--- title: "Sharing in a ratio" subtitle: "Number Foundations · Ratios · Lesson 22" --- # Sharing in a ratio **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Ana and Ben earn $60 washing cars. Ana did 2 cars, Ben did 3. They agree to share the money in that ratio. How much does each get? :::teacher-note **In one sentence:** Students share a total in a given ratio by cutting it into equal parts (add the parts, find one part, multiply), with two and three people, and work backwards from a share to the total (AC9M7N08, node 3). **Students should be able to say:** I can share an amount in a given ratio, with two or three people. I can find the total number of parts and the value of one part. I can work backwards from one share to the other share or the total. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Should Ben get more or less than half of the money? :::keep-together **$60 is shared between Ana and Ben in the ratio $2 : 3$. How much does Ben get?** ☐ $30 ☐ $24 ☐ $36 ☐ $20 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** $36. There are 2 + 3 = 5 parts, each $12, and Ben has 3 parts. $30 is an equal split; $24 is Ana's share. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Parts first :::keep-together ### One part Here is the whole routine for $60 in the ratio 2 : 3. 1. $2 + 3 = 5$ — Add the parts of the ratio. 2. $\$60 \div 5 = \$12$ — One part is the total divided by the number of parts. 3. $\text{Ana: } 2 \times \$12 = \$24$ — Each share is its number of parts times one part. 4. $\text{Ben: } 3 \times \$12 = \$36$ — Ben has 3 parts. 5. $\$24 + \$36 = \$60$ — Check that the shares add back to the total. Now try one: $40 in the ratio 1 : 3. **$40 is shared in the ratio $1 : 3$. How much is one part, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 10 1 + 3 = 4 parts. $40 ÷ 4 = $10 for one part. ::: :::keep-together ### Find the mistake **Dee shares $60 between Ana and Ben in the ratio 2 : 3. Click the line where her working goes wrong.** ``` 1 Share $60 between Ana and Ben in the ratio 2 : 3. 2 Ana: 60 ÷ 2 = $30 3 Ben: 60 ÷ 3 = $20 4 Check: 30 + 20 = $50, near enough to 60. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: dividing $60 by Ana's 2 does not give her share. First add the parts (2 + 3 = 5), find one part ($12), then Ana has 2 × $12 = $24. The check on line 4 shows the shares do not add to $60. ::: :::keep-together ### The bigger share **35 stickers are shared in the ratio $3 : 4$. How many stickers are in the bigger share?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 20 3 + 4 = 7 parts. 35 ÷ 7 = 5 stickers a part. The bigger share is 4 × 5 = 20. ::: :::typical ## Three people, and working backwards **Three shares.** **Work backwards.** **The whole amount.** **A mortar mix.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Sharing in a ratio :::keep-together ### The bigger share **$72 is shared in the ratio $5 : 4$. What is the bigger share, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 40 5 + 4 = 9 parts. 72 ÷ 9 = 8. The bigger share is 5 × 8 = 40. ::: :::keep-together ### The smaller share **45 marbles are shared in the ratio $2 : 3$. How many are in the smaller share?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 18 2 + 3 = 5 parts. 45 ÷ 5 = 9. The smaller share is 2 × 9 = 18. ::: :::keep-together ### Three people **$120 is shared among three people in the ratio $1 : 2 : 3$. What is the largest share, in dollars?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 60 1 + 2 + 3 = 6 parts. 120 ÷ 6 = 20. The largest has 3 parts: 60. ::: :::keep-together ### Review: simplest form **Review: simplify $18 : 24$. It is $3 : ?$** Answer: {{field-15}} ::: :::teacher-note **Answer:** 4 Divide both by 6: 3 : 4. ::: ## Make: exactly $15 Then find two different ratios (with their totals) that give the same share. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Share $84 between Sam and Tia in the ratio 3 : 4. How much does Tia get?** {{lines-3}} ::: :::teacher-note **Answer:** 3 + 4 = 7 parts. 84 ÷ 7 = 12. Tia has 4 parts: $48. :::