In this practice worksheet, we take a look at 10 common mixed numbers and 10 common improper fractions and how to convert them from one form to another. You can download these notes as a worksheet to do in class or at home. If you know the difference between an improper fraction and a mixed number, skip the definitions and go straight to the questions.
Definition: improper fraction vs. mixed number with example
Improper fraction: a fraction with ‘heavy top is called an improper fraction. For example, ^{10}/_{7} is an improper fraction, where the
- top number 10 (numerator) is big.
- bottom number 7 (denominator) is small.
Mixed number: A whole number and a proper fraction form a ‘mixed number’. Also called mixed fraction. For example, the fraction 3^{ 1}/_{3} is a mixed number, where the
- 3 is a whole number,
- ^{1}/_{3} is a proper fraction, and
- 3 and ^{1}/_{3} together form the mixed number 3^{ 1}/_{3} 😎
How to convert an improper fraction to a mixed number
A mixed number (or mixed fraction) is formed as a result of the ‘remainder’ when dividing a top number by a bottom number.
Here are the steps for converting improper fractions to mixed numbers:
- 1: Divide the top number by the bottom number
- 2: Write down the whole number in front
- 3: Write down the remainder at the top
- 4: Keep the bottom number
Example 1: Write the improper fraction ^{20}/_{9} as a mixed number using the 4 steps above.
- 1: Divide the top number by the bottom number ✏ ^{20}/_{9 }= 20 ÷ 9 = 2R2
- 2: Write down the whole number at the front ✏ 2 ^{Top Number (R)}/_{Bottom number}
- 3: Write down the remainder at the top✏ 2 ^{2}/Bottom number
- 4: Keep the ‘bottom’ number ✏ 2^{2}/_{9 }
Maths Fun fact: Back-check to confirm the starting improper fraction
‘Back-checking’ is making sure that your answer is correct. It is done by converting from the mixed number back to its original improper fraction. We will use the mixed fraction 2^{2}/_{9} in example 1 to confirm it is equal to ^{20}/_{9}
Example 2: Write mixed number ^{20}/_{9 }as the improper fraction
Follow these steps:
- 1: Multiply the whole number and the denominator 2 x 9 = 18
- 2: Add the product to the numerator 18 + 2 = 20
- 3: Keep the bottom number 9
- 4: Write the improper fraction as ^{20}/_{9}
🔁We can confirm that 2^{2}/_{9} = ^{20}/_{9}
Get the 20 most searched questions
For the students and parents, download this note and the practice questions. See the link below. Ideally, have a go at the questions, record your answers and confirm the answers on the worksheet. All answers are given.
For teachers or maths tutors, the best way to get questions like these is to use Google Trends. Search for keywords like ‘convert improper fractions to mixed numbers, improper fractions, mixed numbers, etc. It will help you to identify the problems that many students or parents search online.
If you need help, let us know on Twitter, our handle is @PNG_Insight.
Converting improper fraction to mixed number
Write improper fractions as a mixed numbers exercise
The 10 improper fractions and 10 mixed numbers in exercises below were the widely searched fractions in Google Searches in the last five years. Instead of using other fractions, I thought these fractions will make a good practice. You can download these practice exercises from the link at the end of this work.
The 20 most searched problems can be download for free. It contains the:
- explanations, examples and images in this article,
- 10 most searched mixed number to improper fraction problems,
- 10 most searched improper fractions to mixed number problems, and
- Answers to the 20 problems in the tables.
If you are a primary school teacher, assistant, or tutor (or a parent of a primary school child), here is a book of great value.
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Practice exercise 1: Write the 10 improper fractions as mixed numbers.
Improper fraction | Mixed number equivalent | |
1 | ^{21}/_{9} | |
2 | ^{32}/_{3} | |
3 | ^{17}/_{3} | |
4 | ^{17}/_{12} | |
5 | ^{28}/_{9} | |
6 | ^{12}/_{5} | |
7 | ^{13}/_{4} | |
8 | ^{10}/_{7} | |
9 | ^{4}/_{3} | |
10 | ^{32}/_{15} |
Practice Exercise 2: 10 most searched questions on converting mixed numbers to improper fractions
Mixed number | Improper fraction | |
1 | 2 ^{1}/_{6} | ^{13}/ |
2 | 3 ^{2}/_{9} | ^{29}/ |
3 | 4 ^{2}/_{3} | ^{14}/ |
4 | 7 ^{3}/_{5} | ^{38}/ |
5 | 6 ^{3}/_{4} | ^{27}/ |
6 | 4 ^{1}/_{2} | /_{2} |
7 | 5 ^{2}/_{3} | /_{3} |
8 | 3 ^{1}/_{3} | /_{3} |
9 | 2 ^{1}/_{2} | /_{2} |
10 | 2 ^{2}/_{3} | /_{3} |
Fractions skill worksheets downloads
Working with fractions at Year 6 (Grade 6) level can be challenging. But practising these basic fractions, percentages and decimals skills will help. Check this (10 common repeating fractions) and this (Turn Decimal to Fraction or Percentage Q & A) fractions skill practice exercise and worksheets.
The three articles above are a part of the work on decimals, fractions and percentages. It is aimed to reinforce the concepts learnt at primary school. We will continue to add to maths/fraction resources.
The articles below are free maths resources for students at Grades 6 and 8 entry levels. We hope that the resources are helpful. Check them out and let us know what you think.
Fractions Worksheets: converting an improper fraction to a mixed number and vice versa
Converting mixed fractions to improper fractions Worksheet on this page is a free resource, created by us for students and teachers. It may be printed, downloaded or saved and used in the classroom, at home school, or in other educational settings to help students learn how to convert from mixed number to improper fraction or vice versa.
Download this worksheet, PDF.
Teachers and maths tutors can use the Fractions worksheets as teaching tools to introduce lessons or consolidate prior student’s knowledge. Parents can use them to give their children extra practice. Students can use them to master a math skill through practice, in a study group or for peer tutoring.