Riddles Mr Smith has 4 daughters. Each of his daughters has a brother. How many children does Mr Smith have? During which month do people sleep the least? There is an ancient invention, still used in some parts of the world today, that lets people see through walls. What is it called? What goes up and never comes down?

Ratio & Proportion Week 05: Calculate ratio and proportion, including problems using currency conversion Understand ratio as a number of parts, simplify and solve for a given number of parts Solve ratio problems where one number is a multiple of another Understand direct proportion is the same rate of change Understand ratio notation written in the form 3:2. Link fractions, decimals, percentages, ratio and proportion

What did we do last week?

12/20 4/10 16/20 £240 1/4 8/10 2/5 12/16 6/11

Work out 3/5 of 120 Work out 30% of 250 Write 0.27 as a percentage Which is larger: 35% or 1/3? Which is larger: 25% of 200 or 1/12 or 1000? What does BIDMAS stand for? Use BIDMAS to solve 3 + 5 – 2 x 2

Why do we need to convert currency? Currency Conversion Why do we need to convert currency? What is an Exchange Rate? Are Exchange Rates always the same?

Thai Baht Jamaican Dollar Canadian Dollar Indian Rupee Russian Ruble Euro

£100 x €1.39 = €139 £1 = €1.39 (Euros) What is £100 in Euros? Convert the following amounts to Euros: a) £20 b) £150 c) £210 €291.90 €27.80 €208.50

€200 ÷ €1.39 = £143.88 £1 = €1.39 (Euros) What is €200 in Pounds? Convert the following amounts to Pounds: a) €50 b) €80 c) €325 £35.97 £57.55 £233.81

Ratio Ratio is a way of comparing amounts It shows how much bigger one part is compared to another Ratio is written 1 : 2 This ratio has 3 parts altogether as 1 + 2 = 3. This is important!

250 million users How many users?

12 million viewers How many viewers?

CD sales Digital album sales

Calculating Ratio Divide each amount into the given ratio Step 1: Add up the total number of parts: For example: share 30 in the ratio 1:2 1 + 2 = 3 parts Step 2: Divide the amount by the total number of parts (this gives you the value of one part): 30 ÷ 3 = 10 10 is the value of 1 share Step 3: Multiply by each part of the ratio: 10 x 1 = 10 10 x 2 = 20 So, sharing 30 in the ratio 1:2 = 10 : 20

£20

£350 £??

£800 Jim Jemima Find the value of Jim and Jemima’s shares.

£?? £280 £?? Find the value of the whole amount and the missing share.

Painting You have decided to paint your hallway purple. You need 3:2 blue and red paint. If you need 500ml of paint in total to cover the wall, how many ml of blue and red paint will you need?

Cement You decide to cement your patio. The cement mix requires 3 parts cement, 2 parts sand and 1 part water. If you need 250kg of mix, how much cement, water and sand will you need?

Ratio £16 in the ratio 5 : 3 £99 in the ratio 7 : 2 £60 in the ratio 7 : 3 £28 in the ratio 3 : 4 £140 in the ratio 6 : 3 : 1

Daniel Freddie George Bobby Cathy Alan Ellie Total Prague Zurich Paris Milan Madrid Berlin Munich Prison sentence The total amount stolen was __________ The robber who made the most money was __________

The total amount stolen was €240 million Daniel Freddie George Bobby Cathy Alan Ellie Total Prague 2 6 4 12 Zurich 18 Paris 3 9 21 Milan 8 16 20 80 Madrid 10 Berlin 24 Munich 15 25 5 75 33 23 50 51 37 28 240 Prison sentence 11 72/3 162/3 17 121/3 91/3 The total amount stolen was €240 million The robber who made the most money was Bobby

Proportion There are 30 children in a class in the ratio 2:1. There are 20 boys. What proportion are boys? With words: As a fraction: 20 out of 30 20 30 As a decimal: As a percentage: 0.66666 66%

Direct Proportion We can use the ratio of something to multiply or divide a quantity as required, e.g: 3 tins of blue paint : one tin of white If you need to mix 9 tins of blue paint you will need 3 of white

Using Ratio to describe statistics There are 3 people with green eyes to every 1 person with blue eyes : Direct Proportion: If there are 4 people in a class with blue eyes, then there is likely to be 12 people with green eyes.

Exam Question Year 10 and Year 11 students are in assembly: Year boys : girls Student data 10 4:5 84 boys 11 2:3 150 students Work out the total number of girls in the assembly.