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diamong [38]
2 years ago
12

Mary ran 3/4 mile, Lila ran 2/3 mile, and sue ran 3/8 mile.Who ran the farthest?Draw a diagram to solve.

Mathematics
1 answer:
Jlenok [28]2 years ago
8 0

Answer: Mary ran the farthest.

Step-by-step explanation:

To be able to see who ran the farthest you have to find the GCD (greatest common denominator) of all the denominators 4, 3, and 8, which turns out to be 24. If you multiply all the fractions, numerator and denominator, by what makes each individual denominator equal to 24, you can find the biggest one.

4 times 6 is 24, 3 times 8 is 24, and 8 times 3 is 24, so you multiply each fraction by those respective numbers to get 3/4 = 18,24, 2/3 = 16/24, and 3/8 = 9/24.

So, Mary ran the farthest.

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Man this one is a world of its own :D Just a quick question are you a fellow Add Math student in O levels i remember this question from back in the day :D Anyhow Lets get started

For this question we need to know the following identities:

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1-\frac{1}{1-sec^2x} \\\\\frac{1-sec^2x-1}{1-sec^2x} \\\\\frac{-sec^2x}{1-sec^2x} \\\\\frac{-(1+tan^2x)}{-tan^2x}

now break the LCM

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because 1/tan = cot x

and furthermore,

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now we solve the above part and replace the bottom most part that we solved with cosec^2x

\frac{1}{1-\frac{1}{cosec^2x} } \\\\\frac{1}{1-sin^2x} \\\\\frac{1}{cos^2x}\\\\sec^2x

Hence proved! :D

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