By what percent will a fraction increase if its numerator is increased by 60% and its denominator is decreased by 20%?
(n*1.60)/(d*0.80) = (n/d)(1.60/.80) = (n/d)(2)
so, the fraction is doubled. What percent increase is that? And it is not 200%!
Steve, it is.
THE MATH IS RIGHT BUT THE ANSWER IS 100% BECAUSE THE FRACTION IS DOUBLED BY ITSELF, LIKE STEVE SAID.
To determine the percentage increase in a fraction when the numerator is increased and the denominator is decreased, you need to follow these steps:
Step 1: Start with the original fraction, let's call it A/B.
Step 2: Increase the numerator by the given percentage. In this case, the numerator is increased by 60%, so the new numerator would be (A + (A * 60%)).
Step 3: Decrease the denominator by the given percentage. In this case, the denominator is decreased by 20%, so the new denominator would be (B - (B * 20%)).
Step 4: Calculate the new fraction with the updated numerator and denominator. The new fraction is ((A + (A * 60%)) / (B - (B * 20%))).
Step 5: Calculate the percentage increase by subtracting the original fraction from the new fraction, dividing it by the original fraction, and multiplying by 100.
Let's calculate it step by step:
Step 1: Original fraction = A/B.
Step 2: Increased numerator = A + (A * 60%) = A + (0.6A) = 1.6A.
Step 3: Decreased denominator = B - (B * 20%) = B - (0.2B) = 0.8B.
Step 4: New fraction = (1.6A) / (0.8B) = 2A/B.
Step 5: Percentage increase = ((2A/B - A/B) / (A/B)) * 100.
Simplifying further:
Percentage increase = ((2A - A) / A) * 100.
Percentage increase = A / A * 100.
Percentage increase = 100%.
Therefore, the fraction will increase by 100% when the numerator is increased by 60% and the denominator is decreased by 20%.