Question 4 - Figure it out - Page 126 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

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Question 4 How many multiples of 9 are there between the numbers 4300 and 4400?Step 1: Find the first multiple after 4300 Sum of digits of 4300 is 4 + 3 = 7 To get to 9, we need 2 more. So, 4302 is the first multiple. Step 2: Find the last multiple before 4400 Sum of digits of 4400 is 4+4=8. We have a remainder of 8. If we subtract 8 from 4400, we get 4392. This is the last multiple. Step 3: Count them The sequence is: 4302, 4311, 4320 ... 4392 We can just count this manually by continuing the sequence The extended sequence is 4302, 4311, 4320, 4329, 4338, 4347, 4356, 4365, 4374, 4383, 4392 Thus, there are 11 multiples of 9 We can also count by quick math (𝑳𝒂𝒔𝒕 𝑵𝒖𝒎𝒃𝒆𝒓 − 𝑭𝒊𝒓𝒔𝒕 𝑵𝒖𝒎𝒃𝒆𝒓)/𝟗+𝟏 =(4392 − 4302)/9+1 =90/9+1 = 10 + 1 = 11 Thus, there are 11 multiples of 9