When we need to find the percent of the part and the quantity, a new format with which to write our formula (1) needs to be introduced.
From (1) q = (p /100) x w. We move variables to get:
(4) p = (q / w) x 100 =
(q x100)/ w
This formula now allows students to solve for percent, p. Students will need to be shown how the letters or variables have been moved around, yet remain consistent with the meaning of the percent formula (1). Consider our practice type of example: What percent of 25 is 20?
Students now familiar with using formulas (1-3), should not have difficulty using our new formula (4): p = (20/25) x 100= (20 x100) /25 p = 80%
Consider this word problem using the formula (4): On the last quiz, Sheila answered 18 out of 20 questions correctly. What was her percentage of correct answers on the quiz? Or
What is Kevin’s free throw percentage if he made 30 baskets out of 40 attempts?
These problems require the student to divide the quantity by the whole and then multiply by 100. Students before trying to solve, need to examine the problem to see what they already know and what they need to find out.
The last formula we will introduce to the students that is developed from formula (1) is finding the whole,
w
, when we know the quantity, q, and the percentage,
p
: (5) w = (q / p) x 100 = (q x 100) / p
Consider the word problem using formula (5): James scored 85% on his quiz. He answered 17 questions correctly. How many total questions were on the quiz?
Students will need to put in the correct quantity, q, 17 and multiply by 100; then divide the result by the percent, p, 85. 17 x 100/ 85 = 20 questions on the quiz
Another-Katie’s free throw percentage was 90%. She successfully made 45 shots. How many free throws did she attempt? 45 x 100/90 = 50 free throws
Again careful examination of the problem must be performed. Are you looking for the QUANTITY, PERCENT OR WHOLE? Students can work in pairs or groups to brainstorm the problem and try to agree on the formula to find the solution. They should be able to support their decision and if their answer is reasonable. Sets of word problems involving finding quantity, percent and whole follow the unit. Activities follow the unit.
