How many 1/4-litre portions fit into 3/2 litres?
Give me a hint
Use quarters to count the groups.
Compare a worked response
6 portions
3/2 L = 6/4 L, which contains six quarter-litre portions.
Divide fractions & mixed numbers
Ask how many groups fit—or how large each share is—before using a reciprocal.
Your learning goal
Model fraction division, explain the reciprocal rule and solve problems involving mixed or whole numbers.
Understand the idea
Division can count groups
3/4 ÷ 1/8 asks how many one-eighth groups fit into three quarters. Rename 3/4 as 6/8. Six groups of 1/8 fit, so the quotient is 6. The answer counts groups, not eighths of the original whole.
Words worth knowing
- Dividend
- The starting amount being divided.
- Divisor
- The amount used to divide; it cannot be zero.
- Quotient
- The result of division.
- Reciprocal
- The number that multiplies a non-zero number to give 1; the reciprocal of a/b is b/a when a is non-zero.
Make it visible
How many groups fit?
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.
A quotient can include part of a group
1 ÷ 2/3 = 1 1/2. One complete group of 2/3 fits into 1, leaving 1/3. That remaining third is half of a two-thirds group. The fractional part of the quotient refers to the group size, not the original whole.
Equal units explain the reciprocal
For 3/4 ÷ 2/3, rename in twelfths: (9/12) ÷ (8/12) = 9 ÷ 8 = 9/8. In general, (a/b) ÷ (c/d) = (ad)/(bc) = (a/b) × (d/c). Multiplying by the reciprocal of the divisor is a consequence of counting common units. The divisor must be non-zero.
Khan AcademyWatch · pause · explain
Understanding division of fractions
Pause before the next step. Explain what the shaded region or group represents, then compare it with the model above.
Open on YouTube →The player loads when you choose to watch. Captions and availability depend on the provider.Convert, keep the order, then check
Convert mixed numbers to improper fractions. Leave the dividend unchanged, multiply by the reciprocal of the divisor, then simplify. To check, multiply quotient × divisor; it should recover the dividend. For positive numbers, dividing by a value less than 1 increases the numerical result.
Follow the reasoning
One decision at a time.
Work out the next step before opening the explanation.
Calculate 2/3 ÷ 1/6
- Rename 2/3 as 4/6. Four one-sixth groups fit.
- The reciprocal method agrees: 2/3 × 6/1 = 12/3 = 4.
- Check: 4 × 1/6 = 4/6 = 2/3.
Calculate 2 1/4 ÷ 1 1/2
- Convert: 9/4 ÷ 3/2.
- Multiply by the reciprocal of the divisor: 9/4 × 2/3 = 18/12 = 3/2.
- The answer is 1 1/2 groups. Check: 3/2 × 3/2 = 9/4.
Try with support
Make your thinking visible.
Use paper or a whiteboard. Show the equal parts, calculation and explanation before comparing your response.
Calculate 4/5 ÷ 2.
Give me a hint
Write the whole-number divisor as 2/1 before finding its reciprocal.
Compare a worked response
2/5
4/5 × 1/2 = 4/10 = 2/5. Splitting the amount into two equal shares halves it.
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 2 1/4-metre ribbon cut into 3/4-metre lengths makes three complete lengths. Division counts how many of the specified size fit.