Suppose the pizzas at the two tables are shared equally by everyone seated at the table. Does a person seated at the small table get the same amount of pizza as a person seated at of the large table?

10 : 4people: pizza

1 : ÷ 10 ÷ 10

0,4 8 : 3

people: pizza

1 : ÷ 8 ÷ 8

0,375

You would need to know that four tenths of a pizza is more than three eights.

2:3concentrate: water

1:2concentrate: water

5:9concentrate: water

3:5concentrate: water

How do we compare these ratios?

2 cups concentrate3 cups water

3 cups concentrate9 cups water

1 cups concentrate2 cups water

3 cups concentrate5 cups water

25

312

13

38

120

120

120

120

48 30 40 45

Strongest taste – most concentrate

The heights of Jane and Jess are in the ratio 7:9. The shorter one of the two is 154cm. Who is taller and what is her height?

7 : 9

short : tall

Jane : Jess

154:

The heights of Jane and Jess are in the ratio 7:9. The shorter one of the two is 154cm. Who is taller and what is her height?

x 22 x 22198

Three children share R75 in the ratio 1: 2: 3

1 : 2 : 3 = 6 : : = 75

x 12.5 x 12.512.5 25 37.5

Energade energy drink, needs be to mixed in the ratio 1 part concentrate to 3 parts water. How much water is and concentrate is needed for a litre of Energade energy drink?

1 : 3 4concentrate : water Energade

: 1000mlx 250

250x 250

750

Write down in words what you have

Write down the ratios

How many times bigger is the given

Multiply to find the unknown

Words

7 : 9

Jane : Jess

154: 154 ÷ 7 = 22

1989 x 22= 198

Ratios

÷ up

x down

5,7 : 100litres : km

35 :

A Fiat 500 has an average consumption of 5,7 /100 km. If the car has a 35 tank, how far can it go on one tank of petrol?

÷ x

35 ÷ 5,7 x 100 ≈ 614 km

This is a topic that always confuses learners and does not have to. Write 8 cm as m

100 : 1cm : m

8 : 8 ÷ 100 x 1 = 0,08 m²

100 :1cm : m

Write 8 cm² as m²

100² :1²cm² : m²

10000 :18 :

8 ÷ 10000 x 1 = 0,0008 m²

1 : 11,94Dollar : Rand

199 :

The dollar-rand exchange rate on 5 January 2014 is: R11,94 for $1. If the price of the new iPhone 6 is $199, what would the cost of the phone me in rands?

11,94 x 199 = R2 376,06

USING THE RATIO METHOD…. Again…

A R250 pair of jeans has been marked down with 20%. What is the new sale price?

100% : 80%

Original price : Sale price

R250 : 250 ÷ 100 x 80 = R200

÷ x

A R250 pair of jeans has been marked down with 20%. What is the new sale price?

Fraction method:

The sale price on a pair of jeans after a discount of 20% is R140. What was the original price?

100% : 80%

Original price : Sale price

: R140140 ÷ 80 x 100 = R175

÷x

The sale price on a pair of jeans after a discount of 20% is R140. What was the original price?

Fraction method:

The price of bread has increased with 5% to R8,40. What was the price before the increase?

100% : 105%

Original price : Increase

: R8,408,40 ÷ 105 x 100 = R8

÷x

The price of bread has increased with 5% to R8,40. What was the price before the increase?

Fraction method:

Calculate the VAT inclusive price on a pair of shoes that cost R150 before 14% VAT.

100 : 114VAT exclusive : VAT inclusive

R150 : 150 ÷ 100 x 114 = R171

÷ x

Calculate the VAT inclusive price on a pair of shoes that cost R150 before 14% VAT.

Fraction method:

The VAT inclusive price on a pair of shoes is R285. Calculate the VAT exclusive price

100 : 114VAT exclusive : VAT inclusive

: R285285 ÷ 114 x 100 = R250

÷x

The VAT inclusive price on a pair of shoes is R285. Calculate the VAT exclusive price

Fraction method:

In GEOMETRY

7 cm on a 1:50 000 map, would amount to how many kilometers in real life?

1: 50000

Map : Real life

7 : 7 x 50000 = 350000 cm

100 000 cm : 1 km350 000 cm :

3,5km

This picture is an enlargement of a bee. A scale of 1:0,25 is used and on this drawing the bee has a wingspan of 6 cm. What is the bee’s real life wingspan?

1: 0,25

Drawing : Real life bee

6 : 6 ÷ 1 x 0,25 = 1,5 cm

÷ x

The following house plan has a scale of 1: 150. If the length of the house in the real life is 12 m, then what is the length of the house on the house plan?

The following house plan has a scale of 1: 150. If the length of the house in the real life is 12 m, then what is the length of the house on the house plan in cm?

1: 150House plan : Real life

: 1200 cm11 ÷ 120 x 1 = 8 cm

÷x

6 painters paint a house in 5 days. 5 painters will paint the same house in?

Painters : Days6 : 5

Therefore, twice the amount of painters will take half the time

12 : 2,5And half the amount of painters, will take

double the time3 : 10

Look at these numbers. Do you notice the following?

6 x 5 = 3 x 10 = 12 x 2,5 = 30

6 painters paint a house in 5 days. 5 painters will paint the same house in?

6 : 5Painters : Days

5 : 30 ÷ 5 = 6 days

6 x 5 = 30

5 x = 30

It takes 10 recycle team members 40 minutes to sort all the recycled items. How long (to the

nearest minute) will it take 6 members?

People : Minutes10 : 40

Twice the amount of people will take half the time

20 : 20And half the amount of people, will take double

the time5 : 80

10 x 40 = 20 x 20 = 5 x 80 = 400

It takes 10 recycle team members 40 minutes to sort all the recycled items. How long (to the

nearest minute) will it take 6 members?

10 : 40

People : Days

6 : 400 ÷ 6 ≈ 67 min

10 x 40 = 400

6 x = 400

RATIO / DIRECT PROPORTION

As the one value increase, so the other value increases

Constant growth

INDIRECT / INVERSE PROPROTION

As the one value increase, so the other value decreases

Non-constant growth

1 2 3 4 55 10 15 20 25

1 2 3 4 612 6 4 3 2