Subtract 5/6 − 1/3.
Give me a hint
Rename one third as two sixths.
Compare a worked response
1/2
5/6 − 2/6 = 3/6 = 1/2.
Subtract fractions & regroup
Find the difference with equal-sized parts. Rename a whole when you need more of those parts.
Your learning goal
Subtract fractions and mixed numbers, including regrouping, and verify by addition.
Understand the idea
Subtract counts of equal units
For 5/6 − 1/4, use twelfths: 10/12 − 3/12 = 7/12. Keep the denominator because the difference is still measured in twelfths. Changing both numerator and denominator by subtraction does not preserve value.
Words worth knowing
- Difference
- The result of subtraction.
- Regrouping a whole
- Replacing one whole with an equivalent fraction, such as 1 = 12/12.
- Inverse operation
- An operation that undoes another; addition can check subtraction.
Make it visible
See the parts that remain.
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.
Check whether regrouping is needed
For 3 1/4 − 1 3/4, the first fractional part is smaller. Rename 3 1/4 as 2 5/4 by exchanging one whole for 4/4. Then subtract 1 3/4 to obtain 1 2/4 = 1 1/2.
Improper fractions provide another route
Convert mixed numbers to improper fractions, find a common denominator, then subtract. This avoids a separate regrouping step. It still depends on equal units, and it should agree with a drawing or a mixed-number method.
Estimate and check by adding back
If a positive amount is removed from a larger amount, the result must be smaller than the starting amount. Add the difference to the amount removed; you should recover the start. In this unit, everyday quantity problems use non-negative results; negative differences connect to rational-number work later.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Subtract 4 2/5 − 3 1/2
- Convert to improper fractions: 22/5 − 7/2.
- Rename in tenths: 44/10 − 35/10 = 9/10.
- Check: 3 1/2 + 9/10 = 3 5/10 + 9/10 = 4 4/10 = 4 2/5.
Subtract 2 1/6 − 3/4
- Use twelfths: 2 2/12 − 9/12.
- Regroup: 2 2/12 = 1 14/12. Subtract 9/12.
- The result is 1 5/12. Adding back 3/4 gives 1 14/12 = 2 1/6.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Subtract 3 1/5 − 1 4/5.
Give me a hint
Trade one of the three wholes for five fifths.
Compare a worked response
1 2/5
3 1/5 = 2 6/5; subtracting 1 4/5 leaves 1 2/5.
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?
To find how much ribbon remains, subtract the length used from the starting length. Label the result in metres or centimetres.