Ratios, proportions & percents · Topic 7 of 15

Percentages & Percent Problems

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Math · percentages

Change the percent to a decimal, then part = percent × whole; for percent change, divide the change by the original amount.

01 · The formulaPart = percent × whole

02 · Translate the wordsis → = of → × what → x

03 · Percent change% change = change ÷ original × 100

Percent = per 100; change it to a decimal before calculating must know

Solution strength % = grams per 100 mL (5% = 5 g/100 mL)

Translate: "is" → =, "of" → ×, "what" → x must know

Whole = part ÷ percent (as a decimal): 27 ÷ 0.45 = 60

Sale price = original − discount = original × (1 − rate) ($60 × 0.80 = $48)

Total with tax or tip = price × (1 + rate) ($48 × 1.05 = $50.40)

Percent proportion: part / whole = percent / 100

Part = percent × whole (percent as a decimal) must know

Percent = part ÷ whole × 100 (18 ÷ 72 = 0.25 = 25%) must know

% change = (new − original) ÷ original × 100 must know

Worked examples

15% of 60 = 0.15 × 60 = 9

80 kg → 84 kg: 4 ÷ 80 = 0.05 = 5% increase

500 mL of 5% dextrose = 5 × 5 = 25 g

Commonly confused

	Percent of a number	Percent change
Question sounds like	"What is 15% of 60?"	"From 80 to 84, what % increase?"
Method	Percent (as decimal) × whole	Change ÷ original × 100
Answer is	An amount (9)	A percent (5%)
Divide by	Nothing (just multiply)	The original, never the new value

Successive percents multiply: 20% then 10% off = 28% off, not 30%

Divide by the original: 50→60 is +20%, but 60→50 is −16.7%

Show 1 more fact

Over 100% → bigger than the whole: 150% of 40 = 60

Pearl

Percent change always divides by where you started, never by where you ended.

Practice this topic, then test the whole section.

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