B. The scale of a map is 1cm : 50 km. Exit Questions A. The scale of a map is 1 : 5 000 000. The distance between Leeds and London on this map is 6.5 cm. Calculate the actual distance between Leeds and London. Give your answer in kilometres. B. The scale of a map is 1cm : 50 km. If the actual distance from A to B in real life is 200km. How far away are A and B on the map?

Pg 100 Ex 5d 7,9 7. The map ratio of a map is 1 : 50 000. The distance between A and B on the map is 6cm. What is the true distance between A and B MAP : REAL 1 : 50 000 6 : ? The true distance between A and B is 300 000cm or 3km x 6 x 6 300 000

Pg 100 Ex 5d 7,9 9. The map ratio of a map is 1 : 10 000. Find the actual length represented by 2cm MAP : REAL 1 : 10 000 2 : ? The actual length is 20 000cm or 200m x 2 x 2 20 000

Pg 101 Ex 5d 10,11 10. The map ratio of a map is 1 : 200 000. The distance between two towns is 20km. What is this in centimetres? Find the distance on the map between the points representing the towns MAP : REAL 1 : 200 000 ? : 20 km 20 km = 2 000 000 cm The distance on the map is 10 cm x 10 x 10 10 2 000 000

Pg 101 Ex 5d 10,11 11. The map ratio of a map is 1 : 2 000 000. Find the distance on the map which represents an actual distance of 36km MAP : REAL 1 : 2 000 000 ? : 36 km 36 km = 3 600 000 The distance on the map is 1.8 cm x 1.8 x 1.8 1.8 3 600 000

Warm-up Fraction of a Quantity 𝟒 𝟓 𝒐𝒇 𝟑𝟓 𝟑 𝟒 𝒐𝒇 𝟏𝟔 12 28 𝟐 𝟑 𝒐𝒇 𝟏𝟓 10 𝟒 𝟓 𝒐𝒇 𝟑𝟓 𝟑 𝟒 𝒐𝒇 𝟏𝟔 12 28 𝟐 𝟑 𝒐𝒇 𝟏𝟓 10 𝟕 𝟏𝟎 𝒐𝒇 𝟒𝟎 Fraction of a Quantity 28

L.O. To be able to divide a quantity in a given ratio By the end of the lesson, we will be able to: understand when a question is asking to divide a quantity in a given ratio divide a quantity in a given ratio

Partner up with the person behind you! You managed to steal €200 You and your partner robbed a bank But one of you did more work than the other, so to be fair you must share the money in the ratio 1 : 3

Divide €200 in the ratio 1 : 3 In all 1 + 3 = 4 parts 𝟏 𝟒 𝒐𝒇 €𝟐𝟎𝟎= 𝟏 𝟒 × €𝟐𝟎𝟎=€𝟓𝟎 𝟑 𝟒 𝒐𝒇 €𝟐𝟎𝟎= 𝟑 𝟒 × €𝟐𝟎𝟎=€𝟏𝟓𝟎 50 + 150 = €𝟐𝟎𝟎 50 50 50 50

Example: Johnny shares a chocolate bar that has 24 pieces with Tanya and Joe. They share the bar in the ratio 3 : 1 : 2 Work out each persons share. Johnny : Tanya : Joe 3 : 1 : 2 THERE ARE 3 + 1 + 2 = 6 SHARES ALTOGETHER 𝐽𝑜ℎ𝑛𝑛𝑦 → 3 6 𝑜𝑓 24=12 𝑇𝑎𝑛𝑦𝑎→ 1 6 𝑜𝑓 24=4 𝐽𝑜𝑒→ 2 6 𝑜𝑓 24=8

Method: Divide a QUANTITY in a RATIO Add up the total number of parts of the ratio Find the fraction of the quantity of separate parts all over this total Make sure that the sub-quantities found in step 2 add up to the whole quantity Make sure to answer the question properly

1a) Share €250 in the ratio 1 : 4 Batman : Robin 1 : 4 1 : 4 1 + 4 = 5 parts in all Batman: 1 5 𝑜𝑓 €250 = €50 Robin: 4 5 𝑜𝑓 €250 = €200

1b) Share €250 in the ratio 7 : 3 Spongebob: Patrick 7 : 3 7 : 3 7 + 3 = 10 parts in all Spongebob : 7 10 𝑜𝑓 €250 = €175 Patrick : 3 10 𝑜𝑓 €250 = €75

1c) Share €250 in the ratio 9 : 12 : 4 Simon : Alvin : Theodore 9 : 12 : 4 9 + 12 + 4 = 25 parts in all Simon: 9 25 𝑜𝑓 €250 = €90 Alvin: 12 25 𝑜𝑓 €250 = €120 Theodore: 4 25 𝑜𝑓 €250 = €40

2. Share €80 in the ratio 3 : 2 Tom : Jerry 3 : 2 3 : 2 3 + 2 = 5 parts in all Tom : 3 5 𝑜𝑓 €80 = €48 Jerry : 2 5 𝑜𝑓 €80 = €32

3. 3. The angles in a triangle are in the ratio 6 : 5 : 7 L1 : L2 : L3 6 : 5 : 7 6 + 5 + 7 = 18 parts in all Quantity? 180° L1 : 6 18 𝑜𝑓 180° = 60° L2 : 5 18 𝑜𝑓 180° = 50° L3 : 7 18 𝑜𝑓 180° = 70°

Dividing in a given quantity worksheet

Tim, Shula and Carol share the running costs of the car in the ratio 1 : 2 : 3. Last year it cost €1860 to run the car. How much did Carol pay? Tim : Shula : Carol 1 : 2 : 3 Total parts: 1+2+3 = 6 Carol has 𝟑 𝟔 𝒐𝒇 €𝟏𝟖𝟔𝟎=€𝟗𝟑𝟎

Paul is making grey paint Paul is making grey paint. He mixes black and white paint in the ratio 2 : 3. He makes 35 litres of grey paint. How much white paint does he use? Black : White 2 : 3 Total parts: 2+3 = 5 He must use 𝟑 𝟓 𝒐𝒇 𝟑𝟓=𝟐𝟏𝒍 of white paint

The ratio of adults to children in the sports club is 5 : 2 The ratio of adults to children in the sports club is 5 : 2. There are 560 members in the club. How many children are there? Adults : Children 5 : 2 Total parts: 5+2 = 7 There are 𝟐 𝟕 𝒐𝒇 𝟓𝟔𝟎=𝟏𝟔𝟎 children

Archie and Charlie share 45 Thomas the tank engine toys in the ratio 1:4, how many toys do they each get? Archie : Charlie 1 : 4 Total parts: 1+4 = 5 Archie gets 𝟏 𝟓 𝒐𝒇 𝟒𝟓=𝟗 toys Charlie gets 𝟒 𝟓 𝒐𝒇 𝟒𝟓=𝟑𝟔 toys

Jon : Adel 2 : 7 Total parts: 2+7 = 9 Adel gets 𝟕 𝟗 𝒐𝒇 𝟖𝟏=𝟔𝟑 socks Jon and Adel share 81 socks in the ratio 2 : 7, how many socks does Adel get? Jon : Adel 2 : 7 Total parts: 2+7 = 9 Adel gets 𝟕 𝟗 𝒐𝒇 𝟖𝟏=𝟔𝟑 socks

Mike : Dave : Henry 1 : 2 : 3 Total parts: 1+2+3 = 6 Mike, Dave and Henry share 72 little pieces of blue tack in the ratio 1 : 2 : 3, how many do they each get? Mike : Dave : Henry 1 : 2 : 3 Total parts: 1+2+3 = 6 Mike gets 𝟏 𝟔 𝒐𝒇 𝟕𝟐=𝟏𝟐 pieces Dave gets 𝟐 𝟔 𝒐𝒇 𝟕𝟐=𝟐𝟒 pieces Henry gets 𝟑 𝟔 𝒐𝒇 𝟕𝟐=𝟑𝟔 pieces

DO NOT MIX UP THESE OBJECTIVES To be able to find an unknown quantity in a given ratio To be able to share a quantity in a given ratio