Ratio and rate
Compare amounts, share in a ratio and find the best buy. Read one step, play with it, then tap “I understand this”.
What is a ratio?
A ratio compares two amounts: 4 yellow and 6 blue beads is a ratio of 4 : 6 (read “4 to 6”). The order matters.
The bead ratio
Change the number of yellow and blue beads.
Equivalent ratios and simplifying
Just like fractions, you can multiply or divide both sides of a ratio by the same number: 4 : 6 = 2 : 3 = 8 : 12.
Simplify by dividing both sides by their highest common factor.
4 : 6 and 2 : 3 describe the same mix: for every 2 yellow there are 3 blue. You have just put the beads into smaller groups.
Sharing in a ratio
To share R60 in the ratio 2 : 3:
- Add the parts: 2 + 3 = 5.
- Find one part: R60 ÷ 5 = R12.
- Multiply: A gets 2 × R12 = R24, B gets 3 × R12 = R36.
The sharing strip
Change the amount and the ratio.
Do not split R60 into 2 and 3! 2 : 3 means 5 equal parts, not 2 rand and 3 rand.
2 : 3 means: every time A gets 2, B gets 3. So every “round” you hand out 5. How many rounds fit into R60? R60 ÷ 5 = 12 rounds.
Rate: per unit
A rate compares two different things: km per hour (speed), rand per kilogram (price). To find the best buy, compare the price for the same amount.
The best buy
Which pack is cheaper for the same amount?
Correct: 0
The bigger pack is not always the cheapest. Always work out the price per 100 g or per 1 ℓ.
Check yourself
- A ratio compares two amounts; the order matters: 2 : 3 is not 3 : 2.
- Simplify: divide both sides by the HCF.
- Share in 2 : 3: add the parts (5), find one part, multiply.
- A rate is per unit: R per kg, km per hour. Compare for the best buy.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 4 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers9 pages · PDFPaperMemo
Ready for more? The Grade 7 ratio quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Compare prices on the shelf together: “Is the 1 kg bag or the two 500 g bags cheaper?” That is rate in real life.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.