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1: (above this)

 

2: A student accidentally added five to both the numerator and denominator of a fraction, changing the fraction's value to 1/2. If the original numerator was a 2, what was the original denominator?

 

3: The perimeter of a rectangle of width 6 feet is 10 yards. In square feet, what is the area of the rectangle?

 

4: Sarah and her friends are going blueberry picking. Sarah picks b blueberries. Michael picks 3 more than half as many as Sarah, and David picks 5 more than Michael. In addition, Kaycee picks 10 less than 3 times as many as David, and Hannah picks twice as many as Kaycee. Find an expression in terms of b for the number of blueberries that Hannah picked.

 Sep 23, 2019
 #1
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1.Re-writting this with fractional exponents gets: \(\frac{8^\frac{1}{4}}{4^\frac{1}{3}}\)

Now write 8 and 4 as powers of two, and then multiply the two exponents by the power-of-a-power exponent law (or whatever its called, been a while since I've done this) yields \(\frac{(2^3)^\frac{1}{4}}{(2^2)^\frac{1}{3}}=\frac{2^\frac{3}{4}}{2^\frac{2}{3}}\)

By the exponent division law (again, might have gotten the name wrong), you subtract the exponent in the denominator from the exponent in the numerator to get the exponent in the quotient.

\(\frac{2^\frac{3}{4}}{2^\frac{2}{3}}=2^{\frac{3}{4}-\frac{2}{3}}=\boxed{2^\frac{1}{12}}\)

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 Sep 23, 2019
 #2
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2. Call the original fraction \(\frac{n}{d}\), and the modified fraction \(\frac{n+5}{d+5}=\frac{1}{2}\)

You are told that the original numerator was 2, so n=2 and \(\frac{2+5}{d+5}=\frac{1}{2}\). To find the original denominator all you need to do now is solve the equation. I'll leave that to you. I would start by multiplying both sides by d+5.

 Sep 23, 2019

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