Математика18 мин

Percents

Increase, decrease, reverse, and compound percentages without falling into the most common traps.

The percentage multiplier

Treat $p\%$ as the multiplier $1 + p/100$ (increase) or $1 - p/100$ (decrease). This converts every percent problem into multiplication.

\text{New} = \text{Old} \times \left(1 \pm \dfrac{p}{100}\right)

Increase

A laptop costs $800. Price rises 15%. New price?

Жауап: $920

If a sale price is given after a discount, divide by the multiplier — don't add the percent back.

Reverse

After a 20% discount, a coat costs $96. Original price?

Жауап: $120

$96 + 20\% = 115.20$ is wrong — that adds 20% of the discounted price, not the original.

\text{Final} = \text{Initial} \times m_1 \times m_2 \times \cdots \times m_n

Compound

A stock rises 10%, then falls 10%. Net change?

Жауап: Down 1%

Жаттығу

What single multiplier equals two successive 25% increases?

Жауап пен түсініктемені көру

Жауап: 1.5625

$1.25 \times 1.25 = 1.5625$ — a single 56.25% increase.