Question 18 of 18advanced🔧 ApplyNumerical3 marks

Here is a problem posed by the ancient Indian Mathematician Mahaviracharya (850 C.E.). Add together 8/15, 1/20, 7/36, 11/63 and 1/21. What do you get? How can we find this sum efficiently?

Correct Answer

Given: Add 8/15 + 1/20 + 7/36 + 11/63 + 1/21

Method: Find LCM of denominators to get common denominator

Prime Factorizations: 15 = 3×53 \times 5 20 = 2² × 5 36 = 2² × 3² 63 = 3² × 7 21 = 3×73 \times 7

LCM Calculation: LCM = 2² × 3² × 5×75 \times 7 = 4×94 \times 9 × 5×75 \times 7 = 1260

Converting fractions: 8/15 = 672/1260 1/20 = 63/1260 7/36 = 245/1260 11/63 = 220/1260 1/21 = 60/1260

Calculation: Sum = (672 + 63 + 245 + 220 + 60)/1260 Sum = 1260/1260 Sum = 1

Answer: The sum is 1.

Exercise: Figure it Out (Section 6) | Q: 22 | (Page Page 18)
For More Understanding

Explanation

The efficient method to add fractions is to find the LCM of all denominators, which gives the common denominator. LCM(15, 20, 36, 63, 21) = 1260. Converting all fractions to this denominator and adding gives exactly 1. This demonstrates how LCM is essential for adding fractions with different denominators.

Solution Steps

  1. Step 1: Find LCM of denominators 15, 20, 36, 63, 21.

  2. Step 2: LCM = 2² × 3² × 5×75 \times 7 = 1260.

  3. Step 3: Convert each fraction to denominator 1260.

  4. Step 4: Add numerators: 672 + 63 + 245 + 220 + 60 = 1260.

  5. Step 5: Result = 1260/1260 = 1.

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