The pattern
Dividing fractions
Share a fraction equally, or count how many small portions fit.
Juice split into cup-sized fractions asks how many cups fit inside the total, a dividing question even though the fraction looks like it should shrink the answer. Dividing by a fraction smaller than one whole can give an answer bigger than the starting amount, five cups from one litre if each cup holds a fifth. Sharing that fraction among several bottles instead grows the bottom number, so each bottle gets a smaller share.
How to spot it
A total amount split into fraction-sized cups or pieces, asking how many fit, points here. A single fraction shared equally among several parts does too.
Common mistake
Children expect dividing to make the answer smaller, so a bigger result than the starting amount looks wrong to them and they flip the calculation.
4 worked solutions
Standard
- 1/2 L shared among 4 bottles Share 1/2 L of juice equally among 4 bottles. How much juice goes in each bottle?
- 1/5 L shared among 3 bottles Share 1/5 L of juice equally among 3 bottles. How much juice goes in each bottle?
- 12 L measured in 1/2 L cups There are 12 L of juice. Each cup holds 1/2 L. How many full cups can be filled?
- 2 L measured in 1/5 L cups There are 2 L of juice. Each cup holds 1/5 L. How many full cups can be filled?
All the problem patterns → · the revision list
The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
A PDF, and a note when new solutions go up.