A bag contains 8 blue and 12 gold counters. Write blue : gold and blue : total.
- Blue : gold = 8 : 12 = 2 : 3.
- Total = 8 + 12 = 20 counters.
- Blue : total = 8 : 20 = 2 : 5; 2/5 of the counters are blue.
Understanding ratios
Name the quantities. Keep their order.
A ratio compares quantities
A ratio of 2 blue counters to 3 gold counters means 2 blue for every 3 gold. Write blue : gold = 2 : 3. Order matters: gold : blue is 3 : 2. A ratio is a relationship, not necessarily the actual count.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
Part-to-part and part-to-whole tell different stories
There are 5 counters altogether. Blue : gold is 2 : 3, while blue : total is 2 : 5. The fraction of counters that are blue is 2/5, not 2/3. State what each term measures.
Compare like measurements fairly
Before comparing lengths as a same-unit ratio, convert them to the same unit. A comparison of 2 m to 50 cm is 200 : 50 = 4 : 1. Different-unit comparisons can instead be written as rates.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
Khan AcademyWatch · pause · explain
Intro to ratios
Explain why reversing the named quantities reverses the ratio.
Open on YouTube →Worked examples
Compare 1.5 m of ribbon with 60 cm.
- Convert 1.5 m to 150 cm.
- 150 : 60 = 5 : 2, dividing both terms by 30.
- The first ribbon is 2.5 times as long.
Try it before checking.
There are 6 red and 9 green tiles. What fraction are red?
A first hint
Find the total before forming the fraction.
Compare your reasoning
6/(6 + 9) = 6/15 = 2/5.
Practise the skill.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Explain a little more.
How can 2 : 3 describe both 5 counters and 50 counters? Explain with a diagram.
Use this thinking in the If… project →