SOLUTION: How do I explain to a 6th grader the process to figure out, "64% of what number is 84". thanks.

Question 863607: How do I explain to a 6th grader the process to figure out, "64% of what number is 84".
thanks.
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
64%=.64=64/100
% of means multiply
Let x be the missing number
64% of x=84
.64x=84
64/100x=84
64x=8400
x=131.25
Who picked that number?
Bad example for learning percents.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i would start with discussing the reversibility of operations, such as:

if 3 * 4 = 12, then 12 / 4 = 3 and 12 / 3 = 4
this is a basic rule of reversibility of operations that states that, in general:
if a * b = c, then b = c/a and a = c/b.

this rule of reversibility applies to all mathematical operations.

for example:

if 4 + 3 = 7, then 7 - 4 = 3 and 7 - 3 = 4

etc.

you can demonstrate this rule by several examples, such as:

4 * 2 = 8
8 / 4 = 2
8 / 2 = 4

or:

20 * 5 = 100
100 / 20 = 5
100 / 5 = 20

you can then tell the student that the questions involves this same principle, because:

64% of a number is equal to .64 * the number.

this is another rule that the student should know in order to solve this problem.

now you can introduce the problem again such as:

64% of what number is equal to 84.

this is the same as:

.64 * what number is equal to 84.

by the reversibility of operations rule, this means that:

84 / .64 = the number

or:

84 / the number = .64

the student, by this time, should know how to divide 84 by .64.

for a problem as sophisticated as this one, however, i would resort to the calculator so the student doesn't get bogged down in the arithmetic.

after applyig the division, the studet should get:

84 /.64 = 132.25

now you can confirm for the student that this answer is good by applying the rule of reversibility to get:

.64 * 132.25 = 84

84 / .64 = 132.25

84 / 132.25 = .64

you can use your calculator again for this part.

if you want to show the student without using the calculator, then choose a simpler problem, such as:

50% of what number = 200

same deal applies

this means that .5 times what number = 200

this is true if and only if:

200 / .5 = the number or:
200 / the number = .5

you then divide 200 by .5 to get 200 / (1/2) which becomes 200 * (2/1) which becomes 400

400 is the number.

you confirm by applying the rule.

.5 * 400 = 200

200 / .5 = 400

200 / 400 = .5

the rule of reversibility is how the students check their work all the time so this should not be a novel idea to the student.

by now the student should have learned that 64% of a number is the same as .64 times the number.

if not, you may have to sped some time teaching about that concept.

at the end, you can show the student the short cut.

if 64% of a number is equal to 84, the you find the number by dividing 84 by .64.

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