Question 6 - Figure it out - Page 93, 94, 95 - Chapter 4 Class 7 - Another Peek beyond the Point (Ganita Prakash II)

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Question 6 The following problem was set by Sridharacharya in his book, Patiganita. “ 6 1/4 is divided by 2 1/2 , and 60 1/4 is divided by 3 1/2 . Tell the quotients separately.” Can you try to solve it by converting the fractions into decimals?First, we convert fractions into decimals Now, 𝟏/𝟒 = 0.25 and 𝟏/𝟐 = 0.5 So, we can write 𝟔 𝟏/𝟒=𝟔.𝟐𝟓 𝟐 𝟏/𝟐=𝟐.𝟓 And, 60 1/4=60.25 3 1/2=3.5 Now, we solve the division separately 𝟔 𝟏/𝟒 is divided by 𝟐 𝟏/𝟐 This means 6.25 ÷ 2.5 = 6.25/2.5 Removing decimal points = 6.25 × 1/2.5 = 625/100× 1/(25/10) = 625/100× 10/25 = 𝟔𝟐𝟓/𝟐𝟓× 𝟏𝟎/𝟏𝟎𝟎 = 25 × 1/10 = 2.5 𝟔𝟎 𝟏/𝟒 is divided by 𝟑 𝟏/𝟐 This means 60.25 ÷ 3.5 = 60.25/3.5 Removing decimal points = 60.25 × 1/3.5 = 6025/100× 1/(35/10) = 6025/100× 10/35 = 𝟔𝟎𝟐𝟓/𝟑𝟓× 𝟏𝟎/𝟏𝟎𝟎 = 1205/7× 1/10 = 𝟏𝟐𝟎𝟓/𝟕𝟎 Let’s divide by long division Thus, 60.25 ÷ 3.5 = 17.214… We stop after 3 decimal places because the division will become very long