Chpt 2 - Ratio, Rate & Proportion

RATIO, RATE AND PROPORTION Mathematics Preparatory Course for Direct Entry to Higher Nitec 2-1 CHAPTER 2 2.1 RATIO A ratio is a comparison between two or more quantities. The symbol used to show ratio is "a : b". The example below shows how 750 metres and 2 kilometres can be compared by writing them as a ratio. 750 m to 2 km = 750 m : 2 km = 750 m : 2 000 m = 750 : 2000 = 3 : 8 A ratio can also be written in fractional form. For example, the ratio 3 : 8 can be written as 8 3 . The numbers 3 and 8 are called the terms of the ratio. Sometimes three quantities are compared using a three-term ratio. Example 1 Line XZ is 56 cm long. If XY : YZ is 2 : 5, find the length of YZ. Example 2 Three girls share $ 120 in the ratio 3:4:5. Find the smallest share. Example 3 The lengths of the three sides of a triangle XYZ are such that XY : YZ : XZ is 2 : 3 : 5. If XZ is 20 cm, find the length of XY.

RATIO, RATE AND PROPORTION Mathematics Preparatory Course for Direct Entry to Higher Nitec 2-2 Example 4 A sum of m oney is divided between Iris, Jimmy and Karen in the ratio 3 : 5 : 6. Jimmy receives $ 60. (a) How much does Karen receive? (b) What is the total sum of money? Example 5 The perimeter of a rectangular piece of land is 96 m. The ratio of its length to breadth is 7 : 5. Find the length and breadth of the piece of land. 2.2 PROPORTION A proportion is an expression showing that two ratios are equal such as 3 : 7 = 6 : 14. Many mathematical problems can be solved by using proportion in the form comparing and equating equivalent ratios. The following examples illustrate the use of proporti on in problem solving. Consider the proportion p : q = r : s. It can be written in two other forms, q p = s r and ps = qr.Either of these forms can be used when finding the unknown value in a proportion Example 6 Find the value of y in the proportion 48 : 7 = 12 : y.

RATIO, RATE AND PROPORTION Mathematics Preparatory Course for Direct Entry to Higher Nitec 2-3 Example 7 4 men take 6 hours to paint a house. How long will it take 3 men to paint the house, if they work at the same rate? Example 8 32 out of every 40 students travel to Col lege East by bus. How many students out of every 100 travel to College by bus? Example 9 A picture measuring 10 cm by 7 cm is enlarged to make a copy 16 cm long. What is the width of the copy? Direct and Inverse Proportion Quantities which increase in the same ratio are in direct proportion. If one quantity increases in the same ratio as the other decreases, then they re in inverse proportion.

RATIO, RATE AND PROPORTION Mathematics Preparatory Course for Direct Entry to Higher Nitec 2-4 Example 10 10 writing pads cost $ 11. Find the cost of 3 writing pads. Example