Question

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A rabbit’s fur grows at the rate of 5 over 2 inches per month.

How many months will it take the rabbit’s fur to grow 15 over 4 inches?

Explain your answer using expressions and words.

Answers

  1. Answer:
    1.5 months
    Step-by-step explanation:
    First, make \frac{5}{2} so it has a common demoninator as \frac{15}{4}.
    We need the demoninator to be the same so we can multiply \frac{5}{2} by 2 to make it \frac{10}{4}.
    So, a rabbit’s ear grows \frac{10}{4} of an inch in a month.
    To find how many months, it will take, we have to divide \frac{15}{4} by \frac{10}{4}.
    To divide fractions, we can multiply with the reciprocal.
    So,  \frac{15}{4} * \frac{4}{10} is \frac{60}{40} which reduces to \frac{6}{4} which, in decimal form is equal to 1.5 months.

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  2. Growth rate = 5/2 inches per month
    The fur length after y months:
    Fur length = 5/2 × y
    Therefore, to have a fur length of 15/4 inches :
    15/4 = 5/2 × y
    3.75 = 2.5y
    Divide both sides by 2.5 to isolate y
    3.75/2.5 = y
    1.5 = y
    it will take a month and half to have a fur of 15/4 inch length

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