MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Simplifying Ratios Ratio Calculations Ratio & Proportion Direct Proportion

MNU 3-08aMNU 4-08a

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Simplifying Ratios

Ratio Calculations

Ratio & Ratio & ProportionProportion

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Direct Proportion

Graph of Direct Proportion

Inverse Proportion

Proportional Division

Proportion

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Starter QuestionsStarter Questionsw

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2. Calculate 20% of 220

(a) 123 (b) 202 (c) 0.09

1. 3x + 5 = 17

3. How many significant numbers

4. Car depreciates by 20% in its first year. I f it was bought new for £10 000. How much is it worth now.

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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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1.1. Understand the term ratio. Understand the term ratio. ..

1. We are learning what a ratio is and explain how we can sometimes simplify them.


2.2. Calculate and simplify Calculate and simplify basic ratios showing basic ratios showing appropriate working.appropriate working.

What is a ratio ?


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Ratios can be used to compare different quantitiesRatios can be used to compare different quantities

What is a ratio ?

Example : There are 2 triangles and 3 rectangles.

The ratio of triangles to rectangles is said to be 2 : 3

Note: The ratio of rectangles to triangles is said to be 3 : 2

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Simplifying a ratio is like simplifying fractionsSimplifying a ratio is like simplifying fractions

Simplifying a ratio ?

Fraction :÷2

÷2

6 6 3= =

8 8 4

Ratio : ÷2 ÷26 : 8 = 6 : 8 = 3 : 4

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Sometimes we need to multiply to simplifySometimes we need to multiply to simplify


Ratio :1 : 5 =

31

×3 : 5×3 = 3

1 : 15

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When working with ratios, When working with ratios, the two units the two units MUSTMUST be the same be the same


Ratio :1 hour : 40 minutes

4

= 15 minutes : 40 minutes

= 3 minutes : 8 minutes

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Now try Exercise 1&2

Ch41 (page 158)

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Ratio & Ratio & ProportionProportionSimplifying a ratio ?

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2. Calculate the area of the shape.

3 2+4 3

(a) 0.13 (b) 0.02 (c) 1.09

1. 3x + 5 = 17

3. How many significant numbers

4.

9

6

8

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1.1. Remember and apply Remember and apply tabular method to work tabular method to work out ratios.out ratios.

1 We are learning to do ratio calculations.


2.2. Show appropriate Show appropriate working.working.

Ratio Calculations


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Ratio & Ratio & ProportionProportionRatio Calculations

Example : The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there.

boys girls

4 5

16 20x 4 x 4

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Ratio & Ratio & ProportionProportionRatio Calculations

Example : The ratio of cars to buses is 3:7. If there are 49 buses, how many cars are there.

cars buses

3 7

21 49x 7 x 7

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Now try Exercise 3Ch41 (page 160)

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Ratio & Ratio & ProportionProportionRatio CalculationsMNU 3-08a

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2. Calculate the area of the shape.

5 1+2 4

(a) 0.853 (b) 0.356 (c) 1.995

1. 6x + 5 = 59

3. Round to 2 decimal places.

4.

9

6

8

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1. We are learning to calculate proportional division by using shares.

1. Calculate one share.

Ratio & Ratio & ProportionProportionProportional Division

2. Solve problems using shares.

3. Show appropriate working.


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Example : Bill and Ben share a raffle win of £400 in the ratio 3:5. How much does each get ?


Step 1 : Since the ratio is 3:5, there are :

3+5 = 8 shares

Step 2 : Each share is worth : 50

8 400

Step 3 : Bill gets 3 x 50 = £150

Ben gets 5 x 50 = £250Check !150 + 250 = 400

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Example : Ryan and Ross share 24 cakes in the ratio3:1. How many cakes does each get ?


Step 1 : Since the ratio is 3:1, there are :

3+1 = 4 shares

Step 2 : Each share is worth : 6

4 24

Step 3 : Ryan gets 3 x 6 = 18

Ross gets 1 x 6 = 6Check !18 + 6

= 24

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Ratio & Ratio & ProportionProportionProportional DivisionMNU 3-08a

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1. Simplfy the ratio 13 : 52

Calculate 2.5

3. I got $650 for £100. How much would I get for £2.

4. Put in order, smallest first.

0.25, 0.19, 0.01, 0.026

5. Find the value

% of 4002.

of x 7x +2.5 = 20

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1 We are learning the term proportion.

1. Understand the idea of proportion.


2. Solve simple proportional problems.

Proportion


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Example : The cost of 5 cakes is £4.00. Find the cost of one.

Cost of one is simply :

If you know the total cost of several items, you caneasily find the cost per item.

0.805 4.00 = 80p

ProportionMNU 3-08aMNU 4-08a



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ProportionMNU 3-08aMNU 4-08a

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2.

4. Calculate 4 5×5 8


Calculate 6.5% of 300

3. Find the mean, median and mode for

25, 20, 55, 20

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1. We are learning the term Direct Proportion.

1. Understand the idea of Direct Proportion.


2. Solve simple proportional problems.

Direct Proportion

Example : The cost of 6 cakes is £4.20. Find the cost of 5 cakes.


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“ .. When you double the number of cakes you double the cost.”

Cakes Cost

Two quantities, (for example, number of cakes and totalcost) are said to be in DIRECT PROPORTION, if :

Direct Proportion

6 4.20 1 4.20 ÷ 6 = 0.70 5 0.70 x 5 = £3.50

Easier methodCakes Pence

6 420 5

Are we expecting more or

less

5

6420

(less)

350 £3.50

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£ $

Direct Proportion

Example : On holiday I exchanged £30 for $45.How many $ will I get for £50.

30 45 1 45 ÷ 30 = 1.5 50 1.5 x 50 = $75

What name do we give to

this valueExchange

rateEasier method£ $30 45

50


less

50

3045

(more)

$75

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Pencils Cost

Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1.

Direct Proportion

Example : 300 pencils cost £6. How much will 200 cost.

300 £6.00 100 £6.00 ÷ 3 = £2.00200 £2.00 x 2 = £4.00

Easier methodPencil Pence300 600

200


less

200

300600

(less)

400 £4

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Direct ProportionMNU 3-08aMNU 4-08a

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2.

4. Calculate 31 1 × 12 2


Calculate 2.5% of 500

3. Find the mean, median and mode for

5, 2, 5, 8

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1. We are learning how Direct Proportion Graph is always a straight line.

1. Understand that Direct Proportion Graph is a straight line.


2. Construct Direct Proportion Graphs.

Direct Proportion Graphs


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The table below shows the cost of packets of “Biscuits”.


No. of Pkts 1 2 3 4 5 6

Cost (p) 20 40 60 80 100 120

We can construct a graph to represent this data.

What type of graph do we expect ?

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Direct Proportion

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

No. of Packets

Cos

t (p

)

Direct Proportion GraphsNotice that the points lie on a straight line

passing through the origin

This is true for any two quantities

which are in Direct Proportion.


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KeyPoint

Two quantities which are in DIRECT PROPORTION

always lie on a straight linepassing through the origin.

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Example : Plot the points in the table below. Are they in direct proportion?


We plot the points (1,3) , (2,6) , (3,19) , (4,12)

XX 11 22 33 44

yy 33 66 99 1212

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1

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Plotting the points

(1,3) , (2,6) , (3,9) , (4,12)


0 1 2 3 4

101112

23456789

Since we have a straight linepassing through the origin

x and y are in direct proportion.

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2.

4. Calculate 1 1 2 4


Calculate 0.5 + 1.45 + 0.06

3. I s there a correlation between the two quanities. I f so describe it.

xx

x

x

xx

x

x

y

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1. We are learning the term Inverse Proportion.

1. Understand the idea of Inverse Proportion.


2. Solve simple inverse proportion problems.

Inverse Proportion

Example : If it takes 3 workers 8 hours to build a wall.How long will it take 4 men.


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Men Hours

Inverse proportion is when one quantity doublesand the other halves. The two quantities are said

to be INVERSELY PROPORTIONAL or (INDIRECTLY PROPORTIONAL) to each other.

3 8 1 3 x 8 = 24 hours

4 24 ÷ 4 = 6 hours

Inverse Proportion

Easier methodWorkers Hours

3 8 4


less

3

48

(less)

6 hours

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8 120 ÷ 8 = 15 months


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Men Months

Example : It takes 10 workers 12 months to build a house. How long should it take 8 men.

10 12 1 12 x 10 = 120

Inverse Proportion

Easier methodWorkers months

10 12 8


less

10

812

(more)

15 months

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Mixed ProblemsExercise 9

Ch41 (page 168)

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MNU 3-08aMNU 4-08a

Documents

MNU 3-08a MNU 4-08a 1-Aug-15Created by Mr. Lafferty Maths Dept. Simplifying Ratios Ratio Calculations Ratio & Proportion Direct Proportion