Percentage Reversal (a% of b = b% of a)

Mental Math · Axiom Academy

of b equals of a — so you may always compute whichever of the two is easier. Picture " of b " as a rectangle a tall and b wide, measured in hundredths. Its area is hundredths — and that area is all the answer depends on. Watch the rectangle change shape while its area never moves : every stop along the way is a different, equally true way of naming the same amount. The same product, split into a percent and a number two ways The swap is only worth making when the reversed version lands on a percentage you already know cold — is a half, is a quarter, is three quarters, is a shift of the decimal point. The animation trades the two numbers between the slots, then settles the easy reading by cutting a bar into those parts. of 50 becomes of 18 — half of eighteen, which is 9 . of 25 becomes of 24 — a quarter of twenty-four, which is 6 . of 350 becomes of 2 — three and a half twos, which is 7 . of 43 becomes of 37 . Both are awkward; the swap has gained you nothing. Look at the two numbers and ask which one you would rather take a percentage of . If either number is a benchmark percentage — 10 , 20 , 25 , 50 , 75 , 100 — put that one in the percent slot and read off the answer. Reversal is a fact about the phrase " percent of ". It says nothing about " percent change ", and the two are easy to confuse. Raising a quantity by and then lowering it by does not return it to where it began — watch the bar finish below the line it started on.

This is the written version of the interactive lesson above. See the full Mental Math course.