Math words (glossary)

absolute value: How far a number is from 0 on a number line. It is never negative.; Example: $|-6| = 6$ and $|6| = 6$ .
area: The amount of flat space inside a shape. It is measured in square units.; Example: A rectangle 5 feet by 3 feet has an area of $5 \times 3 = 15$ square feet.
circumference: The distance around a circle. `C = \pi d` or `C = 2\pi r`.; Example: A circle with a diameter of 10 inches has a circumference of about 31.4 inches.
coefficient: The number multiplied by a variable.; Example: In $7x$ , the coefficient is 7.
cone: A solid shape with a circle at the bottom that comes to a point at the top.; Example: Volume of a cone: $V = \frac{1}{3}\pi r^2 h$ .
consecutive: Coming one right after another, in order.; Example: 7, 8, and 9 are consecutive whole numbers.
cylinder: A solid shape with two equal circles as its top and bottom, like a can.; Example: Volume of a cylinder: $V = \pi r^2 h$ .
decimal: A number written with a decimal point. Digits after the point are parts of a whole: tenths, hundredths, and so on.; Example: 0.75 means 75 hundredths, the same as $\frac{3}{4}$ .
denominator: The bottom number of a fraction. It tells how many equal parts make a whole.; Example: In $\frac{3}{4}$ , the denominator is 4.
diagonal: A straight line from one corner of a shape to the opposite corner.; Example: A TV's size is the length of its diagonal.
diameter: The distance across a circle, through its center. It is twice the radius.; Example: A circle with a radius of 4 cm has a diameter of 8 cm.
difference: The answer when you subtract one number from another.; Example: The difference between 10 and 3 is 7, because $10 - 3 = 7$ .
discount: An amount taken off the regular price.; Example: A 20% discount on a $40 shirt is $8, so you pay $32.
distribute: Multiply a number by each term inside parentheses.; Example: $3(x + 2) = 3x + 6$
equation: A math sentence that says two things are equal. It has an equal sign.; Example: $2x + 1 = 9$ is an equation.
estimate: A close guess, found by rounding or quick figuring.; Example: $49 \times 21$ is about $50 \times 20 = 1000$ .
evaluate: Find the value of an expression by putting in numbers for the letters.; Example: Evaluate $2x + 1$ when $x = 4$ : $2(4) + 1 = 9$ .
exponent: A small raised number that tells how many times to multiply a number by itself.; Example: $2^3 = 2 \times 2 \times 2 = 8$ . The exponent is 3.
expression: Numbers, letters, and operation signs put together, with no equal sign.; Example: $3x + 5$ is an expression.
factor: As a noun: a number or expression that divides another evenly. As a verb: write something as a product of factors.; Example: 3 and 4 are factors of 12. $x^2 - 9$ factors as $(x - 3)(x + 3)$ .
fraction: A number that shows part of a whole. The top number is the numerator. The bottom number is the denominator.; Example: $\frac{3}{4}$ means 3 out of 4 equal parts.
function: A rule that gives exactly one output for each input.; Example: $f(x) = x + 4$ is a function. When the input is 2, the output is 6.
greatest common factor: The largest number (or expression) that divides each term evenly.; Example: The greatest common factor of 12 and 18 is 6.
hypotenuse: The longest side of a right triangle. It is across from the square corner.; Example: In a right triangle with sides 3, 4, and 5, the hypotenuse is 5.
improper fraction: A fraction whose top number is bigger than or equal to its bottom number.; Example: $\frac{5}{2}$ is an improper fraction. It equals $2\frac{1}{2}$ .
inequality: A math sentence that compares amounts with `<`, `>`, `\le`, or `\ge`.; Example: $x > 4$ means $x$ is greater than 4.
input: The number you put into a function, often `x`.; Example: In $f(3)$ , the input is 3.
integer: A whole number or its negative. Integers have no fraction or decimal part.; Example: $-3$ , 0, and 8 are integers. 2.5 is not.
like terms: Terms with the same variable raised to the same power. You can add or subtract like terms.; Example: $3x$ and $5x$ are like terms: $3x + 5x = 8x$ .
mean: Add all the values, then divide by how many values there are.; Example: The mean of 2, 4, and 9 is $(2 + 4 + 9) \div 3 = 5$ .
median: The middle value when the data are in order. With an even number of values, it is the mean of the two middle values.; Example: The median of 3, 7, 8, 10, 12 is 8.
mixed number: A whole number and a fraction written together.; Example: $2\frac{1}{2}$ means 2 and one half.
mode: The value that appears most often in a data set.; Example: In 2, 5, 5, 7, 9, the mode is 5.
numerator: The top number of a fraction. It tells how many parts you have.; Example: In $\frac{3}{4}$ , the numerator is 3.
order of operations: The order for doing math steps: parentheses, exponents, multiply and divide (left to right), then add and subtract (left to right).; Example: $2 + 3 \times 4 = 2 + 12 = 14$
ordered pair: Two numbers in parentheses that name a point on a graph: (x, y).; Example: (3, 5) means go 3 to the right and 5 up.
outcome: One possible result of an event.; Example: Flipping a coin has 2 outcomes: heads or tails.
output: The number a function gives back, often `y` or `f(x)`.; Example: If $f(x) = 2x$ , the output for an input of 3 is 6.
parabola: The U-shaped graph of a quadratic function.; Example: The graph of $y = x^2$ is a parabola.
parallel: Lines that never cross. Parallel lines have the same slope.; Example: $y = 2x + 1$ and $y = 2x - 4$ are parallel.
percent: Per hundred. A percent is a part out of 100.; Example: 25% means 25 out of 100, or 0.25.
percent change: How much an amount went up or down, compared with the starting amount, as a percent.; Example: From 50 to 60 is a change of 10. $10 \div 50 = 0.2$ , a 20% increase.
perimeter: The distance all the way around a flat shape.; Example: A rectangle 5 feet by 3 feet has a perimeter of $5 + 3 + 5 + 3 = 16$ feet.
perpendicular: Lines that cross at a square corner (90°). Their slopes are negative reciprocals.; Example: $y = 2x$ and $y = -\frac{1}{2}x$ are perpendicular.
principal: The amount of money first borrowed or saved, before interest.; Example: If you put $500 in the bank, the principal is $500.
probability: How likely something is to happen, from 0 (impossible) to 1 (certain). Probability = ways to win ÷ total outcomes.; Example: The probability of rolling a 3 on a number cube is $\frac{1}{6}$ .
product: The answer when you multiply numbers.; Example: The product of 6 and 4 is 24, because $6 \times 4 = 24$ .
proportion: An equation that says two ratios are equal.; Example: $\frac{2}{3} = \frac{8}{12}$ is a proportion.
quadratic equation: An equation with a squared variable, like `ax^2 + bx + c = 0`. It can have 0, 1, or 2 solutions.; Example: $x^2 - 9 = 0$ has the solutions 3 and $-3$ .
quotient: The answer when you divide one number by another.; Example: The quotient of 20 and 5 is 4, because $20 \div 5 = 4$ .
radius: The distance from the center of a circle to its edge. It is half the diameter.; Example: A circle with a diameter of 10 inches has a radius of 5 inches.
range: The largest value minus the smallest value in a data set.; Example: In 4, 9, 15, the range is $15 - 4 = 11$ .
rate: A comparison of two amounts with different units, like miles and hours.; Example: 120 miles in 2 hours is a rate of 60 miles per hour.
ratio: A comparison of two amounts.; Example: 3 cats and 2 dogs: the ratio of cats to dogs is 3 to 2, or $3:2$ .
reciprocal: The fraction you get when you flip a fraction upside down. A number times its reciprocal is 1.; Example: The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$ .
rectangular prism: A box shape. All 6 faces are rectangles.; Example: A shoebox is a rectangular prism. Its volume is length × width × height.
right triangle: A triangle with one square corner (a 90° angle).; Example: The sides 3, 4, and 5 make a right triangle.
scientific notation: A short way to write very large or very small numbers: a number from 1 to 10 times a power of 10.; Example: $3{,}500{,}000 = 3.5 \times 10^{6}$
simple interest: Money paid for borrowing or saving money. Simple interest is `I = Prt`: principal × rate × time in years.; Example: $1,000 at 5% for 2 years earns $1000 \times 0.05 \times 2 = 100$ dollars.
simplify: Write something in a shorter, easier form without changing its value.; Example: $2x + 3x$ simplifies to $5x$ .
slope: How steep a line is: the change in `y` divided by the change in `x`. Rise over run.; Example: A line through (0, 1) and (2, 5) has slope $\frac{5 - 1}{2 - 0} = 2$ .
solution: A value that makes an equation or inequality true.; Example: $x = 5$ is the solution of $x + 2 = 7$ .
square root: A number that, times itself, gives the number you started with.; Example: $\sqrt{49} = 7$ , because $7 \times 7 = 49$ .
squared: Multiplied by itself. A number squared has an exponent of 2.; Example: 5 squared is $5^2 = 25$ .
sum: The answer when you add numbers.; Example: The sum of 4 and 5 is 9, because $4 + 5 = 9$ .
surface area: The total area of all the outside faces of a solid shape.; Example: A cube with 2-inch sides has 6 faces of 4 square inches each, so its surface area is 24 square inches.
system of equations: Two or more equations that share the same variables. The solution makes all of them true at the same time.; Example: $x + y = 5$ and $x - y = 1$ have the solution $x = 3$ , $y = 2$ .
unit rate: A rate for exactly one unit, such as per hour, per ounce, or per item.; Example: $3.00 for 12 ounces is a unit price of $0.25 per ounce.
variable: A letter that stands for a number you don't know yet.; Example: In $x + 3 = 10$ , $x$ is the variable. Here $x = 7$ .
vertex: The highest or lowest point of a parabola.; Example: The vertex of $y = x^2$ is (0, 0).
volume: The amount of space inside a solid shape. It is measured in cubic units.; Example: A box 2 × 3 × 4 feet has a volume of 24 cubic feet.
whole number: One of the numbers 0, 1, 2, 3, and so on. No fractions, decimals, or negatives.; Example: 0, 7, and 150 are whole numbers.
x-intercept: The point where a line crosses the x-axis. There, `y = 0`.; Example: The line $y = x - 4$ has an x-intercept of 4.
y-intercept: The point where a line crosses the y-axis. There, `x = 0`.; Example: The line $y = 2x + 3$ has a y-intercept of 3.