HESI A2 Math flashcards
HESI A2 Math · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Order of Operations
- A fixed sequence for evaluating expressions: parentheses first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.
- Least Common Denominator
- The smallest number divisible by every denominator in a set of fractions; rewriting fractions over it lets you add or subtract them accurately.
- Reciprocal
- The fraction formed by swapping numerator and denominator. Multiplying a fraction by its reciprocal gives 1, and dividing by a fraction means multiplying by its reciprocal.
- Improper Fraction
- A fraction whose numerator is greater than or equal to its denominator, such as 7/4. Convert mixed numbers to this form before multiplying or dividing.
- Greatest Common Factor
- The largest number dividing two or more numbers evenly. Dividing numerator and denominator by it puts a fraction in simplest form.
- Equivalent Fractions
- Fractions that name the same value, produced by multiplying or dividing numerator and denominator by the same nonzero number, as in 2/3 = 8/12.
- Mixed Number
- A whole number combined with a proper fraction, such as 3 1/2. Convert it to an improper fraction before multiplying or dividing.
- Comparing Fractions
- Cross-multiply to compare: for a/b and c/d, compare a·d with b·c. The larger product sits under the larger fraction.
- Percent to Decimal
- Divide the percent by 100, moving the decimal point two places left. For example, 6.5% becomes 0.065 before any multiplication.
- Solving a Proportion
- Cross-multiply the two ratios, set the products equal, then divide to isolate the unknown. Example: 3/4 = x/20 gives 4x = 60, so x = 15.
- Percent of a Number
- Convert the percent to a decimal and multiply by the whole. For instance, 15% of 240 equals 0.15 × 240 = 36.
- Percent Change
- Subtract the original value from the new value, divide by the original value, then multiply by 100. A positive answer is an increase.
- Finding the Original Amount
- After a percent change, divide the final value by the growth factor. After a 20% increase, divide by 1.20; after a 20% decrease, divide by 0.80.
- Decimal Multiplication Places
- The product of two decimals has as many decimal places as the two factors combined. Multiply as whole numbers, then place the decimal point.
- Part Over Whole
- The core percent relationship: part ÷ whole = percent ÷ 100. Identify which quantity is the whole before setting up the equation.
- Decimal to Percent
- Multiply the decimal by 100, moving the point two places right and adding a percent sign. Thus 0.375 becomes 37.5%.
- Percent Greater Than 100
- A percent above 100 represents more than the whole. Converting 150% gives the decimal 1.5, so 150% of 40 is 60.
- Unit Cancellation
- Write each conversion as a fraction equal to 1, arranging the unwanted unit opposite its existing position so it cancels, leaving only the desired unit.
- Metric Prefix Values
- Kilo- means 1000 base units, centi- means one hundredth, and milli- means one thousandth. These prefixes attach to meters, grams, and liters.
- Metric Length Equivalents
- One kilometer equals 1000 meters; one meter equals 100 centimeters or 1000 millimeters; one centimeter equals 10 millimeters.
- Customary Length Equivalents
- One foot equals 12 inches, one yard equals 3 feet or 36 inches, and one mile equals 5280 feet or 1760 yards.
- Customary Volume Equivalents
- One gallon equals 4 quarts, 8 pints, or 16 cups; one quart equals 2 pints, and one cup equals 8 fluid ounces.
- Customary Weight Equivalents
- One pound equals 16 ounces, and one ton equals 2000 pounds. Convert to ounces first when a problem mixes pounds and ounces.
- Metric Volume Equivalents
- One liter equals 1000 milliliters, and one milliliter equals one cubic centimeter. A cubic centimeter of water also has a mass near one gram.
- Time Unit Equivalents
- One minute equals 60 seconds, one hour equals 60 minutes or 3600 seconds, and one day equals 24 hours.
- Distance, Rate, Time
- Distance equals rate multiplied by time. Rearranged, rate equals distance divided by time, and time equals distance divided by rate.
- Mean of a Data Set
- Add all values and divide by how many there are. Reversing it, the total of a data set equals its mean times the count.
- Simple Interest Formula
- Interest equals principal times annual rate times time in years, written I = P × r × t, with the rate expressed as a decimal.
- Discount and Tax
- A discount multiplies price by (1 − rate); tax multiplies price by (1 + rate). Apply the discount before adding sales tax.
- Ratio Part Method
- Add the ratio terms to get total parts, divide the total quantity by that number to find one part, then multiply by each term.
- Combined Work Rate
- Add the individual rates to get the joint rate, then divide 1 job by that combined rate to find the time working together.
- Unit Rate
- The amount per single unit, found by dividing the quantity by its number of units. It lets you scale to any other quantity by multiplying.