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# Mathematics

This section is your guide to the language of mathematics. It lists and defines many of the common (and not so common) mathematical signs, symbols, shapes, and terms. The section also includes helpful math tables.

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# Math Terms

**Addition** (+) is combining numbers to get a total, which is called a sum. The sum of 3 plus 5 is 8; 3 + 5 = 8.

An **angle** is made when two rays (lines) share a common endpoint. An angle is measured in degrees.

**Area** is the total surface within a closed figure (circle, square, etc.). The area of a rectangle is figured by multiplying the length by the width. Area is measured in square units such as square inches or square feet.

The **average** is found by adding a group of numbers together and then dividing that sum by the number of separate numbers (addends). The average of 7, 8, and 9 is 8, because 7 + 8 + 9 = 24, and 24 ÷ 3 (numbers) = 8. This is also called the mathematical *mean*.

A **circle** is a round, closed figure. All the points on its circumference (edge) are the same distance from the center of the figure.

**Circumference** is the measure of distance around the edge of a circle.

A **common denominator** is a multiple shared by the denominators of two or more fractions. For example, 6 is a common denominator of 1/2 and 1/3 because 6 is a multiple of both 2 and 3. To add or subtract fractions, you must find a common denominator; 1/2 + 1/3 = 3/6 + 2/6 = 5/6. The lowest common denominator is also called the least common multiple (LCM) of the denominators.

**Congruent** (≅) is the term for two figures, angles, or line segments that are the same size and shape.

**Data** are numbers collected to compare.

A **decimal** is a fraction written in the decimal number system. (Decimal means “based on the number 10.”) Decimals are written using a decimal point and place values—tenths, hundredths, thousandths, and so on. The fraction 1/2 is 0.5, or 5/10.

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A **degree** is a unit of measurement for angles and arcs. It is written as a small circle [°]. You can write 90° or 90 degrees. There are 360 degrees in a circle.

The **denominator** is the bottom number of a fraction. In the fraction 1/3, the denominator is 3. It indicates the number of parts needed to make a whole unit.

A **diagonal** is a line from one vertex (corner) of a quadrilateral to the opposite vertex.

The **diameter** is the length of a straight line through the center of a circle.

A **dividend** is a number to be divided. In the equation 12 ÷ 2 = 6, 12 is the dividend.

**Division** (÷) is a basic math operation used to determine how many times one quantity is contained in another. Division tells you how many times you have to subtract a number to reach zero. For example, 10 ÷ 5 = 2 because you subtract 5 two times to reach zero (10 – 5 = 5; 5 – 5 = 0).

The **divisor** is the number that divides the dividend. In the statement 12 ÷ 2 = 6, 2 is the divisor.

An **equation** is a statement that says two numbers or mathematical expressions are equal to each other (2 + 10 = 12 or *x* + 4 = 9). Equations use the equal sign (=).

An **estimate** is a reasonable guess at an answer. If you add 6.24 and 5.19, you can estimate the answer will be around 11, because 6 + 5 = 11.

An **even number** is a number that can be divided by 2 without having a remainder (2, 4, 6, and so on). For example, 4 ÷ 2 = 2.

An **exponent** is the small, raised number to the right of the base number that shows how many times the base is to be multiplied by itself. In the expression 2^{3}, 3 is the exponent (2 is the base). So 2^{3} means you need to multiply 2 three times (2 × 2 × 2 = 8).

A **factor** is a number that is being multiplied. In 4 × 3 = 12, the factors are 4 and 3.

A **fraction** is a number that expresses a part of a whole. In the fraction 3/4, 4 is the denominator—the number of equal parts that make up the whole. The number 3 is the numerator—the number of parts being talked about.

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**Geometry** is the study of two-dimensional shapes (circles, triangles), three-dimensional solids (spheres, cubes), and positions in space (points).

A **horizontal** is a line parallel to the earth’s surface, or horizon, going across rather than up and down. A **vertical** is a line that is straight up and down and perpendicular to the horizon.

A **hypotenuse** of a right triangle is the side opposite the right angle.

An **intersection** is the point where two lines in geometry cross each other.

An **isosceles triangle** is a triangle with two sides of equal length and two equal angles. (See *triangle.*)

Length is the distance along a line from one point to another.

A **line** is all points formed by extending a line segment both directions, without end.

**Lowest common denominator** (See *common denominator.*)

**Mean** is another word for average. (See *average*.)

The **median** is the middle number when a group of numbers is arranged in order from the least to the greatest, or the greatest to the least. In 1, 4, 6 the median (middle number) is 4. In 1, 4, 6, 8 the median is 5, the average of the two middle numbers: 4 + 6 = 10; 10 ÷ 2 = 5.

A **multiple** is a quantity into which another quantity can be divided, with zero as the remainder (both 6 and 9 are multiples of 3).

**Multiplication** (×) is like addition because you add the same number a certain number of times (2 × 4 = 4 + 4). When you multiply numbers, the answer is called the product. The product of 2 times 4 is 8 because 2 ✕ 4 = 8. (A raised dot also means multiplication. 2 × 3 is the same as 2 • 3.)

The **numerator** is the top number of a fraction. In the fraction 6, the numerator is 5.

An **obtuse** angle is an angle greater than 90 degrees and less than 180 degrees. (See *angle*.)

An **odd number** is a number that cannot be divided evenly by 2. The numbers 1, 3, 5, 7, and so on, are odd numbers.

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**Opposite numbers** are any two numbers whose sum is zero (–2 and +2 are opposite numbers).

**Parallel** refers to lines that never intersect.

**Percent** is a way of expressing a number as a fraction of 100. (*Percent* means “per hundred.”) The percent symbol is %. So 1/2 expressed as a percentage is 50/100, which is 50%.

The **perimeter** is the distance around the edge of a multi-sided figure. If a triangle has three sides, each 3 feet long, its perimeter is 9 feet (3 + 3 + 3 = 9).

**Perpendicular** refers to two lines that intersect, forming right angles (90° angles).

**Pi** (π) is the ratio of the circumference of a circle to its diameter. Pi is approximately 3.14.

**Place value** is the value of the place of a digit depending on where it is in the number.

3,497 is 3 thousands, 4 hundreds, 9 tens, 7 ones

0.3497 is 3 tenths, 4 hundredths, 9 thousandths, 7 ten-thousandths

A **point** is an exact location on a line or plane or in a space.

A **positive number** is a number greater than 0.

A **prime number** is a number that cannot be divided evenly (without a remainder) by any number except itself and 1. The number 6 is not a prime number because it can be divided evenly by 1, 2, 3, and 6. The number 5 is a prime number because it can be divided evenly only by itself (5) and 1.

**Product** is the word used to indicate the result of multiplication. For example, 8 is the product of 2 times 4, because 2 × 4 = 8.

The **quotient** is the number you get when you divide one number by another number. If 8 is divided by 4, the quotient is 2, because 8 ÷ 4 = 2.

The **radius** (r) is the distance from the center of a circle to its circumference. (The radius is half the diameter.)

A **ratio** is a way of comparing two numbers by dividing one by the other. The ratio of 3 to 4 is 3/4. If there are 20 boys and 5 girls in your class, the ratio of boys to girls is 20/5 (4/1 in lowest terms), or 4:1.

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A **rectangle** is a four-sided closed figure with four right angles and with opposite sides parallel and congruent.

A **right angle** is an angle that measures 90 degrees. A right angle is formed when two perpendicular lines meet. (See *angle*.)

**Rounding** gives you an approximate number if you don’t need an exact one. If 2,323 people attended a soccer game, about 2,000 people were there. If 2,857 people attended, about 3,000 were there. Round up if the number is halfway or more to the next highest number (2,500 is halfway between 2,000 and 3,000). Round down if the number is less than halfway.

A **solid** is a three-dimensional figure in geometry, like a cube, a cone, a prism, or a sphere.

A **square** is a rectangle that has four sides of equal length and four right angles. *Square* also refers to the product of a number multiplied by itself. The square of 4 is 16 (4^{2} = 16; 4 × 4 = 16). (See *area* for another use of “square.”)

The **square root** of a number is a number that, when multiplied by itself, gives the original number as the product. The symbol for square root is √. The square root of 4 is 2, because 2 × 2 = 4 ( √4 = 2).

**Subtraction** (–) is the inverse (opposite) of addition. Instead of adding one number to another, you take one number away from another. When you subtract two numbers, you find the difference between them. So 11 – 6 = 5.

The **sum** is the number you get when you add numbers. For example, 7 is the sum of 4 and 3, because 4 + 3 = 7.

A **triangle** is a closed figure with three sides. The sum of the angles in every triangle is 180°. Triangles can be classified by *sides:* equilateral, isosceles, or scalene; or by *angles:* right, equiangular, acute, or obtuse.

A **vertex** is the point where two sides of a plane (flat) figure meet (corner). The plural of *vertex* is *vertices*.

**Vertical** (See *horizontal*.)