4. Convert 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 the same.

Worked example: Convert 11/4

  1. Divide 11 by 4. The quotient is 2 and the remainder is 3.
  2. Write the quotient as the whole number: 2.
  3. Write the remainder over the original denominator: 3/4.
  4. Combine them: 11/4 = 2 3/4.
Check: Two wholes contain 8 quarters. Add 3 more quarters to make 11 quarters, so 2 3/4 = 11/4.

Another example: Convert 17/5

17 ÷ 5 = 3 remainder 2. Therefore, 17/5 = 3 2/5.

5. Convert a Mixed Number to an Improper Fraction

Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

Worked example: Convert 2 3/5

  1. Multiply the whole number by the denominator: 2 × 5 = 10.
  2. Add the numerator: 10 + 3 = 13.
  3. Keep the denominator: 5.
  4. Write the improper fraction: 2 3/5 = 13/5.
Check: 13 ÷ 5 = 2 remainder 3, which returns 2 3/5.

Another example: Convert 4 1/3

4 × 3 = 12; 12 + 1 = 13. Therefore, 4 1/3 = 13/3.

6. Convert in Both Directions: Quick Reference

Starting formMethodResult
13/413 ÷ 4 = 3 remainder 13 1/4
2 2/32 × 3 + 2 = 88/3
19/519 ÷ 5 = 3 remainder 43 4/5
1 5/61 × 6 + 5 = 1111/6

7. Compare the Values

When comparing a mixed number and an improper fraction, convert one form so both numbers can be compared more easily.

Example: Is 1 2/3 greater than 7/4?
  1. Convert 1 2/3 to an improper fraction: (1 × 3 + 2)/3 = 5/3.
  2. Use a common denominator of 12: 5/3 = 20/12 and 7/4 = 21/12.
  3. Since 20/12 is less than 21/12, 1 2/3 is less than 7/4.

8. Common Mistakes to Avoid

Forgetting the remainder: When converting an improper fraction, the remainder becomes the numerator of the fractional part.
Changing the denominator: Keep the original denominator when converting between mixed and improper forms.
Adding instead of multiplying: To convert a mixed number, multiply the whole number by the denominator first, then add the numerator.
Thinking every improper fraction is more than one: A fraction such as 6/6 equals exactly one whole.

9. Practice Exercises

Try these before revealing the answers.

  1. Is 4/7 a proper or improper fraction?
  2. Is 9/5 a proper or improper fraction?
  3. Convert 13/4 to a mixed number.
  4. Convert 22/6 to a mixed number and simplify the fractional part.
  5. Convert 3 2/7 to an improper fraction.
  6. Convert 5 3/4 to an improper fraction.
  7. Which is greater: 2 1/2 or 11/4?
Show practice answers and working
  1. Proper fraction; 4 is smaller than 7.
  2. Improper fraction; 9 is greater than 5.
  3. 13 ÷ 4 = 3 remainder 1, so 3 1/4.
  4. 22 ÷ 6 = 3 remainder 4, so 3 4/6 = 3 2/3.
  5. 3 × 7 + 2 = 23, so 23/7.
  6. 5 × 4 + 3 = 23, so 23/4.
  7. 2 1/2 = 10/4, and 11/4 is greater.

10. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

1. Which is a proper fraction?
2. What is 11/3 as a mixed number?
3. What is 2 1/4 as an improper fraction?
4. What is 17/5 as a mixed number?
5. Which is greater: 1 1/2 or 7/4?

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics

Mixed Numbers and Improper Fractions Worksheet

Name: __________________________ Date: _______________

Instructions: Show your working and simplify where possible.

  1. Write whether 5/9 is proper or improper.
  2. Write whether 12/7 is proper or improper.
  3. Convert 15/4 to a mixed number.
  4. Convert 23/6 to a mixed number.
  5. Convert 3 1/5 to an improper fraction.
  6. Convert 4 3/8 to an improper fraction.
  7. Compare 2 1/4 and 9/4. Are they equal?

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. Proper fraction.
  2. Improper fraction.
  3. 15 ÷ 4 = 3 remainder 3, so 3 3/4.
  4. 23 ÷ 6 = 3 remainder 5, so 3 5/6.
  5. 3 × 5 + 1 = 16, so 16/5.
  6. 4 × 8 + 3 = 35, so 35/8.
  7. 2 1/4 = (2 × 4 + 1)/4 = 9/4, so they are equal.

12. Lesson Summary

Next learning goal: Use mixed numbers in addition, subtraction and real-life measurement problems.

Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.