Share 30 sweets between two children in the ratio 2 : 3.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Count the parts
The bar has 2 parts for one child and 3 for the other, so 5 parts in all.
Find one part
5 parts make 30, so one part is 30 ÷ 5 = 6.
Then build each share
One child gets 2 parts, so 12. The other gets 3 parts, so 18. Together that is 30.
What a tape diagram shows
Draw one box for each part of the ratio: 3 boxes for red and 2 for blue. Every box is the same size, whatever that size turns out to be. The picture holds the relationship steady while you work out what one box is worth.
Find the value of one box
If a 3 : 2 mix makes 40 litres altogether, there are 5 boxes and 40 ÷ 5 = 8 litres per box. So red is 3 × 8 = 24 and blue is 2 × 8 = 16. Almost every ratio problem reduces to finding what one box is worth.
When the difference is given
If there are 12 more red than blue in a 3 : 2 mix, the difference is 1 box, so a box is 12. Red is 36 and blue is 24. The diagram tells you which quantity corresponds to the number you were given, which is what makes these problems tractable.
Check against the original ratio
Once you have both amounts, reduce them: 36 : 24 reduces to 3 : 2. If it does not match the ratio you were given, something went wrong. This check is quick and it verifies the answer rather than the arithmetic.
Step 2: Try It Yourself
Tap and try it out.
First share
12
6
Second share
18
18 is 6 more than 12.
Step 3: Watch an Example
One step at a time.
Watch Leo Share 40 in the Ratio 3 : 5
Leo shares 40 marbles in the ratio 3 : 5.
- Step 1
He counts the parts: 3 and 5 make 8 parts.
Step 4: Your Turn
Practice makes it stick.
The Sweets
Problem 1 of 3
Share 30 in the ratio 2 : 3. What is the smaller share?
The Money
Problem 2 of 3
Share 60 pounds in the ratio 1 : 5. What is the larger share?
pounds
The Difference
Problem 3 of 3
Share 45 in the ratio 4 : 5. How much bigger is the larger share?
Count the Parts
1 of 4
Share 24 in the ratio 1 : 2. What is the smaller share?
2 of 4
Share 35 in the ratio 2 : 5. What is the larger share?
3 of 4
Share 50 in the ratio 3 : 7. What is one part worth?
4 of 4
Share 36 in the ratio 4 : 5. What is the smaller share?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Share 48 in the ratio 1 : 3. What is the larger share?
Question 2 of 2
To share a total in a ratio, what do you find first?
What You Learned
- Draw the ratio as parts of a bar.
- Divide the total by the number of parts to find one part.
- Then build each share from the parts it has.