In a canteen fridge, the number of bottles of water to the number of cartons of milk is 3 : 4. The number of cartons of milk to the number of cans of juice is 6 : 5. There are 45 bottles of water in the fridge. How many drinks are there in the fridge altogether?
There are 155 drinks in the fridge.
Ans: 155
How to solve it
Write the two ratios one under the other, with the shared quantity, the milk, in the middle: 3 to 4 and 6 to 5.
Make the milk the same number in both. 4 and 6 both go into 12, the lowest common multiple.
Multiply the first line by 3 and the second line by 2: 9 to 12, and 12 to 10.
Join them on one line: water to milk to juice is 9 to 12 to 10.
Use what the question gives: 9 units is 45 bottles, so 1 unit is 5. All 31 units are 31 times 5, which is 155.
Make the milk the same number of units in both ratios. Then every unit means the same amount, and the three terms fit on one line.
Practice questions with worked solutions
Question 1 is free to try. The other 8 open in the free trial, each with its full working.
Question 1 of 9 · Basic · free to tryA stationery cupboard holds pens, markers and highlighters. The number of…A stationery cupboard holds…
A stationery cupboard holds pens, markers and highlighters. The number of pens to the number of markers is 3 : 2. The number of markers to the number of highlighters is 5 : 4. There are 45 pens in the cupboard. How many highlighters are there?
How do you combine two ratios with a common term in P6?
When a question gives A : B and B : C, the B is one quantity counted twice.
What your child learns here
When a question gives A : B and B : C, the B is one quantity counted twice. Your child learns to make it the same number in both ratios, using the lowest common multiple, before writing a single three-term ratio.
Write the two ratios one under the other, with the shared quantity in the same column.
Multiply each ratio so the shared term becomes the lowest common multiple of its two values.
Join them into one ratio of three terms, then use the value of 1 unit as usual.
Handle a shared term that is a group, such as two kinds counted together.
Does the answer make sense?
When the question links A to B and B to C, the shared quantity appears as one number in your child's joined ratio, and both of its given values must divide into it. An answer that is a fraction of everything, like the share of pegs that are green, must be less than 1.
How to practise these questions
The Basic questions train making the shared quantity equal in both ratios so that they combine. Intermediate questions add shared terms that must be built, ratios given as percentages, and three ratios at once. Challenge questions nest one group inside another, or link two money ratios. If two ratios refuse to join, read the written step-by-step solution together.
Questions parents ask
Does my child need bar models to combine two ratios? Not for the combining step. This page writes the ratios one under the other with the multipliers beside them, and draws bars only once a unit value is needed.
What is a common term in a ratio? It is the quantity that appears in both ratios, such as B in A : B and B : C. It is one quantity counted twice, so it must have the same number in both before the ratios can be joined.
Is a three-term ratio in the Primary 6 syllabus? Yes. The syllabus covers the notation and interpretation of a : b : c and finding the ratio of three given quantities. Combining two ratios through a shared term uses those outcomes together with equivalent ratios.
