HESI A2 Math common mistakes
HESI A2 Math · Understand the traps and how to avoid them.
When adding or subtracting fractions with unlike denominators, the candidate adds the numerators and adds the denominators (for example, 1/2 + 1/3 written as 2/5) instead of building a common denominator first.
This happens because whole-number addition was learned first and the candidate carries the same 'add the parts' reflex into fraction notation. The fraction bar reads as a separator rather than as a division that defines a value, so the two denominators feel like separate objects to be combined rather than a shared unit that must be matched before quantities can be joined.
What to do instead
Before any fraction addition or subtraction, write the prime factorization of each denominator and build the least common multiple, then rewrite each fraction with a matching multiplier on top and bottom. Check the result against a rough estimate: 1/2 + 1/3 must land between 1/2 and 1, so any answer below 1/2 signals the error. Practice 10 mixed-denominator problems and state the LCM aloud before computing.
The candidate inverts the wrong fraction when dividing, flipping the first fraction instead of the divisor, or multiplying straight across without inverting at all.
The rule 'keep, change, flip' is memorized as a chant without the underlying reason, so the candidate cannot tell which of the two fractions is the divisor. Under time pressure the chant is applied to whichever fraction is written first, producing a reciprocal of the wrong quantity.
What to do instead
Rewrite every division as a complex fraction first: (a/b) ÷ (c/d) becomes (a/b)/(c/d). Then multiply numerator by the reciprocal of the denominator, which mechanically forces the flip onto the divisor. Verify with a whole-number analogue: 6 ÷ 2 must equal 3, so 6 × 1/2 is correct while 1/6 × 2 is not.
The candidate misaligns decimal points when adding or subtracting decimals, or drops trailing zeros and then compares digit strings of different length as if they were whole numbers.
Decimals are read as strings of digits rather than as sums of tenths, hundredths, and thousandths, so place value is not tracked. Writing numbers flush left feels natural because that is how integers are written, and the shorter number appears smaller or larger purely by digit count.
What to do instead
Pad every number to the same number of decimal places with zeros before computing, and stack them so the decimal points form a single vertical line. For comparisons, append zeros until all numbers have equal decimal length, then compare digit by digit from the left. Do a magnitude sanity check: 0.7 is larger than 0.65 because 70 hundredths exceeds 65 hundredths.
When converting a percent to a decimal or a decimal to a percent, the candidate moves the decimal point the wrong number of places or in the wrong direction, for example turning 4% into 0.4 or 0.06 into 60%.
The rule 'move it two places' is recalled without a reference case, and the direction is guessed. Percent is not connected to the idea of 'per hundred', so there is no internal check that the decimal and percent forms must describe the same size.
What to do instead
Anchor on one fact: 50% equals 0.5 and 100% equals 1. Percent to decimal divides by 100, so the number shrinks; decimal to percent multiplies by 100, so it grows. After converting, ask whether the decimal is smaller than the percent for values above 1%, and confirm that 4% lands near 0.04 rather than 0.4.
On percent-change and percent-of problems, the candidate computes the change but then applies it to the wrong base, or subtracts the percent itself from the original number instead of the computed amount.
The phrase 'increased by 20%' is processed as an operation on the number 20 rather than as 20% of a stated base. The candidate also assumes the base is always the first number mentioned, which fails when the question asks for the original price given a sale price.
What to do instead
Write the base explicitly before calculating: 'base = original amount; change = rate × base; new = base ± change.' For reverse problems, set up new = base × (1 ± rate) and solve for base by division. Test with easy numbers: a 100 item marked up 20% then discounted 20% returns to 96, not 100, which exposes base confusion immediately.
The candidate sets up a proportion with the ratios inverted relative to each other, so the units in the two fractions do not correspond, and then cross-multiplies a structurally wrong equation.
Cross multiplication is treated as a purely numerical procedure, so once the numbers are in place the unit labels are abandoned. The candidate does not check that the numerator of the first ratio and the numerator of the second ratio describe the same kind of quantity.
What to do instead
Label every term with its unit before writing the proportion, and place matching units in matching positions: (items)/(hours) = (items)/(hours). Cross-multiply only after the labels line up. Finish by checking that the answer's unit matches what the question asked for, and that doubling one side plausibly doubles the other.
The candidate converts between metric units by moving the decimal the wrong number of places, for example treating a kilogram as 100 grams or a centimeter as 100 millimeters.
Metric prefixes are memorized as a list without their powers of ten attached, so kilo, centi, and milli blur together. Because the metric system is decimal, candidates assume any shift of the decimal is acceptable and guess at the count.
What to do instead
Memorize the prefix ladder with exponents in one line: kilo 10^3, base 10^0, centi 10^-2, milli 10^-3. Count the exponent difference between the two prefixes and move the decimal exactly that many places, in the direction that makes the smaller unit produce the larger number. Confirm with a body-scale fact: 1 kilogram is 1000 grams and 1 centimeter is 10 millimeters.
On customary unit conversions, the candidate uses the wrong equivalence, such as 12 ounces in a pound, 2 feet in a yard, or 16 cups in a gallon, or mixes a weight unit with a volume unit.
Customary equivalents are irregular and must be memorized, but they are often studied as a vague cluster rather than as distinct families. Ounces appear in both weight and fluid volume, so the candidate substitutes one for the other without noticing the dimension change.
What to do instead
Build a written conversion card by family: length (12 in = 1 ft, 3 ft = 1 yd, 5280 ft = 1 mi), weight (16 oz = 1 lb, 2000 lb = 1 ton), volume (8 fl oz = 1 cup, 2 cups = 1 pt, 2 pt = 1 qt, 4 qt = 1 gal). Tag each entry as weight or volume and reject any setup that crosses families. Recite the card before practicing mixed conversion problems.
In multi-step word problems, the candidate grabs the two most prominent numbers and performs an operation on them, ignoring the remainder of the question and the actual quantity requested.
Reading is done once for gist rather than for structure, and numbers attract attention before the goal is identified. Under time pressure the candidate starts computing to feel productive, then rationalizes whatever result appears as the answer.
What to do instead
Read the problem twice: first to identify the requested quantity and its unit, second to list the given data. Write a one-line plan naming each step and its output before touching the calculator. At the end, restate the question and confirm the computed number answers it in the right unit; if a step's output is not used, the plan was wrong.
The candidate leaves answers in the wrong form or unit for the question, giving an improper fraction where a mixed number or decimal is expected, omitting units, or failing to round to the requested place.
Computation consumes all attention, and answer formatting is treated as cosmetic. The candidate also assumes any mathematically equivalent form will be accepted, without checking how the answer must be entered or whether the question specifies rounding.
What to do instead
Before solving, underline the required form: fraction, decimal, mixed number, nearest tenth, or whole number. Convert at the end and re-read the requirement to verify. For word problems, attach the unit to the final number and confirm it matches the unit asked for. When rounding is specified, keep full precision through intermediate steps and round only the final result.