What Is A Mixed Number: Explained For Elementary School
Mixed numbers and improper fractions are introduced once children are secure in their understanding of proper fractions. A mixed number is the combination of a whole number and a fraction to represent a number between two whole numbers.
Mixed Numbers to Improper Fractions Worksheet
Test your students' understanding of writing and representing mixed numbers as improper fractions. Includes 15 questions and an answer key!
Download Free Now!What is a mixed number?
A mixed number, also sometimes called a mixed fraction, is an integer (whole number) and a fraction (part of a whole number).
Mixed numbers represent numbers between whole numbers. For example, 1 2⁄4, or one and two-fourths, is a mixed number, it sits between 1 and 2.
Parts of mixed numbers
Mixed numbers have three parts:
- The whole number part of the mixed number
- Numerator – the top number
- Denominator – the bottom number
Students can write mixed numbers with or without ‘and’, for example 5 and ¾ or 5¾.
The fractional part of the mixed number must be a proper fraction. This means the fraction is less than one whole. In a proper fraction, the numerator (top number) is less than the denominator (bottom number), for example 3⁄7, or 11⁄15.
A mixed number can consist of an integer and a unit or non-unit fraction but it cannot be an improper fraction, a fraction that is more than one whole. For example, 5 and 5⁄4. This should be corrected to a mixed number – in this case, 6 and ¼.
When do children learn about mixed numbers?
Children first encounter mixed numbers in upper elementary. In 4th grade, students must recognize mixed numbers and improper fractions, converting from one form to the other. Learners must write mathematical statements for mixed numbers. For example, 2⁄5 + ⅘ = 6⁄5 = 1 and ⅕.
In 5th grade math lessons, students should be adding and subtracting fractions, including adding and subtracting mixed numbers with different denominators, using the concept of equivalent fractions.
How do mixed numbers relate to other areas of math?
Mixed numbers often appear in measurement topics, requiring children to convert between units of measure. For example, children should know that 1½ liters is equivalent to 1,500ml, or that 2¾ hours = 165 minutes.
Some mixed numbers may require simplifying fractions, e.g. 4 2⁄4 = 4½.
These types of fractions and measures are also sometimes represented as decimals, such as 1.5 or 2.75. Children should know fraction-decimal equivalents in 4th grade.
How are mixed numbers used in real life?
To make math relatable, children need to know how the math they are learning is applicable in real-life contexts. As previously mentioned, mixed numbers are most commonly found in real life when referring to units of measure, e.g. 1½ tablespoons, 1¾ hours, 5½ pizzas, etc.
3 worked examples for mixed numbers
1) Convert between mixed numbers and improper fractions.
How to teach children to convert an improper fraction to a mixed number:
Divide the numerator (in a division, this is also known as the dividend) by the denominator (also known as the divisor).
The answer to this (also known as the quotient) becomes the whole number part; the remainder (if there is one) becomes the numerator; the denominator (which was the divisor) remains the same.
For example, to convert 23⁄5 to a mixed number, step-by-step:
Step 1. Divide 23 by 5.
Step 2. 5 fits into 23 4 whole times, so the whole number is 4.
Step 3. There is a remainder of 3, so the new numerator is 3 in the fraction part of the mixed number (the denominator remains the same as the original improper fraction).
Therefore, the answer is 4⅗.
Bar models can help students visualize these calculations clearly:
As shown above, learners can write twenty-three fifths as four wholes and three-fifths.
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.
The answer to this becomes the new numerator; the denominator remains the same.
For example, to convert 2⅔ to an improper fraction step-by-step:
Step 1. 2 (whole number) x 3 (denominator) = 6
Step 2. 6 + 2 (numerator) = 8 (the new numerator).
Therefore, the answer is 8⁄3.
As shown above, students can also write two wholes and two-thirds as eight-thirds.
2) Add or subtract mixed numbers.
Example 1: 1¼ + 1½ Example 2: 2⅓ – 1⅖
Students can approach addition or subtraction such as these in one of two ways:
- First partition the mixed numbers into integers and proper fractions, calculate and then recombine, such as example 1: 1 + 1 = 2, ¼ + ½ = ¾, then 2 + ¾ = 2¾.
- First convert the mixed numbers into improper fractions, calculate and then convert back into mixed numbers if necessary, such as example 2: 2⅓ – 1⅖ = 7⁄3 – 7⁄5 = 35⁄15 – 21⁄15 = 14⁄15.
3) Multiply mixed numbers by whole numbers
1⅓ x 5
Again, students can approach this in one of two ways:
- First partition the mixed number into an integer and proper fraction, calculate and then recombine: 1 x 5 = 5, ⅓ x 5 = 1⅔, 5 + 1⅔ = 6⅔.
- First convert the mixed number into an improper fraction, calculate and then convert back into a mixed number if necessary: 1⅓ = 4⁄3, 4⁄3 x 5 = 20⁄3 = 6⅔.
5 mixed number practice questions, word problems and answers
- 2½ + 1⅗
Answer: 5⁄2 + 8⁄5 = 25⁄10 + 16⁄10 = 41⁄10 = 4 and 1⁄10 - 3 x 2⅖
Answer: 3 x 12⁄5 = 3⁄5 = 7⅕ - The length of a day on Earth is 24 hours. The length of a day on Mercury is 58⅔ times the length of a day on Earth. What is the length of a day on Mercury, in hours?
Answer: 24 x 58⅔ = 1,408 hours - Which improper fraction is equivalent to 6⅞?
67⁄8 48⁄8 62⁄8 55⁄8 76⁄8
Answer: 55⁄8 - Potatoes cost $1.50 per lb and carrots cost $1.80 per lb. Jack buys 1½lb of potatoes and ½lb of carrots. How much change does he get from $5?
Answer: $1.50 x 1½ = $2.25, ½ of $1.80 = $0.90, $2.25 + $0.90 = $3.15
Read more about adding, subtracting and multiplying fractions in this fractions for kids article.
Both are larger than one whole but represented differently: an improper fraction has only a numerator and a denominator (the former of which is larger than the latter, e.g. 5⁄3, the equivalent of 1⅔); a mixed number has a whole number and a proper fraction (e.g. 1⅔, the equivalent of 5⁄3).
See the ‘worked examples’ section above
Read more: How to Teach Fractions: adding, subtracting, multiplying and dividing fractions.
For more explanations on teaching elementary math topics, see our Math Dictionary.
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The content in this article was originally written by primary school teacher Sophie Bartlett and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.
