Percent and percent change

Percent is a ratio with denominator 100, so p% of a quantity is p/100 times it. Students find a percent of a number, find the whole from a part and a percent, and handle increase, decrease, tax, discount, and markup. Percent change is measured against the original amount unless the problem says otherwise. Two things to show with a bar: increasing 80 by 25% is not 80 + 25, and decreasing by 20% then increasing by 20% does not return to the start (it lands at 96%). Reverse-percent problems (the sale price is known, find the original) appear at a basic level here and in full in Math 7.

Specification · for a parent or teacher
Part no.
percent-change
Course
Advanced Math 6 · Unit 7
Also in
High School Math 1
Realm
Applied
Difficulty
3 of 4 Grade 6–7 core. Multi-step, first symbolic work.
Qty
5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

p%=p100p\% = \frac{p}{100}; percent of a quantity; whole given a part and a percent; increase, decrease, tax, discount, markup.

Ready when

they can show that −20% then +20% is not identity, with a bar.

Formulas

Percent of
p% of Q=p100Qp\% \text{ of } Q = \frac{p}{100} \cdot Q
Percent change
% change=neworiginaloriginal×100%\%\ \text{change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100\%
After a change
new=original×(1±p100)\text{new} = \text{original} \times \left(1 \pm \tfrac{p}{100}\right)

Watch for

increase 80 by 25% as 80 + 25; decrease 80 by 25% then increase by 25% and expect 80 back.

Before · requires

After · used by

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percent-change

Items: percent-change-01 · percent-change-02 · percent-change-03 · percent-change-04 · percent-change-05