Ratio and Proportion 
        
       In this lesson, we will learn how to: 
       • define ratio and direct proportion. 
       • compare two quantities multiplicatively in terms of a ratio and proportion.  
       • solve word problems involving ratios and proportions. 
        
       Real life examples 
       We use ratios and proportions in our daily life without realising it. 
       You must have heard your mum saying “for every 2 cups of flour, we add half cup of sugar” 
       whenever she shares a recipe with someone.  
       Little friends, have you ever prepared a juice mixture from concentrated juice and water? 
       If you ever have, what proportion of concentrated juice to water did you use? 
        
       Ratios 
       Ratios are used to compare two quantities of the same kind or quantities measured in the 
       same unit. A ratio can be written in the form: a:b or  a . 
                            b
        
       Example 
                                      
        
       The ratio of Fidget Spinners to Top Spinners is 
                3 : 2 
        
        
                       Example 
                       Write down the following quantities in terms of a (i) ratio and a (ii) fraction. 
                            (a) 4 girls to 3 boys 
                            (b) 12 blue pens to 17 red pens 
                       Solution 
                            (a) (i) Girls : Boys = 4 : 3                                 (ii) Girls : Boys =  4  
                                                                                                                     3
                            (b) (i) Blue Pens : Red Pens = 12 : 17                       (ii) Blue Pens : Red Pens = 12  
                                                                                                                                  17
                        
                       Example of simplifying ratios 
                                                                                                                                                            
                       The ratio Doughnuts: Cupcakes = 2 : 4 which can be simplified to: 
                                                  ÷ 2              2 : 4           ÷ 2 
                                                                   1 : 2 
                       The H.C.F. of 2 and 4 is 2. So, we divide both numbers by 2 
                       Answer: 1 : 2 
                        
                       Example 
                       Simplify the following ratios 
                                                                                   13:21
                            (a) 5 : 15                                        (b)                                         (c) 1.2 : 3.6  
                                                                                      4      8
                       Solution  
                             (a) The H.C.F. of 5 and 15 is 5. So, we divide both numbers by 5. 
                                         ÷ 5            5 : 15         ÷ 5 
                                                        1 : 3 
                             Answer : 1 : 3 
                        Solution  
                                         13:21                  7 :17
                              (b)                          =                                 Convert to improper fraction 
                                            4      8            4 8
                                    
                                                                78:178
                                                           =  4           8                  Multiply by 8, the L.C.M. of 4 & 8 
                         
                                                          =   14 : 17  
                         
                        Solution  
                              (c) 1.2 : 3.6  = 12 : 36                           Multiply by 10 to obtain whole numbers 
                                                  = 1 : 3                        Divide by 12 which is the H.C.F. of 12 and 36 
                                                
                         
                        Sharing In Ratio 
                        Example 
                        Share Rs 5 000 between Shania and Diya in the ratio 3 : 2.   
                        Solution 
                        Number of equal parts = 3 + 2 = 5 
                        Amount in 1 part = 5 000 ÷ 5 = Rs 1 000 
                        Shania’s share = Rs1 000 × 3 = Rs 3 000  
                        Diya’s share = Rs1 000 × 2 = Rs 2 000  
                         
                        Example 
                        The heights of Ronny and his father are in the ratio 2 : 3. If Ronny is 120 cm tall, find the 
                        height of his father.  
                                  120cm                                                                  ? 
                                                                                            
                        Solution 
                                    Ronny’s Height    :                  Father’s height 
                                                2                :             3  
                         × 60                                                               × 60 
                                            120 cm        :              ?  
                        Ronny’s father’s height = 3 × 60  
                                                               = 180 cm 
                         
                        Example 
                        An orange drink is obtained by mixing orange juice and water in the ratio 2 : 5. If there is 15 
                        ml more water than orange juice, find the amount of orange juice used.  
                        Solution 
                        Orange juice  : Water = 2 : 5  
                        Difference in ratios = 5 – 2 = 3  
                        3 parts = 15 ml 
                        1 part = 15 ÷ 3 = 5 ml  
                        Amount of orange juice = 2 parts × 5 = 10 ml  
                         
                        Direct proportion 
                        Two quantities are in direct proportion if an increase or decrease in one quantity results in an 
                        increase or decrease in the other quantity in the same ratio.  
                        For example 
                                                                       1 box of chips costs Rs 25  
                                                                       2 boxes of chips will cost Rs 50