It is a way of writing and making a numerical comparison between two or

more quantities

8 to 5What is ratio?

3:51:2:5:4

A way of looking at numerical data-

• Making numerical comparisons between ingredients in a recipe

• Making numerical comparisons between a mixture of paint colours

• Making numerical comparisons between a scale drawing of a room and the actual dimensions of a room

Ratio

• It is pronounced as – ray show

• It is usually written with a colon (:) which is read as ‘to’

3 to 2 is written as 3 : 2

An example of ratio

If there are two boys and three girls in the room-

The ratio of boys to girls in the room is two to three.

boys to girls can be written in shorthand asboys : girls

two to three can be written in shorthand as2 : 3

The order is important

If there are two boys and three girls in the room-

The ratio of girls to boys is.

girls to boys can be written in shorthand asgirls : boys

three to two can be written in shorthand as3 : 2

Another example of ratio

If there are two apples for every five grapes in the fruit basket.

The ratio of apples to grapes is two to five.

apples to grapes can be written in shorthand asapples : grapes

two to five can be written in shorthand as2 : 5

Remember the order

If there are two apples for every five grapes in the fruit basket.

What is the ratio of grapes to apples?

Remember the order

If there are two apples for every five grapes in the fruit basket.

The ratio of grapes to apples is 5 to 2

or

The ratio of grapes : apples is 5 : 2

If there must always be two apples for every five grapes in your fruit basket.

• if you have four apples in the basket there must be 10 grapes

• If you have twenty grapes then there must be eight apples

Keeping the ratio proportional

2:5

4:10

8:20

These ratios are all the same

Keeping the ratio proportional

2:54:10 8:20

The middle one is the simplest way of expressing the ratio and that is always the way you would choose to write a ratio

You can make a comparison of more than

two quantities

The ratio of Twix to Mars to Dairy Milks is 2 to 3 to 4

In shorthand –

The ratio of Twix : Mars : Dairy Milks is

2 : 3 : 4

At the sweet shop, John bought some sweets.

He bought 2 Twix, 3 Mars, 4 Dairy Milks.

The order is important

At the sweet shop, John bought some sweets He bought 2 Twix, 3 Mars, 4 Dairy Milks.

What is the ratio of Mars to Twix to Dairy Milks ?

The order is important

At the sweet shop, John bought some sweets He bought 2 Twix, 3 Mars, 4 Dairy Milks.

What is the ratio of Mars to Twix to Dairy Milks ?

The ratio of Mars : Twix : Dairy Milks is 3 : 2 : 4

This is a result of a survey of how some children get to school

Bus 4

Car 7

Cycle 2

Walk 5

What is the ratio of children walking to taking the bus to get to school?

Ratio from a table of values

Comparingtwo

quantities

This is a result of a survey of how some children get to school

Bus 4

Car 7

Cycle 2

Walk 5

What is the ratio of walking to taking the bus?

Ratio from a table of values

The ratio is 5 : 4

Comparingtwo

quantities

Bus 4

Car 7

Cycle 2

Walk 5

What is the ratio of getting to school by car to cycling to walking?

This is a result of a survey of how some children get to school

Ratio from a table of values

Comparingthree

quantities

Bus 4

Car 7

Cycle 2

Walk 5

What is the ratio of getting to school by car to cycling to walking?

This is a result of a survey of how some children get to school

Ratio from a table of values

The ratio is 7 : 2 : 5

Comparingthree

quantities

Getting values from a Pictogram

What is the ratio of prawn to bacon?

Getting values from a Pictogram

What is the ratio of prawn to bacon?

The ratio of prawn : bacon is 3 : 5

Simplifying a ratio

What is the ratio of Ready Salted to Cheese and Onion?

Simplifying a ratio

What is the ratio of Ready Salted to Cheese and Onion?

The ratio is 6 : 2

Simplifying a ratio

A ratio of 4 : 8 can be simplified to

2 : 4 which can be simplified to

1 : 2

Can you see how?

Simplifying a ratio

4 : 8

2 : 4

1 : 2

÷2

÷2

Simplifying a ratio

9 : 3

3 : 1÷3

Simplifying a ratio

25 : 10

5 : 2÷5

Favourite Crisps

Looking at the ratio of Ready Salted to Cheese and Onion, can it be simplified?

The ratio of

6 : 2

Simplifying a ratio

Simplifying a ratio

6 : 2

3 : 1

÷2

Favourite Crisps

The ratio of Ready Salted to Cheese and Onion, should be written as 3 : 1

The ratio of

6 : 2

Simplifying a ratio where possible

Simplifying a ratio uses the same process as simplifying a fraction

6

8

24

16

1020

12

10

8 8 : 10

12 : 20

16 : 24

When writing a ratio

• You have to consider the order of the numbers

• You also must simplify it as much as possible the way you would with a fraction – finding a common divisor

Red 50

Black 35

Green 15

Silver 20

Blue 45

Yellow 10

This table shows the colour of cars in a car park.

What is the ratio of red cars to black cars?Write it in simplest form.

Red 50

Black 35

Green 15

Silver 20

Blue 45

Yellow 10

What is the ratio of red cars to black cars?Write it in simplest form.

:

Red 50

Black 35

Green 15

Silver 20

Blue 45

Yellow 10

What is the ratio of red cars to black cars?Write it in simplest form.

:

50 : 35

Red 50

Black 35

Green 15

Silver 20

Blue 45

Yellow 10

What is the ratio of red cars to black cars?Write it in simplest form.

:

50 : 35

10 : 7÷5

The colour of cars

Red 50

Black 35

Green 15

Silver 20

Blue 45

Yellow 10

What is the ratio of black to green to silver cars?

The colour of cars

Red 50

Black 35

Green 15

Silver 20

Blue 45

Yellow 10

What is the ratio of black to green to silver cars?

: :

35 : 15 : 20

7 : 3 : 4

Keep the order

Simplify

Drawings, Maps, Diagrams

Sometimes a diagram is made with a note

This means the drawing will not be in proportion but is only a rough sketch. You would not take a ruler and start measuring because it is not an accurate drawing

Not drawn to scale

Scales on maps and drawings

If a map or drawing

shows a legend with scale

This means for every one unit on the map it is 20 units in real size.

You could take measures of this drawing with a ruler.

1 : 20

The unit must be the same

Scale of

1 mm on the map would actually be 20 mm or 2cm

2 cm on the map would actually be 40 cm

1 inch on the map would actually be 20 inches

1 : 20

Scales on maps

Sometimes the scale might be worded this way

(where the units are included in the scale)

2 cm : 1 m

Scales on maps

2 cm on the map actually represents 1 metre actually

4 metres in real life would be represented by 8 cm on the scale

What would 12 cm on the map represent in real life?

2 cm : 1 m

Scales on maps

What would 12 cm on the map represent in real life?

2 cm : 1 km

Scales on maps

What would 12 cm on the map represent in real life?

2 cm : 1 km

12 cm : 6 km

2 cm : 1 km

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