Work out when a dog catches a rabbit with a head start, and add five fractions from Mahaviracharya using the LCM.
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In a chase, what matters is how much the gap shrinks each time.
When a chaser moves further each step than the one ahead, the gap shrinks by the difference each step.
A 150-foot head start, 9-foot leaps against 7-foot leaps.
Problem. A dog chases a rabbit that has a 150 ft head start. The dog jumps 9 ft every time the rabbit jumps 7 ft. In how many leaps does the dog catch the rabbit? (Textbook p. 64, Q11)
Catch-up questions with different numbers.
The book's dog (9 ft leaps) chases a rabbit (7 ft leaps) with a 150 ft head start. How many leaps?
The LCM of the denominators is the smallest common denominator.
To add fractions, rewrite them with the same denominator. Any common multiple of the denominators works, but the LCM is the smallest, so it keeps the numbers small.
8/15 + 1/20 + 7/36 + 11/63 + 1/21, and a surprising answer.
Problem. Add , , , and . How can we do it efficiently? (Textbook p. 64, Q13)
Fill in the steps of a smaller fraction sum.
Add 1/6 + 3/8 + 5/12 using the LCM of the denominators.
LCM of 6, 8 and 12 = .
1/6 = /24, 3/8 = /24, 5/12 = /24.
Sum = /24.