Numbers and Operations on Numbers
What you need to know
This domain covers the arithmetic that everything else rests on: place value, the four operations with whole numbers, fractions, decimals, percents, signed numbers, exponents, square roots, scientific notation, ratios, proportions, and order of operations. You should be able to move a value between fraction, decimal, and percent form without hesitation, and you should be comfortable estimating before you compute.
Traps to watch for
- Order of operations: multiplication and division before addition and subtraction, and exponents before either. Work left to right within the same tier. In
3 + 4 × 2the answer is 11, not 14. - Negative signs: subtracting a negative becomes addition; a negative squared is positive, but a negative raised to an odd power stays negative.
- Percent change: a 20% discount followed by 20% off the reduced price is not a 40% discount. Apply each percent to the current amount.
- Fraction division: invert and multiply, and remember the whole number needs a denominator of 1.
- Unit rates: keep the units attached so you can tell whether to multiply or divide.
Rule of thumb
When a problem mixes fractions and decimals, convert everything to one form first. Fractions are usually safer when the decimals repeat; decimals are faster when the answer choices are decimals.
Worked example
A jacket costs $80 and is marked down 25%, then an additional 10% is taken off the sale price. Final price: 80 × 0.75 = 60, then 60 × 0.90 = $54. The total discount is 32.5%, not 35%.