Study card

The formulas, the moves, and the traps for Topic 2, in one printable page.

Key formulas

The moves to memorize. Each one shows up multiple times across the topic.

Percent ↔ decimal

shift the decimal two places:
25% ↔ 0.25

Decimal → percent: shift right (number gets bigger). Percent → decimal: shift left (number gets smaller). Always two places, never one.

Three percent shapes

Find the part: part = rate × base  (20% of 50 = 10)

Find the percent: rate = part ÷ base × 100  (12 is 24% of 50)

Find the whole: base = part ÷ rate  (8 is 25% of 32)

Always convert the percent to a decimal first. Always identify which piece is missing before you decide multiply vs. divide.

Multiplier shortcut

Percent ON: × (1 + rate)  | 
Percent OFF: × (1 − rate)

Tip 18% → ×1.18. Sale 25% off → ×0.75. Stack moves on a single price: $120 × 0.75 × 1.07 = $96.30.

Unit conversion (multiply by 1)

A conversion factor (e.g. 5280 ft / 1 mi) equals 1.

Set it up so the unwanted unit cancels on the bottom.

Chain factors when one isn't enough: 5 mi × (5280 ft/mi) × (12 in/ft) = 316,800 in.

Temperature (the exception)

F = (9/5) × C + 32  |  C = (5/9) × (F − 32)

Different zero points means dimensional analysis breaks. Use the formula. Multiply BEFORE you add or subtract.

Budget

income = expenses + savings

savings rate = savings ÷ income × 100

10–20% savings rate is solid for an early-career budget.

Common mistakes

The traps that cost real points. Memorize these as much as the formulas.

Forgetting to convert percent to decimal. 7% of 80 is 0.07 × 80 = 5.6, not 7 × 80 = 560. Always strip the % sign first.
Shifting the decimal one place instead of two. 0.4 = 40%, not 4%. 28.5% = 0.285, not 2.85.
Wrong direction on a discount. "30% off" means you PAY 70%, not 30%. The discount AMOUNT is 30% of price; the FINAL price is what you pay.
Tax on the wrong price. When stacking discount + tax, tax applies to the SALE price, not the original. Discount first, then tax.
Conversion factor upside down. If you got an answer in weird units (ft²/in or kg²/lb), the fraction was backwards. The unit you want to cancel goes on the BOTTOM.
Compound units only converted on top. Converting mph to ft/sec needs BOTH conversions: mi → ft on top, hr → sec on the bottom. Don't forget the time piece.
Squared units only converted once. in² to cm² needs the in/cm factor TWICE. The hint to look for: "one factor is applied twice."
F↔C order of operations. Multiply by 9/5 (or 5/9) BEFORE adding or subtracting 32. The parentheses in the formula are not optional.
Rounding too early. When ALEKS says "do not round," carry full precision through every step. Rounding 1.6 to 2 in a speed conversion will throw the answer off by 25%.
Hand-typing numbers in Excel. Always reference cells (=A2*0.07 or =$B$1*A2) so the formula updates if any input changes. The grader and your future self will thank you.

Quick reference

Conversion factors worth memorizing. ALEKS gives you these in the prompt, but knowing them speeds you up.

Distance

mi = 5,280 ft  ·  1 ft = 12 in  ·  1 yd = 3 ft

in = 2.54 cm  ·  1 m = 3.28 ft  ·  1 km = 0.621 mi

Weight

lb = 16 oz  ·  1 T = 2,000 lb  ·  1 kg = 2.2 lb

oz ≈ 28.35 g  ·  1 g = 1,000 mg

Volume

gal = 4 qt  ·  1 qt = 2 pt  ·  1 cup = 8 fl oz

L ≈ 33.81 fl oz  ·  1 L ≈ 0.264 gal  ·  1 tsp ≈ 4.93 mL

Time

d = 24 h  ·  1 h = 60 min  ·  1 min = 60 sec

h = 3,600 sec  ·  1 yr = 365 d

Common percents

50% = 0.5 = 1/2  ·  25% = 0.25 = 1/4  ·  75% = 0.75 = 3/4

20% = 0.2 = 1/5  ·  33.3% ≈ 0.333 = 1/3  ·  10% = 0.1 = 1/10

Topic 2 overview Glossary