A roll has 5/6 m of ribbon. You use 1/4 m. How much remains?
Give me a hint
The question asks for a difference, measured in metres.
Compare a worked response
7/12 m
5/6 − 1/4 = 10/12 − 3/12 = 7/12.
Fraction problems & mathematical decisions
Decide what the quantities mean. Then choose an operation, calculate and explain the answer in context.
Your learning goal
Solve one- and multi-step fraction problems using models, units and reasonableness checks.
Understand the idea
Choose an operation from the relationship
Combine amounts with addition; find a difference with subtraction. Taking a fraction of an amount uses multiplication. Finding how many groups of a given size fit uses division. Keywords alone are unreliable: describe what the result will measure.
Words worth knowing
- Quantity
- An amount together with a unit or context.
- Part of the remainder
- A fraction of what is left, using a new reference whole.
- Reasonableness
- Whether a result fits the quantities, units and expected size.
- Assumption
- A condition accepted when building a mathematical model.
Make it visible
Scale every ingredient together.
Predict a result, change a value, and use the diagram to explain your reasoning.
| Ingredient | Original: 4 servings | Your batch |
|---|
The recipe is an example for practising proportional scaling, not an assigned classroom project.
Draw and label before calculating
A bar model can distinguish the total, the part already used and the amount remaining. Write an expression with units beside the diagram. If the question asks for a number of portions, the answer counts portions rather than litres.
Watch when the reference whole changes
A hiker travels 2/5 of a route, then 1/3 of the remaining route. The second fraction is taken from 3/5 of the original route, so the second distance is 1/3 × 3/5 = 1/5 of the original. Altogether the hiker has completed 3/5, not 2/5 + 1/3.
Interpret the calculation, not just the digits
If 2 1/2 metres of ribbon is cut into 3/4-metre pieces, the quotient is 10/3 = 3 1/3. This means three complete pieces can be cut, with 1/4 metre left over. It does not mean a fourth full piece. For a capacity or budget, decide whether the context needs a whole-number answer.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
A batch needs 2 1/2 cups of oats. How much is needed for 3/4 of a batch?
- The relationship is a fraction of an amount: 3/4 × 5/2.
- Multiply: 15/8 = 1 7/8 cups.
- A three-quarter batch needs less than 2 1/2 cups. The unit remains cups.
A 3 1/2-litre jug fills 3/4-litre bottles. How many full bottles, and how much remains?
- Compute 7/2 ÷ 3/4 = 7/2 × 4/3 = 14/3 = 4 2/3.
- Four full bottles use 4 × 3/4 = 3 litres.
- The remaining liquid is 3 1/2 − 3 = 1/2 litre. This is 2/3 of the next bottle, not 2/3 litre.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
A cyclist finishes 1/4 of a route, then 2/3 of the remainder. What fraction of the original route is still left?
Give me a hint
The remainder after the first stage is 3/4 of the original route.
Compare a worked response
1/4
The second stage uses 2/3 × 3/4 = 1/2 of the original. Completed: 1/4 + 1/2 = 3/4, leaving 1/4.
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?
Cooking, sharing supplies and planning distances all require the same habit: identify the whole, keep units consistent and explain what the result allows you to do.