HESI A2 Math cheat sheet

Order of operations: Parentheses, Exponents, Multiply/Divide left to right, Add/Subtract left to right.

To add or subtract fractions, rewrite over the least common denominator, then combine numerators and keep the denominator.

To multiply fractions, multiply numerators together and denominators together; cancel common factors first to simplify.

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c.

A fraction is in simplest form when numerator and denominator share no common factor other than 1; divide both by their GCF.

Convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the same denominator.

Multiplying or dividing numerator and denominator by the same nonzero number gives an equivalent fraction.

Any nonzero number divided by itself equals 1, and any number multiplied by 1 keeps its value; zero divided by a nonzero number is 0.

Compare fractions by cross-multiplying or by converting to a common denominator before deciding which is larger.

To convert a percent to a decimal, divide by 100 (move the decimal point two places left); to convert a decimal to a percent, multiply by 100.

A percent is a ratio out of 100, so 45% equals 45/100 = 0.45 = 9/20.

Percent of a number: part = percent × whole, with the percent written as a decimal (e.g., 30% of 80 = 0.30 × 80 = 24).

Percent change = (new value − original value) ÷ original value × 100; a positive result is an increase, a negative result a decrease.

A proportion states two equal ratios: a/b = c/d; cross-multiply to get a·d = b·c, then solve for the unknown.

When adding or subtracting decimals, align the decimal points; when multiplying, the product has as many decimal places as the factors combined.

To find the original amount after a percent increase, divide the final value by (1 + rate); after a decrease, divide by (1 − rate).

Set up percent word problems with the proportion part/whole = percent/100 and label which quantity is the whole.

Multiply by a conversion factor written as a fraction equal to 1, arranging units so the unwanted unit cancels.

Metric prefixes: kilo- = 1000, centi- = 0.01, milli- = 0.001 of the base unit; moving between them shifts the decimal three or two places.

1 kilometer = 1000 meters; 1 meter = 100 centimeters = 1000 millimeters; 1 kilogram = 1000 grams.

1 liter = 1000 milliliters, and 1 milliliter = 1 cubic centimeter.

Customary length: 1 foot = 12 inches, 1 yard = 3 feet = 36 inches, 1 mile = 5280 feet.

Customary weight and volume: 1 pound = 16 ounces, 1 ton = 2000 pounds, 1 gallon = 4 quarts = 8 pints = 16 cups.

Time: 1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours.

For multi-step conversions, chain factors in one expression (e.g., miles to inches) so intermediate units cancel completely.

When converting between metric and customary units, use the given equivalence (e.g., 1 inch = 2.54 centimeters) as the bridge factor.

Rate problems use distance = rate × time, and equivalently rate = distance ÷ time and time = distance ÷ rate.

Average (mean) = sum of all values ÷ number of values; total = average × number of values.

Percent discount: sale price = original price × (1 − discount rate); sales tax is added as price × (1 + tax rate).

Simple interest: I = P × r × t, with r as a decimal rate per year and t in years.

Work or rate problems: combined rate equals the sum of individual rates; time together = 1 ÷ combined rate.

Ratio problems: find the total number of parts, divide the total quantity by that number to get one part, then multiply by each ratio term.

Perimeter of a rectangle = 2(length + width); area of a rectangle = length × width; area of a triangle = ½ × base × height.

Unit rate is found by dividing the quantity by its unit, giving a per-one value used to scale to other amounts.

Check word-problem answers for reasonableness by estimating with rounded numbers and confirming units match the question asked.

Order of operations: Parentheses, Exponents, Multiply/Divide left to right, Add/Subtract left to right.

To add or subtract fractions, rewrite over the least common denominator, then combine numerators and keep the denominator.

To multiply fractions, multiply numerators together and denominators together; cancel common factors first to simplify.

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c.

A fraction is in simplest form when numerator and denominator share no common factor other than 1; divide both by their GCF.

Convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the same denominator.

Multiplying or dividing numerator and denominator by the same nonzero number gives an equivalent fraction.

Any nonzero number divided by itself equals 1, and any number multiplied by 1 keeps its value; zero divided by a nonzero number is 0.

Compare fractions by cross-multiplying or by converting to a common denominator before deciding which is larger.

To convert a percent to a decimal, divide by 100 (move the decimal point two places left); to convert a decimal to a percent, multiply by 100.

A percent is a ratio out of 100, so 45% equals 45/100 = 0.45 = 9/20.

Percent of a number: part = percent × whole, with the percent written as a decimal (e.g., 30% of 80 = 0.30 × 80 = 24).

Percent change = (new value − original value) ÷ original value × 100; a positive result is an increase, a negative result a decrease.

A proportion states two equal ratios: a/b = c/d; cross-multiply to get a·d = b·c, then solve for the unknown.

When adding or subtracting decimals, align the decimal points; when multiplying, the product has as many decimal places as the factors combined.

To find the original amount after a percent increase, divide the final value by (1 + rate); after a decrease, divide by (1 − rate).

Set up percent word problems with the proportion part/whole = percent/100 and label which quantity is the whole.

Multiply by a conversion factor written as a fraction equal to 1, arranging units so the unwanted unit cancels.

Metric prefixes: kilo- = 1000, centi- = 0.01, milli- = 0.001 of the base unit; moving between them shifts the decimal three or two places.

1 kilometer = 1000 meters; 1 meter = 100 centimeters = 1000 millimeters; 1 kilogram = 1000 grams.

1 liter = 1000 milliliters, and 1 milliliter = 1 cubic centimeter.

Customary length: 1 foot = 12 inches, 1 yard = 3 feet = 36 inches, 1 mile = 5280 feet.

Customary weight and volume: 1 pound = 16 ounces, 1 ton = 2000 pounds, 1 gallon = 4 quarts = 8 pints = 16 cups.

Time: 1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours.

For multi-step conversions, chain factors in one expression (e.g., miles to inches) so intermediate units cancel completely.

When converting between metric and customary units, use the given equivalence (e.g., 1 inch = 2.54 centimeters) as the bridge factor.

Rate problems use distance = rate × time, and equivalently rate = distance ÷ time and time = distance ÷ rate.

Average (mean) = sum of all values ÷ number of values; total = average × number of values.

Percent discount: sale price = original price × (1 − discount rate); sales tax is added as price × (1 + tax rate).

Simple interest: I = P × r × t, with r as a decimal rate per year and t in years.

Work or rate problems: combined rate equals the sum of individual rates; time together = 1 ÷ combined rate.

Ratio problems: find the total number of parts, divide the total quantity by that number to get one part, then multiply by each ratio term.

Perimeter of a rectangle = 2(length + width); area of a rectangle = length × width; area of a triangle = ½ × base × height.

Unit rate is found by dividing the quantity by its unit, giving a per-one value used to scale to other amounts.

Check word-problem answers for reasonableness by estimating with rounded numbers and confirming units match the question asked.

Order of operations: Parentheses, Exponents, Multiply/Divide left to right, Add/Subtract left to right.

To add or subtract fractions, rewrite over the least common denominator, then combine numerators and keep the denominator.

To multiply fractions, multiply numerators together and denominators together; cancel common factors first to simplify.

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c.

A fraction is in simplest form when numerator and denominator share no common factor other than 1; divide both by their GCF.

Convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the same denominator.

Multiplying or dividing numerator and denominator by the same nonzero number gives an equivalent fraction.

Any nonzero number divided by itself equals 1, and any number multiplied by 1 keeps its value; zero divided by a nonzero number is 0.

Compare fractions by cross-multiplying or by converting to a common denominator before deciding which is larger.

To convert a percent to a decimal, divide by 100 (move the decimal point two places left); to convert a decimal to a percent, multiply by 100.

A percent is a ratio out of 100, so 45% equals 45/100 = 0.45 = 9/20.

Percent of a number: part = percent × whole, with the percent written as a decimal (e.g., 30% of 80 = 0.30 × 80 = 24).

Percent change = (new value − original value) ÷ original value × 100; a positive result is an increase, a negative result a decrease.

A proportion states two equal ratios: a/b = c/d; cross-multiply to get a·d = b·c, then solve for the unknown.

When adding or subtracting decimals, align the decimal points; when multiplying, the product has as many decimal places as the factors combined.

To find the original amount after a percent increase, divide the final value by (1 + rate); after a decrease, divide by (1 − rate).

Set up percent word problems with the proportion part/whole = percent/100 and label which quantity is the whole.

Multiply by a conversion factor written as a fraction equal to 1, arranging units so the unwanted unit cancels.

Metric prefixes: kilo- = 1000, centi- = 0.01, milli- = 0.001 of the base unit; moving between them shifts the decimal three or two places.

1 kilometer = 1000 meters; 1 meter = 100 centimeters = 1000 millimeters; 1 kilogram = 1000 grams.

1 liter = 1000 milliliters, and 1 milliliter = 1 cubic centimeter.

Customary length: 1 foot = 12 inches, 1 yard = 3 feet = 36 inches, 1 mile = 5280 feet.

Customary weight and volume: 1 pound = 16 ounces, 1 ton = 2000 pounds, 1 gallon = 4 quarts = 8 pints = 16 cups.

Time: 1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours.

For multi-step conversions, chain factors in one expression (e.g., miles to inches) so intermediate units cancel completely.

When converting between metric and customary units, use the given equivalence (e.g., 1 inch = 2.54 centimeters) as the bridge factor.

Rate problems use distance = rate × time, and equivalently rate = distance ÷ time and time = distance ÷ rate.

Average (mean) = sum of all values ÷ number of values; total = average × number of values.

Percent discount: sale price = original price × (1 − discount rate); sales tax is added as price × (1 + tax rate).

Simple interest: I = P × r × t, with r as a decimal rate per year and t in years.

Work or rate problems: combined rate equals the sum of individual rates; time together = 1 ÷ combined rate.

Ratio problems: find the total number of parts, divide the total quantity by that number to get one part, then multiply by each ratio term.

Perimeter of a rectangle = 2(length + width); area of a rectangle = length × width; area of a triangle = ½ × base × height.

Unit rate is found by dividing the quantity by its unit, giving a per-one value used to scale to other amounts.

Check word-problem answers for reasonableness by estimating with rounded numbers and confirming units match the question asked.