Percentages

Per cent means per hundred; every percentage problem is a fraction over 100.

“15% of 80” means 15 hundredths of 80: multiply by 15/100. The same idea handles increases (multiply by 1.15) and decreases (multiply by 0.85), and reverse questions (“80 is 15% of what?”) become a one-line equation.

Umzekelo osebenzelayo: `what is 15% of 80`

Arithmetic · Arithmetic

Evaluate 15% of 80

Inyathelo ngenyathelo

15 \cdot \frac{1}{100} \cdot 80 = 12
Evaluate.

Bonisa impendulo

Symbols used here

\pm

plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.

\neq

not equal
The two sides are different.

\leq,\ \geq

less/greater than or equal
Inequalities that allow equality; < and > exclude it.

\approx

approximately equal
Equal to the precision shown, not exactly.

\sqrt{x},\ \sqrt[n]{x}

square root, n-th root
The non-negative number whose square (n-th power) is x.

a \bmod n

remainder
What is left after dividing a by n.

per cent
Per hundred: 15% = 15/100.

a : b,\ \frac{a}{b}

ratio, fraction
a for every b; a divided by b.

How to: Percentages

Evaluate.

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

Zama ngokwakho

IiNkqubo Arithmetic

Order of operations Fractions Powers and roots

Umzekelo osebenzelayo: what is 15% of 80