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Sharing in a Given Ratio

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Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

Sharing in a Given Ratio

Simon and Jenny share the bar of chocolate in the ratio 5 : 3. How many pieces do they each receive?

This means that for every 5 pieces that Simon gets, Jenny gets 3.

We could share the 24 pieces between them until we run out of chocolate.

9

15

Sharing in a Given Ratio

Use this method to share the bar of chocolate below between Snoopy and Hippo in the ratio 2 : 7. How many pieces do they each receive?

Sharing in a Given Ratio

Use this method to share the bar of chocolate below between Snoopy and Hippo in the ratio 2 : 7. How many pieces do they each receive?

Sharing in a Given Ratio

Use this method to share the bar of chocolate below between Snoopy and Hippo in the ratio 2 : 7. How many pieces do they each receive?

Sharing in a Given Ratio

Sharing in a Given Ratio

Sharing in a Given Ratio

Sharing In a Given Ratio

Sharing in a Given Ratio

Sharing in a Given Ratio

8

28

3

So Snoopy gets

of 80 = 48 pieces

5

2

Hippo gets

of 80 = 32 pieces

5

Sharing in a Given Ratio

Discuss the problem of using this method if Snoopy and Hippo had to share (the very nice) bar of chocolate below in the ratio 3 : 2.

5 x 16 = 80

So this method is not efficient when the quantity to be shared is large and/or the ratios are small. A more efficient method is desirable.

This can be achieved by considering what proportion/fraction of the whole bar they will each receive. In this example we can think of the bar as being divided into 5 parts.

Snoopy will get 3 out of 5 parts and Hippo will get 2 out 5 parts.

Check: 48 + 32 = 80

8 parts

2

5

3

Jenny gets

Hippo gets

of 56 = 16 discs

of £72 = £45

Simon gets

of £72 = £27

7

8

8

Example Question 2

Snoopy and Hippo share 56 coloured discs in the ratio of 5 : 2. How many do they each receive?

7 parts

5

Snoopy gets

of 56 = 40 discs

7

Sharing in a Given Ratio

Examples 1/2

Example Question 1

Simon and Jenny share £72 in the ratio of 3 : 5. How much do they each receive?

Check: 27 + 45 = 72

Check: 40 + 16 = 56

Sharing in a Given Ratio

Questions 1

1. Share £48 between Alan and Barbara in the ratio 2 : 1

£16

£32

2. Share £60 between Laura and Robert in the ratio 1 : 3

£45

£15

3. Share 80 marbles between Stuart and Carl in the ratio 4 : 1

64

16

4. Share 91 sweets between Peter and Becky in the ratio 4 : 3

52

39

5. Share 70 coloured beads between Janet and Christine in the ratio 3 : 2

42

28

6. Share £120 between Carly and Paul in the ratio 3 : 5

£45

£75

Sharing in a Given Ratio

Questions 2

1. Share 350 ml of milk between a cat and her kitten in the ratio 4 : 3

150 ml

200 ml

2. Share 1.2 litres of milk between a dog and a cat in the ratio 7 : 5

500 ml

700 ml

3. Share 240 g of sweets between Alison and Stephen in the ratio 3 : 5

150 g

90 g

4. Share 120 g of cereal between Stuart and Julie in the ratio 3 : 7

36 g

84 g

£2400

£3000

5. Paul is 12 and Gemma is 15. They share a £5400 inheritance from their aunty in the ratio of their ages. How much do they each receive?

£1275

£1445

6. John scored 15 points and Fiona scored 17 points in a TV quiz show. They shared the prize money of £2720 in ratio of points scored. How much did they each receive?

8 parts

4

3

1

Ollie gets

Prof gets

of 64 = 24 cubes

of 64 = 32 cubes

Jumbo gets

of 64 = 8 cubes

8

8

8

Sharing in a Given Ratio

Example Question 3

Ollie, Jumbo and Prof break the large cube into individual small cubes and share them in the ratio 3 : 1 : 4. How many does each receive?

Check: 24 + 8 + 32 = 64

20 parts

4

7

Snoopy gets

of 80 = 16 counters

Ollie gets

of 80 = 28 counters

20

20

3

6

Hippo gets

of 80 = 12 counters

Jumbo gets

of 80 = 24 counters

20

20

Sharing In a Given Ratio

Example Question 4

Snoopy, Ollie, Hippo and Jumbo share the coloured counters shown in the ratio 4 : 7 : 3 : 6. How many counters does each receive?

Check: 16 + 28 + 12 + 24 = 80

Sharing in a Given Ratio

Questions 3

1. Alan, Becky and Charlie share 72 sweets in the ratio 2 : 3 : 4. How many sweets do they each receive?

Alan gets 16 sweets

Becky gets 24 sweets

Charlie gets 32 sweets

2. Paula, Robert and Karl share £240 in the ratio 4 : 5 : 3. How much money do they each receive?

Paula gets £80

Robert gets £100

Karl gets £60

3. A piece of wood 2.8 m long, is cut into 3 pieces in the ratio 4 : 3 : 7. Find the length of each piece.

Piece 1 = 80 cm

Piece 2 = 60 cm

Piece 3 = 140 cm

4. A metal alloy block of mass 56 kg consists of copper, zinc and tin in the ratio 4 : 3 : 1. Find the mass of each metal.

Copper = 28 kg

Zinc = 21 kg

Tin = 7 kg

5. Jack, Jenny, Paul and Kate share 720 marbles in the ratio 2 : 9 : 4 : 3. How much does each receive?

Kate gets 120

Jack gets 80

Jenny gets 360

Paul gets 160

Sharing in a Given Ratio

Questions 1

1. Share £48 between Alan and Barbara in the ratio 2 : 1

2. Share £60 between Laura and Robert in the ratio 1 : 3

3. Share 80 marbles between Stuart and Carl in the ratio 4 : 1

4. Share 91 sweets between Peter and Becky in the ratio 4 : 3

5. Share 70 coloured beads between Janet and Christine in the ratio 3 : 2

6. Share £120 between Carly and Paul in the ratio 3 : 5

Sharing in a Given Ratio

Questions 2

1. Share 350 ml of milk between a cat and her kitten in the ratio 4 : 3

2. Share 1.2 litres of milk between a dog and a cat in the ratio 7 : 5

3. Share 240 g of sweets between Alison and Stephen in the ratio 3 : 5

4. Share 120 g of cereal between Stuart and Julie in the ratio 3 : 7

5. Paul is 12 and Gemma is 15. They share a £5400 inheritance from their aunty in the ratio of their ages. How much do they each receive?

6. John scored 15 points and Fiona scored 17 points in a TV quiz show. They shared the prize money of £2720 in ratio of points scored. How much did they each receive?

Sharing in a Given Ratio

Questions 3

1. Alan, Becky and Charlie share 72 sweets in the ratio 2 : 3 : 4. How many sweets do they each receive?

2. Paula, Robert and Karl share £240 in the ratio 4 : 5 : 3. How much money do they each receive?

3. A piece of wood 2.8 m long, is cut into 3 pieces in the ratio 4 : 3 : 7. Find the length of each piece.

4. A metal alloy block of mass 56 kg consists of copper, zinc and tin in the ratio 4 : 3 : 1. Find the mass of each metal.

5. Jack, Jenny, Paul and Kate share 720 marbles in the ratio 2 : 9 : 4 : 3. How much does each receive?