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Percentage basics

What is a percentage? A friendly introduction

Percentages are fractions of 100 dressed up for everyday conversation.

A percentage is a way of expressing a number as a portion of one hundred. The symbol % is a shorthand for "per cent" — Latin for "per hundred" — and it lets us compare quantities of different sizes on the same scale. Saying you tipped £12 tells the reader nothing without context; saying you tipped 15% tells them you tipped well, regardless of the bill size.

Once you understand that every percent is a fraction with 100 quietly sitting in the denominator, everything else — increase, decrease, change, conversion — falls out of the same idea. This guide starts from that foundation, then walks through the formula you will use most.

The Percent of a number formula

The formula is short:

(p ÷ 100) × N

Convert the percent to a decimal, then multiply by your number. 35% of 280 is 0.35 × 280 = 98.

When to reach for it: Use this whenever a sentence contains the word of: tips, sales tax slices, exam scores, commissions on revenue.

The three ways percentages appear in everyday math

Every percentage problem you meet is one of three sentences:

  • Percent of a number. "What is 18% of $42?" — pure multiplication.
  • Percent change. "What is the percent change from 80 to 110?" — compares two values to one.
  • Percent of a percent. "An extra 10% off the already-20% sale price." — applies one percent on top of another.

Once you can spot which of the three you are looking at, picking the right formula stops being a guess.

Worked examples you can copy

Each example walks the same formula with different numbers so the steps stay familiar.

  • 20% of 150 → 20% × 150 ÷ 100 = 30.
  • 7.5% sales tax on $80 → 7.5% × 80 ÷ 100 = 6.
  • 12% tip on $46 → 12% × 46 ÷ 100 = 5.52.
  • 15% of a 60-min hour → 15% × 60 ÷ 100 = 9.

Common mistakes to avoid

  • Multiplying by the raw percent (e.g. 8) instead of the decimal rate (0.08). Always divide by 100 first.
  • Treating "p% more than N" as "p% of N". They differ by the original N.
  • Reusing the wrong member of the formula family — increase, decrease, change and percent-of all live in the same neighbourhood.
  • Ignoring units. Percentages are dimensionless; both parts of a ratio must share the same unit.

Calculation tips & best practices

  • Write the formula at the top of your scratch paper, then plug in numbers. The visible formula prevents algebra slips.
  • Convert every percentage to a decimal before you do anything else.
  • Sanity-check magnitude: the result should be smaller than the whole when you take a percent of it.
  • Reverse the calculation as a check (a 25% slice times four should give back the whole).

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Note: Percentage results are estimates for informational use only. Always verify critical financial, tax, or business calculations with a qualified professional.

Try the basic percentage calculator

Open the calculator in Basic mode and ask any "what is X% of Y" question. The breakdown shows every step so the formula stays familiar.

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