MATHEMATICS FOR INTERIOR DESIGN GSC 1105 Ratio Proportion
![MATHEMATICS FOR INTERIOR DESIGN GSC 1105 Ratio & Proportion. Prepared by: General Studies Department. MATHEMATICS FOR INTERIOR DESIGN GSC 1105 Ratio & Proportion. Prepared by: General Studies Department.](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-1.jpg)
![Writing and using ratios • A ratio compares two or more quantities. • Ratios Writing and using ratios • A ratio compares two or more quantities. • Ratios](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-2.jpg)
![EXAMPLE To make 12 small cupcakes you need 150 g of flour and 30 EXAMPLE To make 12 small cupcakes you need 150 g of flour and 30](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-3.jpg)
![Simplifying ratios • Simplifying a ratio is similar to simplifying fractions. • If we Simplifying ratios • Simplifying a ratio is similar to simplifying fractions. • If we](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-4.jpg)
![EXAMPLE : Write these ratios in their simplest form. (a) 8 : 12 (b) EXAMPLE : Write these ratios in their simplest form. (a) 8 : 12 (b)](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-5.jpg)
![Writing a ratio as a fraction • A ratio can also be written as Writing a ratio as a fraction • A ratio can also be written as](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-6.jpg)
![EXAMPLE : In a school the ratio of boys to girls is 5 : EXAMPLE : In a school the ratio of boys to girls is 5 :](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-7.jpg)
![Method B (using fractions) Suppose there are x girls. The ratio 5 : 7 Method B (using fractions) Suppose there are x girls. The ratio 5 : 7](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-8.jpg)
![Writing a ratio in the form 1: n or n: 1 • In Example Writing a ratio in the form 1: n or n: 1 • In Example](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-9.jpg)
![EXAMPLE : Write these ratios in the form n : 1. (a) 27 : EXAMPLE : Write these ratios in the form n : 1. (a) 27 :](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-10.jpg)
![Dividing quantities in a given ratio • Ali and Siti share $60 so that Dividing quantities in a given ratio • Ali and Siti share $60 so that](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-11.jpg)
![• where each bag of money contains the same amount. • To work • where each bag of money contains the same amount. • To work](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-12.jpg)
![Proportion Two quantities are in direct proportion , if their ratio stays the same Proportion Two quantities are in direct proportion , if their ratio stays the same](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-13.jpg)
![Inverse proportions When two quantities are in direct proportion • as one increases, so Inverse proportions When two quantities are in direct proportion • as one increases, so](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-14.jpg)
![EXAMPLE : Two people take 6 hours to paint a fence. How long will EXAMPLE : Two people take 6 hours to paint a fence. How long will](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-15.jpg)
![Map Scales • Map scales are written as ratios. A scale of 1 : Map Scales • Map scales are written as ratios. A scale of 1 :](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-16.jpg)
![EXAMPLE: The scale of a map is 1: 40 000. The distance between Gadong EXAMPLE: The scale of a map is 1: 40 000. The distance between Gadong](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-17.jpg)
![ANSWER: 1 M = 100 CM and 1 km = 1000 cm Distance on ANSWER: 1 M = 100 CM and 1 km = 1000 cm Distance on](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-18.jpg)
![EXAMPLE : The distance between two towns is 20 km. How far apart will EXAMPLE : The distance between two towns is 20 km. How far apart will](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-19.jpg)
![Reference: • Core Mathematics for IGCSE 2 nd Edition, Ric Pimentel and Terry Wall, Reference: • Core Mathematics for IGCSE 2 nd Edition, Ric Pimentel and Terry Wall,](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-20.jpg)
- Slides: 20
![MATHEMATICS FOR INTERIOR DESIGN GSC 1105 Ratio Proportion Prepared by General Studies Department MATHEMATICS FOR INTERIOR DESIGN GSC 1105 Ratio & Proportion. Prepared by: General Studies Department.](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-1.jpg)
MATHEMATICS FOR INTERIOR DESIGN GSC 1105 Ratio & Proportion. Prepared by: General Studies Department.
![Writing and using ratios A ratio compares two or more quantities Ratios Writing and using ratios • A ratio compares two or more quantities. • Ratios](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-2.jpg)
Writing and using ratios • A ratio compares two or more quantities. • Ratios occur often in real life. • A scale model of a car is labeled Scale 1: 18. Part Length on model Length on actual car Length of car door 7 cm 7 x 18 = 126 cm Diameter of wheels 3 cm 3 x 18 = 54 cm Length of car 26 cm 26 x 18 = 468 cm
![EXAMPLE To make 12 small cupcakes you need 150 g of flour and 30 EXAMPLE To make 12 small cupcakes you need 150 g of flour and 30](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-3.jpg)
EXAMPLE To make 12 small cupcakes you need 150 g of flour and 30 g of melted butter. Grace is making 36 cupcakes. How much of each ingredient does she need? Answer: 36 ÷ 12 = 3 so she will need three times as much of each of the ingredients. Flour 3 x 150 g= 450 g Melted butter 3 x 30 g= 90 g
![Simplifying ratios Simplifying a ratio is similar to simplifying fractions If we Simplifying ratios • Simplifying a ratio is similar to simplifying fractions. • If we](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-4.jpg)
Simplifying ratios • Simplifying a ratio is similar to simplifying fractions. • If we refer to example 1, the amounts of flour and melted butter were 150 g and 30 g. • We write this as a ratio 150 : 30 • Dividing by 10 gives 15 : 3 • Dividing by 3 gives 5 : 1 • This means that you need 5 times as much flour as melted butter.
![EXAMPLE Write these ratios in their simplest form a 8 12 b EXAMPLE : Write these ratios in their simplest form. (a) 8 : 12 (b)](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-5.jpg)
EXAMPLE : Write these ratios in their simplest form. (a) 8 : 12 (b) 18 : 24 : 6 (c) 40 cm : 1 m Answer: (a) 8 : 12 = 2 : 3 (dividing by 4) (b) 18 : 24 : 6 = 3 : 4 : 1 (dividing by 6) (c) 40 cm : 1 m = 40 cm : 100 cm Units not the same, = 40 : 100 Change m to cm. = 4 : 10 (dividing by 10) = 2 : 5 (dividing by 2)
![Writing a ratio as a fraction A ratio can also be written as Writing a ratio as a fraction • A ratio can also be written as](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-6.jpg)
Writing a ratio as a fraction • A ratio can also be written as fractions, to help you solve problems. When items are divided in a ratio 1 : 2, the fraction ½ gives you another method of solving the problem.
![EXAMPLE In a school the ratio of boys to girls is 5 EXAMPLE : In a school the ratio of boys to girls is 5 :](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-7.jpg)
EXAMPLE : In a school the ratio of boys to girls is 5 : 7. There are 265 boys. How many girls are there? Answer: Method A (using multiplying) Suppose there are x girls. The ratio 5 : 7 has to be the same as 265 : x 265÷ 5 = 53 , so multiply both sides of the ratio by 53 Boys: 5 x 53 = 265 Girls: 7 x 53 = 371 There are 371 girls in the school.
![Method B using fractions Suppose there are x girls The ratio 5 7 Method B (using fractions) Suppose there are x girls. The ratio 5 : 7](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-8.jpg)
Method B (using fractions) Suppose there are x girls. The ratio 5 : 7 has to be the same as 265 : x Using fractions, = 5/7 = 265/x It can also be written as = 7/5 = x / 265 Multiplying both sides by 265, x= (7 x 265)/5 This gives x = 371, therefore there are 371 girls in the school.
![Writing a ratio in the form 1 n or n 1 In Example Writing a ratio in the form 1: n or n: 1 • In Example](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-9.jpg)
Writing a ratio in the form 1: n or n: 1 • In Example 1, 120 : 20 simplified to 6 : 1. • Not all ratios simplify so that one value is 1. For example, 6 : 4 simplifies to 3 : 2. • If you are need to write this ratio in the form n : 1 you cannot leave the answer as 3 : 2.
![EXAMPLE Write these ratios in the form n 1 a 27 EXAMPLE : Write these ratios in the form n : 1. (a) 27 :](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-10.jpg)
EXAMPLE : Write these ratios in the form n : 1. (a) 27 : 4 (b) 6 cm : 25 mm (e) $2. 30 : 85 c ANSWER: (a) 27 : 4 = 6. 75 : 1 (b) 6 cm : 25 mm = 60 mm : 25 mm = 60 : 25 = 2. 4 : 1 (c) $2. 38 : 85 c = 238 : 85 = 2. 8: 1
![Dividing quantities in a given ratio Ali and Siti share 60 so that Dividing quantities in a given ratio • Ali and Siti share $60 so that](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-11.jpg)
Dividing quantities in a given ratio • Ali and Siti share $60 so that Ali receives twice as much as Siti. • You can think of this as, Ali : Siti = 2 : 1. • Ali will get this much Siti will get this much
![where each bag of money contains the same amount To work • where each bag of money contains the same amount. • To work](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-12.jpg)
• where each bag of money contains the same amount. • To work out each man's share, you need to divide the money into 3. (2 + 1 = 3) equal parts (or shares). 1 part = $60 ÷ 3 = $20 Ali receives 2 X $20 = $40 2 parts Siti receives 1 X $20 = $20 1 part Check: $20 + $40 = $60
![Proportion Two quantities are in direct proportion if their ratio stays the same Proportion Two quantities are in direct proportion , if their ratio stays the same](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-13.jpg)
Proportion Two quantities are in direct proportion , if their ratio stays the same as they increase or decrease. • Ratio method For example, a mass of 5 kg attached to a spring stretches it by 40 cm. A mass of 15 kg attached to the same spring will stretch it 120 cm. The ratio mass : extension is 5 : 40 = 1 : 8 (dividing by 5) 15 : 120 = 1 : 8 (dividing by 15) • The ratio mass : extension is the same so the two quantities are in direct proportion.
![Inverse proportions When two quantities are in direct proportion as one increases so Inverse proportions When two quantities are in direct proportion • as one increases, so](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-14.jpg)
Inverse proportions When two quantities are in direct proportion • as one increases, so does the other • as one decreases, so does the other. Or If you travel at an average speed of 50 km/h it will take you 2 hours. If you only average 40 km/h it will take you 2+ hours • As the speed decreases, the time increases. • As the speed increases, the time decreases
![EXAMPLE Two people take 6 hours to paint a fence How long will EXAMPLE : Two people take 6 hours to paint a fence. How long will](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-15.jpg)
EXAMPLE : Two people take 6 hours to paint a fence. How long will it take 3 people? ANSWER: 2 people take 6 hours. 1 person takes 6 x 2 = 12 hours 3 people will take 12 ÷ 3 = 4 hours
![Map Scales Map scales are written as ratios A scale of 1 Map Scales • Map scales are written as ratios. A scale of 1 :](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-16.jpg)
Map Scales • Map scales are written as ratios. A scale of 1 : 40 000 means that 1 cm on the map represents 40 000 cm on the ground. When you answer questions involving map scales you need to • use the scale of the map • convert between metric units of length so that your answer is in sensible units.
![EXAMPLE The scale of a map is 1 40 000 The distance between Gadong EXAMPLE: The scale of a map is 1: 40 000. The distance between Gadong](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-17.jpg)
EXAMPLE: The scale of a map is 1: 40 000. The distance between Gadong conter point and Empire Country club on the map is 40 cm. What is the actual distance between Gadong conter point and Empire Country club? Give your answer in kilometer
![ANSWER 1 M 100 CM and 1 km 1000 cm Distance on ANSWER: 1 M = 100 CM and 1 km = 1000 cm Distance on](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-18.jpg)
ANSWER: 1 M = 100 CM and 1 km = 1000 cm Distance on map = 40 cm Distance on the ground = 40 x 40 000 cm = 1600 000 ÷ 100 m = 16 000 ÷ 1000 km = 16 km
![EXAMPLE The distance between two towns is 20 km How far apart will EXAMPLE : The distance between two towns is 20 km. How far apart will](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-19.jpg)
EXAMPLE : The distance between two towns is 20 km. How far apart will they be on a map of scale 1: 180 000? Distance on the ground = 20 km = 20 x 1000 m = 20 000 x 100 cm = 2 000 cm Distance on map = 2000 cm ÷ 180 000 =11. 1 cm (to 3 s. f. )
![Reference Core Mathematics for IGCSE 2 nd Edition Ric Pimentel and Terry Wall Reference: • Core Mathematics for IGCSE 2 nd Edition, Ric Pimentel and Terry Wall,](https://slidetodoc.com/presentation_image_h/dff359af950e7aa1e831c5faba635e97/image-20.jpg)
Reference: • Core Mathematics for IGCSE 2 nd Edition, Ric Pimentel and Terry Wall, University of Cambridge.
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