"Per cent" means "out of 100," so $X\%$ is the fraction $\frac{X}{100}$ — and also the decimal you get from dividing $X$ by 100. This decimal is the multiplier: to increase by $X\%$, multiply by $(1+\frac{X}{100})$; to decrease by $X\%$, multiply by $(1-\frac{X}{100})$. Finding a plain percentage of an amount is the same idea without any "1 ±" — just the decimal itself.

Build it up from benchmarks you can find by simple division:

• $10\%$: divide by 10
• $5\%$: half of 10%
• $1\%$: divide by 100

Example: Find 16% of 60: $10\%=6$, $5\%=3$, $1\%=0.6$, so $16\% = 6+3+0.6=9.6$.

You can also use common fraction equivalents: $25\%=\frac14$, $50\%=\frac12$, $75\%=\frac34$, $10\%=\frac{1}{10}$. Finding $35\%$ of $60$ via $\frac{7}{20}\times 60$ gives $21$.

Put the part over the whole, then multiply by 100:

Example: Express 40 as a percentage of 50: $\frac{40}{50}\times 100 = 80\%$. This also works above 100% — express 50 as a percentage of 20: $\frac{50}{20}\times100=250\%$.

The multiplier method is fastest: work out $(1 \pm \text{decimal})$ once, then multiply.

• Increase £200 by 30%: multiplier $=1.30$, so $200\times1.3=£260$.
• Decrease 700 g by 20%: multiplier $=0.80$, so $700\times0.8=560$ g.

The "build-up" method (find 30% separately, then add it on) gives the same answer but is slower and more error-prone for awkward percentages like 17.5% — the multiplier does it in one step.

Simple interest adds the same amount of interest every year, calculated only on the original (principal) amount $P$:

where $r$ is the annual rate as a decimal and $t$ is the time in years (matching whatever time unit the rate uses).

Example: £2,100 invested for 3 years at 2% simple interest: $I = 2100 \times 0.02 \times 3 = £126$.

The same formula models depreciation (value falling by a fixed percentage of the original value each year) just by using a negative rate.

Example: A £10,000 car depreciates by 9% of its original value per year for 8 years: $A = 10000(1 - 0.09\times8) = 10000(0.28) = £2800$.

A laptop costs £850 plus VAT at 20%. Find the total price, then find what percentage a £150 deposit is of that total.

1. VAT multiplier: $1.20$. Total price: $850 \times 1.20 = £1020$.
2. Deposit as a percentage of total: $\dfrac{150}{1020}\times100 \approx 14.7\%$ (1 d.p.).