Write 4 1/3 as a single fraction.
Give me a hint
How many thirds are in four wholes?
Compare a worked response
13/3
Four wholes contain 12 thirds; add one more third.
Mixed numbers & improper fractions
One amount can have more than one useful name. Group the parts into wholes, or unpack the wholes into parts.
Your learning goal
Convert between mixed numbers and improper fractions and choose a useful representation.
Understand the idea
Keep one denominator as the unit
Seven thirds means seven equal pieces, with three pieces per whole. Grouping six of the pieces into two wholes leaves one third: 7/3 = 2 1/3. The unit part is still a third.
Words worth knowing
- Proper fraction
- A positive fraction less than 1: its numerator is smaller than its denominator.
- Improper fraction
- A non-negative fraction whose numerator is at least its denominator. It can equal or exceed 1.
- Mixed number
- A whole number plus a proper fractional part, such as 2 3/5.
Make it visible
Group parts into complete wholes.
Predict a result, change a value, and use the diagram to explain your reasoning.
Predict before changing a value. Every whole in a bar diagram uses the same size. The models use non-negative amounts up to two wholes per input.
Convert a mixed number by counting all the parts
In 2 3/5, two wholes contain 2 × 5 = 10 fifths. Add the remaining three fifths: 13/5. The written space means addition, so 2 3/5 is 2 + 3/5, not 2 × 3/5.
Convert back with quotient and remainder
For 17/6, divide 17 by 6. Two complete groups use 12 sixths, leaving five sixths. The mixed number is 2 5/6. Keep the original denominator for the remainder and simplify the fractional part if possible.
Choose the form that supports your reasoning
Mixed numbers make estimates and measurements easy to read. Improper fractions are particularly useful in multiplication and division. Neither form is more mathematically correct. If the division is exact, write a whole number: 12/4 = 3.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Convert 3 2/7 to an improper fraction
- Three wholes contain 21 sevenths.
- 21 sevenths + 2 sevenths = 23 sevenths.
- 3 2/7 = 23/7. Check: 23 ÷ 7 gives 3 with remainder 2.
Convert 22/8 to a mixed number in simplest form
- 22 ÷ 8 gives 2 with remainder 6.
- 22/8 = 2 6/8. Simplify 6/8 by dividing by 2.
- The result is 2 3/4. Also, simplifying 22/8 to 11/4 first gives the same result.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Write 19/5 as a mixed number.
Give me a hint
How many full groups of five fit into 19?
Compare a worked response
3 4/5
Three groups use 15 fifths, leaving four fifths.
Independent practice
Build a strategy you can explain.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Check the concepts, too.
What does the answer mean?
A measurement of 2 3/4 metres is useful on a plan. The equivalent 11/4 metres can be easier when scaling the plan.