Primary 6 Ratio Study Guide
Primary 6 ratio in six steps: reading a ratio in order, sharing with units, then the before-and-after questions, two ratios joined by a shared quantity and the cost of a repeated set.
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What is a ratio in Primary 6?
A ratio compares two or three quantities, in order.
Every tray, Emma bakes 3 cupcakes and Jason bakes 2. The ratio of Emma's cupcakes to Jason's cupcakes is 3 : 2, read as 3 to 2. Emma is named first, so her number goes first. A ratio compares and does not count: after two trays they have 6 and 4 cupcakes, and the ratio is still 3 : 2. In a bar model, each number becomes that many equal units.
In this chapter, your child learns to:
- write a : b and a : b : c in the order the question names them;
- find equivalent ratios, simplest form and a missing number;
- share a quantity in a ratio, and read the same bar as a fraction;
- solve before-and-after questions by finding what stays unchanged;
- join two ratios with a shared quantity, and price a repeated set.
Step 1
Writing a ratio and equivalent ratios
Names in one order, numbers in the same order. Daniel runs 3 laps every morning and Rachel runs 2, so Daniel's laps to Rachel's laps is 3 : 2. Swap the names and the ratio is 2 : 3. Multiply both numbers by the same number, or divide both by the same number, and the ratio does not change. Simplest form uses the smallest whole numbers it can.
Tap Add a morning
A class has 15 boys and 21 girls. What is the ratio of the number of girls to the number of boys, in simplest form?
Step 2
Sharing in a ratio, and ratio as a fraction
Count every unit first. When Priya and Samuel share 45 beads in the ratio 2 : 3, the beads fill all 5 units, not just Samuel's 3. Find 1 unit, then multiply by the units you want. The same bar also gives a fraction: Samuel's 3 units out of 5 is 3/5 of the beads. A ratio compares one part with the other; a fraction compares one part with the whole.
Tap to count the units
Mei and Joe share 56 shells in the ratio 3 : 4. How many shells does Joe get?
Step 3
Before-and-after ratio questions
Find what stays unchanged. When an amount moves from one person to the other, the total stays the same: match the total units before and after. When the same amount is added to both, or removed from both, the difference stays the same. When only one quantity changes, the other stays the same: give it the same number of units in both ratios.
Pick a story, then tap
Chloe and Marcus had marbles in the ratio 7 : 3. Chloe gave Marcus 24 marbles, and then they had the same number each. How many marbles did Chloe have at first?
Jia Hui and Ken had stickers in the ratio 5 : 3. Each of them then bought 12 more stickers. What stays the same?
Step 4
Ratio questions where both quantities change
Cut the units smaller. A florist has roses and tulips in the ratio 3 : 2, and sells 2/9 of the roses and 1/4 of the tulips. Nothing stays the same, so there is nothing to match. Instead, cut every unit into equal small units until both fractions are whole numbers of them, then count from there.
Tap to cut the units
The number of roses to the number of tulips was 3 : 2. 2/9 of the roses and 1/4 of the tulips were sold. Then there were 55 more roses than tulips. How many roses were there at first?
The ratio of red beads to blue beads is 3 : 4. 1/2 of the red beads and 1/3 of the blue beads are used. Into how many small units should each unit be cut?
Step 5
Two ratios with a common term
Make the shared quantity the same number. Water to milk is 3 : 4, and milk to juice is 6 : 5. The milk is one quantity counted twice, as 4 and as 6. Write the ratios one under the other with the milk in the same column, multiply each up to the lowest common multiple, 12, and the three terms fit on one line.
Tap to match the milk
In a canteen fridge, water to milk is 3 : 4 and milk to juice is 6 : 5. There are 45 bottles of water. How many drinks are there altogether?
Apples to pears is 2 : 3, and pears to plums is 4 : 5. What is apples : pears : plums?
Step 6
Ratio and money word problems
Price one set, then count the sets. For every 4 curry puffs a stall sells, it sells 3 egg tarts, so every sale repeats the same set. The money does not split the way the items do, because the items have different prices. Find the cost of one set, divide the total money by it, then count the items asked for.
Tap to price the set
For every 4 curry puffs sold, 3 egg tarts are sold. A curry puff costs $2 and an egg tart costs $3. The stall collected $476. How many egg tarts did it sell?
For every 3 pens a shop sells, it sells 1 file. A pen costs $2 and a file costs $4. The shop collected $70. How many pens did it sell?
Primary 6 ratio questions, worked step by stepDraw the units on paper first. Then open the hint, or reveal the working one line at a time.
Farah and Gopal share 72 stamps in the ratio 5 : 3. How many more stamps does Farah get than Gopal?
- Total units = 5 + 3 = 8
- 8 units = 72, so 1 unit = 72 ÷ 8 = 9
- Farah has 5 minus 3 = 2 units more.
- 2 units = 2 × 9 = 18
In a choir, the ratio of the number of boys to the number of girls is 2 : 7. There are 35 girls. How many children are in the choir?
- 7 units = 35 girls.
- 1 unit = 35 ÷ 7 = 5 children.
- Whole choir = 2 + 7 = 9 units.
- 9 units = 9 × 5 = 45 children.
Wen Li and Hakim had stickers in the ratio 5 : 1. Wen Li gave Hakim 30 stickers. Then they had the same number of stickers. How many stickers did Hakim have at first?
- Total = 5 + 1 = 6 units, before and after.
- After: 6 units ÷ 2 = 3 units each.
- Wen Li gave 5 minus 3 = 2 units. 2 units = 30, so 1 unit = 30 ÷ 2 = 15
- Hakim at first = 1 unit = 15
Mrs Tan is 5 times as old as her daughter. In 8 years, she will be 3 times as old as her daughter. How old is Mrs Tan now?
- Now: daughter = 1 unit, Mrs Tan = 5 units. Difference = 4 units.
- In 8 years: daughter = 1 new block, Mrs Tan = 3 new blocks. Difference = 2 new blocks.
- 2 new blocks = 4 units, so 1 new block = 2 units.
- Daughter in 8 years: 2 units = 1 unit + 8, so 1 unit = 8
- Mrs Tan now = 5 × 8 = 40
The ratio of pens to pencils in a box is 2 : 5. The ratio of pencils to markers is 3 : 4. There are 28 more markers than pens. How many pencils are there?
- pens : pencils = 2 : 5 = 6 : 15 (× 3)
- pencils : markers = 3 : 4 = 15 : 20 (× 5)
- pens : pencils : markers = 6 : 15 : 20
- 20 minus 6 = 14 units = 28, so 1 unit = 28 ÷ 14 = 2
- pencils = 15 × 2 = 30
Step 7
Check yourself
Five ratio questions drawn from the steps above. Each reply explains the answer and names the set that practises it.
1. A tray holds 9 kaya buns and 6 cheese buns. What is the ratio of cheese buns to kaya buns, in simplest form?
2. Ravi and Siti share $90 in the ratio 4 : 5. How much does Siti get?
3. The ratio of red marbles to blue marbles is 2 : 7. What fraction of all the marbles are blue?
4. The ratio of oranges to apples in a basket was 3 : 4. After 15 more oranges were added, the ratio became 2 : 1. How many apples are there?
5. For every 3 notebooks a shop sells, it sells 2 files. A notebook costs $2 and a file costs $5. The shop collected $96. How many files did it sell?
Ask your child to draw the units before any number is worked out. Most ratio questions in this chapter open up once the bar is on paper: count the units, find 1 unit, then multiply. Before a before-and-after question, ask "what stays the same here?" and let your child answer before choosing a method.
Everyday sets make good practice: two scoops of rice for every three cups of water, or a recipe for four doubled to eight. Ask your child to say the ratio in order, give an equivalent one, then share a total in it. Try each worked example on paper before opening the working.
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