Example 5 - Chapter 7 Class 8 - Proportional Reasoning-1(Ganita Prakash)

Transcript

Example 5 Measure the width and height (to the nearest cm) of the blackboard in your classroom. What is the ratio of width to height of the blackboard? Can you draw a rectangle in your notebook whose width and height are proportional to the ratio of the blackboard? Use a measuring tape to measure your classroom blackboard. Example: If Width = 100 cm and Height = 50 cm. Then ratio is Ratio = 100 : 50 To draw a rectangle proportional to the blackboard, we first simplify the ratio Simplifying ratio Ratio = 100 : 50 = 100/50 = 2/1 = 2 : 1 Now, we have to Draw a rectangle which has Ratio of Width to Height as 2 : 1 Let Height of Blackboard = 5 cm Finding Height using Ratio Ratio = 𝑊𝑖𝑑𝑡ℎ/𝐻𝑒𝑖𝑔ℎ𝑡 𝟐/𝟏=𝑾𝒊𝒅𝒕𝒉/𝟓 2 × 5 = Width 10 = Width Width = 10 cm Thus, Dimensions of Rectangle proportional to blackboard are Width = 10 cm Height = 5 cm Example 6 When Neelima was 3 years old, her mother’s age was 10 times her age. What is the ratio of Neelima’s age to her mother’s age? What would be the ratio of their ages when Neelima is 12 years old? Would it remain the same?Given that when Neelima was 3 years old, her mother’s age was 10 times her age. Thus, Mother’s age = 10 × 3 = 30 years Now, Ratio of Neelima’s age to her mother’s age = (𝑁𝑒𝑒𝑙𝑖𝑚𝑎^′ 𝑠 𝑎𝑔𝑒)/(𝐻𝑒𝑟 𝑀𝑜𝑡ℎ𝑒𝑟𝑠 𝑎𝑔𝑒) = 𝟑/𝟑𝟎 = 1/10 = 1 : 10 We need to find Ratio when Neelima is 12 years old Ratio when Neelima is 12 years old We know that when Neelima = 3 years Neelima’s mother = 30 years So, when Neelima = 12 years = 3 + 9 years Neelima’s mother = 30 + 9 = 39 years Now, Ratio of Neelima’s age to her mother’s age = (𝑁𝑒𝑒𝑙𝑖𝑚𝑎^′ 𝑠 𝑎𝑔𝑒)/(𝐻𝑒𝑟 𝑀𝑜𝑡ℎ𝑒𝑟𝑠 𝑎𝑔𝑒) = 𝟏𝟐/𝟑𝟗 = 4/14 = 4 : 13 Thus, ratio changed from 1 : 10 to 4 : 13