## ADVANCED

- Compare the 2 calculations done on a “calculator with a % button” in Episodes 6 and 8. Only portion and base calculations use the % button. Calculating rate (episode 07) can`t possibly use the % button. Why?

- Look at & compare the portion or base calculations done on a “calculator with a % button” and the steps that don’t use the % button. The % button is a convenience shortcut for 1 well-known math operation. What is this exact built-in math operation the calculator does when the % button is pressed?

- Addition and subtraction are reverses of each other. A whole number (1) can be subtracted from a number (4) and added back to the result (3) to get the same number we started with (4):

4 – 1 = 3 , then 3 + 1 = 4

It does not work out the same way with percents:

$4.00 – 25% = $3.00 , but $3.00 + 25% = $3.75 only.

Why does adding and subtracting with percents not work out like it does with whole numbers?

4. Look at Episode 1, adding and subtracting percents. How does that addition or subtraction differ from the above example?

5. To solve % **word problems** efficiently, you need to be able to:

a) Identify which calculation to do (based on word clues) and

b) You have to remember the formula to use accordingly.

Contrary to popular belief, calculators are not much help as they don`t do either one of these 2 things. Calculators are limited tools. They don`t do the thinking or the math. They only calculate.

To help you get started with memorizing the formulas from Episodes 7, 8, and 6, print them out for yourself, study & compare.

portion ÷ base x 100 = rate portion ÷ percent x 100 = base percent ÷ 100 x base = portion

The full words in the formulas can be replaced by a single letter. This is how they look now:

\[\frac{P}{B}\text{ = R}\]

(Episode 7)
\[\frac{P}{R}\text{ = B}\]

(Episode 8) B x R = P (Episode 6)

a) The following visual of a triangle may help with memorizing % formulas and their relationships:

Portion, base and rate can combine in 3 ways (see the 3 formulas above):

If Portion is known, it can only be divided, either by Base or Rate.

(P is always over B or R, “over” implies fractions, and all fractions are divisions) If Base and Rate are known, they are to be multiplied.
(In formulas, amounts for multiplication are always written side-by-side)

b) Some people like the 3 quantities arranged like fractions:

\[\frac{P}{B}\text{ = R}\]

\[\frac{P}{R}\text{ = B}\]

B x R = P
These letters can be replaced by numbers to see an interesting relationship.

Portion (P) can be replaced by 1, base (B) can be 4, and (R) rate can be replaced by 0.25

\[\frac{1}{\color{Blue}4}\]

= **0.25**
\[\frac{1}{\color{Red}{0.25}}\]

= **4** 4 x 0.25 = 1
Notice that in fractions the 4 and 0.25 (the denominator and the result) can trade places. This fraction fact may help memorize the formulas knowing that if portion (P) is given a division must follow by either the base or rate to calculate the missing quantity.

A formula is a symbolic short-hand way to write calculation procedures. Use a memory jogger that`s easiest to remember for you.