Dividing in a ratio
Share a quantity between two or three people in a given ratio; find a share when another is known; find the original total from one share and the ratio.
Worked examples
Dividing a quantity in a two-part ratio
Straightforward
Problem
Divide $150 in the ratio .
1
Find the total number of parts.
parts
2
Find the value of one part.
3
Calculate each share.
First share: \\ Second share:
4
Check: the shares should add to the total.
✓
Answer
The shares are $60 and $90.
Dividing a quantity in a three-part ratio
Moderate
Problem
Three friends share 360 stickers in the ratio . Find each person's share.
1
Find the total number of parts.
parts
2
Find the value of one part.
stickers
3
Calculate each share.
First friend: stickers \\ Second friend: stickers \\ Third friend: stickers
4
Check: the shares should add to the total.
✓
Answer
The three friends receive 60, 90 and 210 stickers.
Finding the total from one share
Challenging
Problem
Sarah and Tom share some money in the ratio . Tom receives $120. Find the total amount shared.
1
Identify how many parts Tom has, and use this to find the value of one part.
Tom has 8 parts \\ One part
2
Find Sarah's share.
Sarah has 3 parts
3
Find the total number of parts and calculate the total.
Total parts: \\ Total amount:
4
Check: Sarah's and Tom's shares should add to the total.
✓
Answer
The total amount shared is $165.
Practise
Q1·Straightforward
Divide $120 in the ratio . What is the larger share?
Explanation
Total parts: . Value of one part: . Larger share: .
Q2·Straightforward
40 marbles are shared in the ratio . How many marbles does the person with the larger share receive?
Explanation
Total parts: . Value of one part: . Larger share: marbles.
Q3·Straightforward
Divide 60 in the ratio . What is the smaller share?
Explanation
Total parts: . Value of one part: . Smaller share: .
Q4·Straightforward
Alice and Bob share $200 in the ratio . How much does Alice receive?
Explanation
Total parts: . Value of one part: . Alice's share: .
Q5·Moderate
$300 is divided among three people in the ratio . Find the smallest share.
Explanation
Total parts: . Value of one part: . Smallest share: .
Q6·Moderate
Three friends share 240 stamps in the ratio . Find the middle share.
Explanation
Total parts: . Value of one part: . Middle share: stamps.
Q7·Moderate
Maria and Jian share some money in the ratio . Maria receives $36. How much does Jian receive?
Explanation
Maria has 3 parts , so one part . Jian has 5 parts .
Q8·Moderate
Two containers hold water in the ratio . The smaller container holds 24 litres. How many litres are in the larger container?
Explanation
Smaller container has 4 parts L, so one part L. Larger container: L.
Q9·Challenging
Ben and Chloe share some money in the ratio . Ben receives $84. What is the total amount shared?
Explanation
Ben has 2 parts , so one part . Total parts: . Total amount: .
Q10·Challenging
Three workers share prize money in the ratio . The largest share is $280. What is the total prize money?
Explanation
Largest share has 7 parts , so one part . Total parts: . Total prize: .
Q11·Challenging
A recipe uses flour, sugar and butter in the ratio . A baker uses 280 g of flour. How many grams of sugar does the baker need?
Explanation
Flour has 4 parts g, so one part g. Sugar has 2 parts g.
Q12·Challenging
A fundraiser divides money among three causes in the ratio . The middle cause receives $360. How much more does the largest cause receive than the smallest cause?
Explanation
Middle cause has 3 parts , so one part . Largest cause: . Smallest cause: . Difference: .