Ratios Changing Demonstration This resource provides animated demonstrations

Ratios – Changing – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

Hannah & Mike share some sweets in the ratio 3 : 4 Mike eats 4 sweets. The sweets are now in the ratio 9 : 10 How many sweets did Mike start with? Then 3 : 4 6 : 8 9 : 12 12 : 15 15 : 20 18 : 24 21 : 28 Now − 4 from Mike’s share Find the ratio that is equivalent to 9 : 10 Is there a quicker method to scale up? 3 : 0 6 : 4 9 : 8 12 : 11 15 : 16 18 : 20 21 : 24

Changing Ratios: Scaling Jess & Andy share some money in the ratio 1 : 2 Andy spends £ 2. The money is now in the ratio 3 : 4 DEMO How much money did Andy start with? We know Jess’s money has not changed. Then Now 1 : 2 3 : 4 × 3 3 : 6 3 : 4 − 2 Andy started with £ 6.

Changing Ratios: Scaling Hannah & Mike share some sweets in the ratio 2 : 3 Mike eats 3 sweets. The sweets are now in the ratio 7 : 9 DEMO How many sweets did Mike start with? We know Hannah’s amount of sweets has not changed. Then Now 2 : 3 7 : 9 × 7 × 2 14 : 21 14 : 18 − 3 Mike started with 21 sweets.

Changing Ratios: Scaling In a university class boys and girls are in the ratio 2 : 3 3 girls leave the class. The boys and girls are now in the ratio 3 : 4 DEMO How many girls are there now? We know the amount of boys has not changed. Then Now 2 : 3 3 : 4 × 3 6 : 9 × 2 6 : 8 × 3 18 : 27 18 : 24 − 1 − 3 There are 24 girls now.

Changing Ratios: Scaling In a bag there are red and blue disks in the ratio 3 : 4 2 blue disks are removed. The disks are now in the ratio 4 : 5 DEMO How many blue disks are there now? We know the amount of red disks has not changed. Then Now 3 : 4 4 : 5 × 4 × 3 12 : 16 12 : 15 × 2 24 : 32 24 : 30 − 1 − 2 There are 30 blue disks now.

Changing Ratios: Scaling YOUR TURN In a bag there are red and blue disks In a class there are boys and girls in the ratio 3 : 4 in the ratio 1 : 3 2 blue disks are removed. 5 girls leave the class. The disks are now in the ratio 4 : 5 The students are now in the ratio 2 : 5 DEMO How many blue disks are there now? How many girls are there now? We know the amount of red disks has not changed. Then Now 3 : 4 4 : 5 1 : 3 2 : 5 × 4 × 3 12 : 16 12 : 15 × 2 24 : 32 24 : 30 × 2 − 1 − 2 There are 30 blue disks now. 2 : 6 2 : 5 × 5 10 : 30 10 : 25 − 1 − 5 There are 25 girls now.

Changing Ratios: Scaling YOUR TURN In a bag there are red and blue disks Sam and Mike share some money in the ratio 3 : 4 in the ratio 3 : 5 2 blue disks are removed. Mike spends £ 10. The disks are now in the ratio 4 : 5 The money is now in the ratio 4 : 5 DEMO How many blue disks are there now? How much money did they start with? We know the amount of red disks has not changed. Then Now 3 : 4 4 : 5 3 : 5 4 : 5 × 4 × 3 12 : 16 12 : 15 × 2 24 : 32 24 : 30 − 1 − 2 There are 30 blue disks now. × 4 × 3 12 : 20 12 : 15 × 2 24 : 40 24 : 30 − 5 − 10 They started with £ 64.

Changing Ratios: Scaling YOUR TURN In a bag there are red and blue disks in the ratio 3 : 4 in the ratio 5 : 6 2 blue disks are removed. 21 red disks are removed. The disks are now in the ratio 4 : 5 The disks are now in the ratio 3 : 5 DEMO How many blue disks are there now? How many disks are there now? We know the amount of red disks has not changed. Then Now 3 : 4 4 : 5 5 : 6 3 : 5 × 4 × 3 12 : 16 12 : 15 × 2 24 : 32 24 : 30 − 1 − 2 There are 30 blue disks now. × 5 × 6 25 : 30 18 : 30 × 3 75 : 90 54 : 90 − 7 − 21 There are now 144 disks.

Changing Ratios: Scaling YOUR TURN In a bag there are red and blue disks in the ratio 3 : 4 in the ratio 2 : 3 2 blue disks are removed. The disks are now in the ratio 4 : 5 DEMO How many blue disks are there now? We know the amount of red disks has not changed. Then Now 3 : 4 4 : 5 × 4 × 3 12 : 16 12 : 15 × 2 24 : 32 24 : 30 How many blue disks are there now? In a year the boys and girls are in the ratio 3 : 4 4 boys join the year. The class is now in the ratio 5 : 6 How many boys are there now? − 1 − 2 There are 30 blue disks now. Jack shares money with his friend in the ratio 3 : 8 His friend already has £ 15. The total money is in the ratio 2 : 7 How much money did Jack give his friend?

Changing Ratios: Scaling YOUR TURN In a bag there are red and blue disks in the ratio 3 : 4 in the ratio 2 : 3 2 blue disks are removed. The disks are now in the ratio 4 : 5 DEMO How many blue disks are there now? We know the amount of red disks has not changed. Then Now 3 : 4 4 : 5 × 4 × 3 12 : 16 12 : 15 × 2 24 : 32 24 : 30 How many blue disks are there now? 10 In a year the boys and girls are in the ratio 3 : 4 4 boys join the year. The class is now in the ratio 5 : 6 How many boys are there now? 40 − 1 − 2 There are 30 blue disks now. Jack shares money with his friend in the ratio 3 : 8 £ 48 His friend already has £ 15. The total money is in the ratio 2 : 7 How much money did Jack give his friend?

When we have equal ratios we can manipulate them to create an equation. 1 : 3 = 3 : 9 = = = 2 : 3 = 4 : 7 =

Hannah & Mike share some sweets in the ratio 2 : 5 Can Mike have 13 sweets? Why not? Express the ratio algebraically. If Mike eats 3 sweets, express the changed ratio algebraically. If Hannah gives Mike 4 sweets, express the changed ratio algebraically.

Changing Ratios: Algebraic In a bag there are red and blue disks in the ratio 1 : 2 2 blue disks are removed. The disks are now in the ratio 3 : 5 DEMO How many blue disks were there to start with? Express the changed ratio algebraically. Create an equation and solve. There were 12 blue disks to start with.

Changing Ratios: Algebraic May and Mark shared some money in the ratio 2 : 3 Mark spent £ 3. The money is now in the ratio 5 : 6 DEMO How much money was there to start with? Express the changed ratio algebraically. Create an equation and solve. There was £ 25 to start with.

Changing Ratios: Algebraic Andy and Alex shared some sweets in the ratio 2 : 3 Andy gave Alex 4 sweets. The sweets are now in the ratio 1 : 4 DEMO How many sweets were there to start with? Express the changed ratio algebraically. Create an equation and solve. There was 20 sweets to start with.

Changing Ratios: Algebraic Tom has £ 10. Alex has £ 5. Tom saves £ 2 a week. Alex saves £ 5 a week. DEMO How many weeks will it take for them to have savings in the ratio 4 : 5 ? Create an equation and solve. It will take 3 weeks.

Changing Ratios: Algebraic YOUR TURN Andy and Alex shared some sweets Sophie and Max shared some money in the ratio 2 : 3 in the ratio 1 : 3 Andy gave Alex 4 sweets. Sophie gave Max £ 3. The sweets are now in the ratio 1 : 4 The money is now in the ratio 1 : 9 DEMO How many sweets were there to start with? How much money did Max start with? Express the changed ratio algebraically. Create an equation and solve. There was 20 sweets to start with. Max started with £ 15.

Changing Ratios: Algebraic YOUR TURN Andy and Alex shared some sweets There are white and black cubes in a box in the ratio 2 : 3 in the ratio 2 : 5 Andy gave Alex 4 sweets. 5 white cubes are replaced with 5 black cubes. The sweets are now in the ratio 1 : 4 The cubes are now in the ratio 1 : 5 DEMO How many sweets were there to start with? How many black cubes are there now? Express the changed ratio algebraically. Create an equation and solve. There was 20 sweets to start with. There are 45 black cubes now.

Changing Ratios: Algebraic YOUR TURN Tom has £ 10. Alex has £ 5. Jack has £ 15. Sal has £ 5. Tom saves £ 2 a week. Jack saves £ 3 a week. Alex saves £ 5 a week. Sal saves £ 4 a week. DEMO How many weeks will it take for them to have savings in the ratio 4 : 5 ? How many weeks will it take for them to have savings in the ratio 6 : 5 ? Create an equation and solve. It will take 3 weeks. It will take 5 weeks.

Changing Ratios: Algebraic YOUR TURN Andy and Alex shared some sweets There are black and green disks in a bag in the ratio 2 : 3 in the ratio 2 : 5 Andy gave Alex 4 sweets. 2 black disks are added. The sweets are now in the ratio 1 : 4 The disks are now in the ratio 1 : 2 DEMO How many sweets were there to start with? How many black disks are there now? Express the changed ratio algebraically. Create an equation and solve. Jess and Tony shared some money in the ratio 3 : 4 Jess gave Tony £ 5. The money is now in the ratio 2 : 3 How much money did Jess have? Seb has £ 6. Minnie has £ 10. Seb saves £ 3 a week. Minnie saves £ 8 a week. There was 20 sweets to start with. How many weeks until their savings are in the ratio 3 : 7 ?

Changing Ratios: Algebraic YOUR TURN Andy and Alex shared some sweets There are black and green disks in a bag in the ratio 2 : 3 in the ratio 2 : 5 Andy gave Alex 4 sweets. 2 black disks are added. The sweets are now in the ratio 1 : 4 The disks are now in the ratio 1 : 2 DEMO How many sweets were there to start with? How many black disks are there now? 10 Express the changed ratio algebraically. Create an equation and solve. Jess and Tony shared some money in the ratio 3 : 4 Jess gave Tony £ 5. The money is now in the ratio 2 : 3 How much money did Jess have? £ 75 There was 20 sweets to start with. 4 weeks Seb has £ 6. Minnie has £ 10. Seb saves £ 3 a week. Minnie saves £ 8 a week. How many weeks until their savings are in the ratio 3 : 7 ?

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