Fractions, Decimals, Percents, and Ratios
What this domain tests
This domain covers fraction fluency, decimal place value, percent relationships, and ratio and proportion reasoning. OAT items often hide a percent or ratio inside a multi-step scenario, so the key skill is identifying the base and keeping units attached.
Core rules
- To add or subtract fractions, rewrite over the least common denominator; to multiply, multiply numerators and denominators; to divide, multiply by the reciprocal.
- Decimal to percent: multiply by 100 and add the percent sign. Percent to decimal: divide by 100.
- Percent change = (new - old) / old x 100%. The original value is the denominator.
- A ratio compares quantities; a proportion sets two ratios equal and is solved by cross multiplication.
- Successive percent changes multiply; they do not add. A 20% increase followed by a 20% decrease gives 1.2 x 0.8 = 0.96, a net 4% decrease.
Worked example
An $80 item is marked down 25%, then 8% sales tax is added to the sale price. Sale price = 80 x 0.75 = $60. Tax is applied to $60, not $80: 60 x 0.08 = $4.80, so the final cost is $64.80. Equivalently, 80 x 0.75 x 1.08 = $64.80.
Traps
A 25% discount is not the same as a 25% tax because the bases differ. Do not add successive percentages. In the question what percent of 40 is 10, the base is 40, so the answer is 25%, not 400%. When converting a fraction to a decimal, divide the numerator by the denominator rather than guessing place value. Check whether a ratio question asks for part-to-part or part-to-whole.