2
Sharing an amount in a given ratio: two and three parts
Mathematics Prep 1 Term 1, Unit 1, Lesson 2
GoalShare an amount in a ratio of two or three parts, and share a profit by the partners’ capital.
New words
share · the part of the whole that one person getsproportional division · sharing an amount in a given ratiocapital · the money a partner puts into a businessprofit · the money left after the costs are paid
Explanation
To share an amount in the ratio 4 : 5, add the parts: 4 + 5 = 9 equal parts. Divide the amount by 9 to find the value of one part, then multiply by 4 and by 5. The first share is 4/9 of the whole and the second is 5/9, so the shares always add up to the whole amount. With three parts such as 2 : 3 : 4 the method is the same: add 2 + 3 + 4 = 9 parts. Partners share a profit in the ratio of their capital. First simplify the ratio by dividing by a common factor, for example 30,000 : 50,000 = 3 : 5.
★Remember
Add the parts, divide the amount by the number of parts, then multiply by each part.
Worked examples
Mona and Karim share 720 LE in the ratio 4 : 5. Parts: 4 + 5 = 9. One part: 720 ÷ 9 = 80 LE. Mona gets 4 × 80 = 320 LE and Karim gets 5 × 80 = 400 LE. Check: 320 + 400 = 720.
Three friends share 450 LE in the ratio 2 : 3 : 4. Parts: 2 + 3 + 4 = 9. One part: 450 ÷ 9 = 50 LE. The shares are 2 × 50 = 100 LE, 3 × 50 = 150 LE and 4 × 50 = 200 LE. Check: 100 + 150 + 200 = 450.
Two partners put in 30,000 LE and 50,000 LE. The profit is 12,000 LE. Simplify the capital ratio: 30,000 : 50,000 = 3 : 5. Parts: 3 + 5 = 8. One part: 12,000 ÷ 8 = 1,500 LE. The first partner gets 3 × 1,500 = 4,500 LE and the second gets 5 × 1,500 = 7,500 LE.
Class activity
Share the sweets. With a grown-up, take 20 small objects (beans or buttons) and share them in the ratio 1 : 3 between two cups. How many go in each cup? Then try 2 : 3 : 5 with 30 objects.
Practice
1
Share 560 LE in the ratio 3 : 4.
7 parts, one part 80 LE. Shares: 240 LE and 320 LE.
2
A painter mixes red and white paint in the ratio 2 : 5 to make 21 L. How much of each?
7 parts, one part 3 L. Red 6 L and white 15 L.
3
Three children share 90 stickers in the ratio 1 : 2 : 3. How many does each get?
6 parts, one part 15. Shares: 15, 30 and 45 stickers.
4
Two partners put in 20,000 LE and 30,000 LE. They make a profit of 15,000 LE. Share it.
20,000 : 30,000 = 2 : 3. Parts: 5, one part 3,000 LE. Shares: 6,000 LE and 9,000 LE.
5
Hana shares 900 LE in the ratio 2 : 3 by working out 900 ÷ 2 and 900 ÷ 3. What is wrong? Find the shares.
She did not add the parts. 2 + 3 = 5 parts, one part 180 LE. Shares: 360 LE and 540 LE.