5. Percents in the Real World

'Percent' means per hundred. \(45\%\) literally means \(\frac{45}{100} = 0.45\). That single idea connects all three forms:
\[ 45\% = \frac{45}{100} = 0.45. \]
Finding a percent of a number: turn the percent into a decimal and multiply. \(30\%\) of \(150 = 0.30 \times 150 = 45\).

Discounts: a \(\$80\) shirt at \(25\%\) off. The discount is \(0.25 \times 80 = \$20\), so you pay \(80 - 20 = \$60\). Shortcut: paying after a \(25\%\) discount means paying \(75\%\), so \(0.75 \times 80 = \$60\) in one step.

Percent change: \(\dfrac{\text{new} - \text{old}}{\text{old}} \times 100\%\). A price rising from \(\$50\) to \(\$65\): \(\frac{65-50}{50} = \frac{15}{50} = 0.30 = 30\%\) increase.

💡 Tip: 'of' usually means multiply, and 'is' usually means equals. 'What is 20% of 60?' becomes \(x = 0.20 \times 60\).