ASVAB Math terms ASVAB Math Formulas.

base a number raised to an exponent. for example the base of 4³ is 4 reciprocal • the reciprocal of 2 is 1/2 • the reciprocal of x is 1/x • the reciprocal of 3/5 is 5/3. Every number has a reciprocal except 0 sum the result of adding 2 or more numbers difference The result of subtracting one number from another. product The answer when two or more numbers are multiplied together. quotient The answer to a division problem. order of operations PEMDAS lists the operations in order P• parentheses E• exponents MD• multiplication and division from left to right AS•addition and subtraction from left to right how to divide by a fraction One way to remember is the Keep, Change, Flip memory tool 4 ÷ 2/3 = 4 x 3/2 KEEP the four, CHANGE the division sign to multiplication, FLIP the fraction to change a fraction into a decimal divide the numerator by the denominator to change a decimal into a percent move the decimal point two spaces to the right (add zeroes if needed) and add a percent sign example: .271 = 27.1%, 0.6 = 60% to change a percent to a decimal drop the percent sign and move the decimal point two places to the left, adding zeros as needed. example: 8.7% = .087 how do you figure out your gas mileage (miles/gallon) by dividing the number of miles traveled by the gallons of gas used ratio shows a relationship between two things, if Margaret invested in her beauty parlor at a 2:1 ratio to her partner Julie, then Margaret put in $2 for every $1 that Julie put in express 5% interest rate as a decimal express 50% interest rate as a decimal 5 % = .05 50% = .50 simple interest formula principle ($$ invested) × interest rate × time irrational numbers numbers that can't be written as a fraction Examples: π , √3, √11 √ of a number means ? √144 = ? √ means square root √144 = is always 12 and can include -12 if not dealing with distance, time or other amount that must always be positive the cube root of 27? the cube root of 27 is 3 because 3×3×3=27 a circle has ___ degrees a semicircle has ___ degrees 360° 180° a quadrilateral a shape with four sides. All the angles will add up to 360° a straight line is ___° 180° a right angle is exactly ___° 90° an acute angle is more than ___° but less than ___° more than 0°, less than 90° an obtuse angle is more than ___° but less than ___° more than 90° and less than 180° complementary angles are two angles that equal 90° when added together supplementary angles are two angles that equal 180° when added together the angles of a triangle add to : always add up to 180° right triangle has one right angle, therefore the remaining two angles are complementary hypotenuse the side opposite the right angle which is the longest side of a right triangle pythagorean theorem a² ⁺ b² = c², where a and b represent the legs and c is the hypotenuse perimeter of a triangle add together the lengths of the three sides area of a triangle 1/2(b)(h) square a quadrilateral with four sides of equal length, and all the angles are right angles rectangle a quadrilateral that has all right angles. Opposite sides are equal parallelogram a quadrilateral that has •opposite sides that are parallel •equal opposite sides and •equal opposite angles. the angles don't have to be right angles. rhombus a quadrilateral that has four sides of equal length. The diagonals form a right angle. trapezoid a quadrilateral that has exactly two sides that are parallel perimeter of a rectangle area of a rectangle circumference of a circle πd which equals 2πr radius the measurement from the center of the circle to any point on the circumference of the circle definition of a diameter a line passing through the center of the circle, from a point on one side of the circle all the way to a point on the other side of the circle diameter of a circle = = 2 x radius volume the space a solid shape takes up, measured in cubic units volume of a rectangular prism (box) L x W x H Key words for equals is, was, are, were, amounts to Key words for multiplication product, total, area, cubic, times, multiplied by, of volume of a cube Side³ commutative property changing the order of terms added or terms multiplied will NOT affect the sum. x + y + z = y + z + x and fgh = hfg associative property regrouping numbes does not affect the answer (8 + 1) + 7 = 8 + (1 + 7) and (2 x 5) x 6 = 2 x (5 x 6) additive identity an example is 7 + 0 = 7 When 0 is added to any number, the result is that number additive inverse example: the additive inverse of 4 is -4 When a number is added to its additive inverse, the answer is always 0 multiplicative identity any number multiplied by 1 will result in that number; example 7 ×1 = 7 multiplicative inverse is the reciprocal of that number (one divided by that number) Multiplicative inverse of 2/3 is 3/2 distributive property a × (b + c) = ab + ac Surface area of a rectangular prism (box) Surface area of a cube the number of degrees in a triangle 180⁰ exterior angle theorem the exterior angle = the sum of the 2 interior angles time distance / rate distance between the points (x₁, y₁) and (x₂, y₂) Find the distance between (8,7) and (5,3) √{(x₁-x₂)² + (y₁-y₂)²} √{(8-5)² + (7-3)²} = √(9 + 16) =√25 = 5 x³•x⁴ = x⁷ (x⁴)³ = x¹² x¹⁰/x⁶ = x⁴ absolute value of a number |-9| = ? |0| = ? the distance from zero on the number line |-9| = 9 |0| = 0 x⁻³ = 2⁻⁴ = x⁻³ = 1/x³ 2⁻⁴ = 1/(2 x 2 x 2 x 2) = 1/16 √50 = √25 •√2 = 5√2 prime factorization of 40 = prime factorization of 75 = 2 x 2 x 2 x 5 3 x 5 x 5 positive + positive = positive negative + negative = negative positive + negative = subtract the numbers and take the sign of the larger number positive x positive = positive negative x negative = positive positive x negative = negative odd + odd = even even + even = even even + odd = odd even x even = even odd x odd = odd even x odd = even range of a set of numbers the largest value minus the smallest value