Pāṭīgaṇita, a book written by Sridharacharya in the 9th century CE,…

Question 15 of 20intermediate🔧 ApplyNumerical3 marks

Pāṭīgaṇita, a book written by Sridharacharya in the 9th century CE, mentions this problem: "Friend, after thinking, what sum will be obtained by adding together $1 \div \frac{1}{6}$ , $1 \div \frac{1}{10}$ , $1 \div \frac{1}{13}$ , $1 \div \frac{1}{9}$ , and $1 \div \frac{1}{2}$ . What should the friend say?

Correct Answer

Rule: Division of fractions uses reciprocals: $1 \div \frac{1}{n} = n$ .

Step 1: $1 \div \frac{1}{6} = 1 \times 6 = 6$ Step 2: $1 \div \frac{1}{10} = 1 \times 10 = 10$ Step 3: $1 \div \frac{1}{13} = 1 \times 13 = 13$ Step 4: $1 \div \frac{1}{9} = 1 \times 9 = 9$ Step 5: $1 \div \frac{1}{2} = 1 \times 2 = 2$

Step 6: Sum = $6 + 10 + 13 + 9 + 2 = 40$

Answer: The sum is 40.

Exercise: Figure it Out (Section 4) | Q: 4 | (Page Page 25)

For More Understanding

Explanation

The chapter explains division of fractions using reciprocals. $1 \div \frac{1}{n} = n$ . So $1 \div \frac{1}{6} = 6$ , $1 \div \frac{1}{10} = 10$ , $1 \div \frac{1}{13} = 13$ , $1 \div \frac{1}{9} = 9$ , $1 \div \frac{1}{2} = 2$ . Sum = $6 + 10 + 13 + 9 + 2 = 40$ .

Solution Steps

Step 1: $1 \div \frac{1}{6} = 1 \times 6 = 6$
Step 2: $1 \div \frac{1}{10} = 1 \times 10 = 10$
Step 3: $1 \div \frac{1}{13} = 1 \times 13 = 13$
Step 4: $1 \div \frac{1}{9} = 1 \times 9 = 9$
Step 5: $1 \div \frac{1}{2} = 1 \times 2 = 2$
Step 6: Sum = $6 + 10 + 13 + 9 + 2 = 40$

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