Logic Masters · Ages 11 to 12
Sharing in a Ratio Word Problems
Divide amounts in a given ratio. Five levels of printable word problems with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Sharing in a Ratio Word Problems
Sharing in a ratio is where a lot of pupils first meet the idea that division does not always mean into equal parts. The method is short — add the parts, divide to find one part, multiply back up — and the mistakes are almost always in the first step, dividing by one of the numbers in the ratio rather than by their sum. These problems give that method somewhere to be practised in context. Each question names the people, states the total and gives the ratio, then asks for one named share, so there is never any ambiguity about which quantity the answer refers to. The totals are built from the ratio rather than picked and then divided, which means every share is a whole number: no half a sweet, no third of a person, and no question that is arithmetically survivable but semantically nonsense. Two-part ratios come first and three-part ratios appear at the higher levels, with totals growing throughout. Each question has ruled working space beneath it, because the intermediate step is where the marks are. Each level prints as a clean A4 sheet and downloads with its own separate answer key. Its on-screen twin is Ratio Divide Share Sim.
Common questions
- Can a share come out as a fraction?
- No. Totals are built from the ratio, so every share is a whole number.
- What is the most common mistake?
- Dividing by one of the numbers in the ratio instead of by their sum. The working space is there for that first step.
- When do three-part ratios appear?
- From the fourth level, once two-part sharing is secure.
- Is it always clear whose share is wanted?
- Yes. Each question names one person and asks for their share specifically.
A hand for grown-ups
- Before you start
- Something you can cut or fold helps enormously — paper, fruit, a sandwich. A half you can see beats a half you are told about.
- While they work
- Keep coming back to "equal parts". A shape split into unequal bits is the classic fractions trap.
- Afterwards
- Fold a piece of paper into halves, then quarters, together. Watching the pieces double is a lightbulb moment for many children.
- Watch out for
- Thinking a bigger bottom number means a bigger fraction (that 1/8 > 1/4). Cutting a real thing into 8 vs 4 pieces settles it fast.
- Away from the screen
- Cut food into equal parts at mealtimes. Fold paper. Talk about "half" and "quarter" of everyday things.
Where to go next
Chosen by the skills this activity practises.