Pre-Algebra — Numbers & First Variables

Fractions, decimals & percents

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: these are three costumes for the same number: ½ = 0.5 = 50%. To add fractions, give them a common denominator first; a percent is just "per hundred," so 20% means ×0.20.

add_{frac} = \frac{1}{3} + \frac{1}{6}

0.5000

common denominator 6: 2/6 + 1/6 = 1/2

✓ pass

add_{frac} == 0.5

the fractions add to one half

discount = 0.2 \cdot 80

16

20% of \$80 is \$16

✓ pass

discount == 16

percent = "per hundred", so ×0.20

Real-world hook: fractions/decimals/percents are tips, taxes, discounts, and interest — the most-used math in daily life.

Try it yourself: add ¾ + ⅛ (common denominator 8).

frac_{you} = \frac{3}{4} + \frac{1}{8}

0.8750

✏️ Your turn: add 3/4 + 1/8. Rewrite 3/4 as 6/8 first. (The answer is 7/8 = 0.875.)

✓ pass

\mathrm{abs}\left(frac_{you} - \frac{3}{4} + \frac{1}{8}\right) < 10^{-9}

green when your sum equals 3/4 + 1/8