How to Solve Linear Equations with Both Multiplication and Division

The letter (pi) from the Greek alphabet refers to the ratio of the circumference of a circle to its diameter, which is approximately 3.14 or 22/7.

An operation that tells you how far a number is from zero.

Number with the same numerical part but the opposite sign (plus or minus) of the given number. If zero is the sum of two numbers, then these two numbers are additive inverses of one another.

Measure of a specified region in a plane.

Characteristic of addition and multiplication that allows the grouping of terms to change without affecting the result.

Value multiplied repeatedly in an exponential expression.

Process requiring two values to produce a third value.

Two terms separated by addition or subtraction.

Grouping symbol that looks like this: { }.

Grouping symbol that looks like this: [ ].

Distance around the outside of a circle.

1. A number that multiplies a variable and tells how many of the variable. 2. The number preceding a variable.

Method of counting that tells how many ways a designated number of objects can be selected from a given set.

Same value on the bottom of more than one fraction.

Characteristic of addition and multiplication that allows the order of the values in an operation to be changed without affecting the result.

Whole number larger than 1 that isn’t prime.

Variable or number that never changes in value in an expression.

Part of an ordered pair that designates a point’s location on a coordinate plane.

Flat region determined by two intersecting, perpendicular, numbered lines called axes.

1. The third power of a number. 2. The result of multiplying a number by itself three times.

Number that you can multiply by itself three times to get a given number. For example, the cube root of eight is two because two multiplied by itself three times equals eight.

Adjective that describes an expression in which the highest power is three.

Fraction with an unwritten denominator of 10 indicated by the decimal point

Number of degrees between 1 and 360 that comprise the measure of an angle.

Highest power occurring in the expression.

Bottom number of a fraction.

Longest distance across a circle.

Result of subtraction.

Numerals from zero through nine, so called because they were originally counted on the fingers.

Characteristic of multiplication and addition that allows for the multiplication of each individual term in a grouped series by a term outside of the grouping without changing the value of the expression.

A number to be divided by another number.

One number can be divided by another with no remainder.

Solution that appears twice when solving an equation because the related factor appears twice in the factored form. For example, in (y – 2)(y – 2) = 0, y = 2 is a double root or solution. In (y – 2)(y – 2)(x + 3) = 0, y = 2 is still a double root or solution.

Mathematical statement with an equal sign showing that two values are equal.

Fractions equal to one another, even though they may have different denominators. (Example: 3/4 and 75/100)

A number that can be divided or is divisible by 2.

Value in smaller type found above and to the right of the base that indicates the number of times the base is multiplied by itself.

Combination of values (variables, numbers, and/or constants) and operation(s).

1. (noun) Any of the values involved in a multiplication problem that when multiplied together produces a result. 2. (verb) To rewrite an algebraic expression as a product.

Operation that multiplies a whole number by every counting number smaller than it.

1. Acronym for first, outer, inner, and last — which indicates the order in which two terms (one from each of two binomials) are multiplied together. 2. The process of multiplying two binomials.

Rule or method that is accepted as true and used over and over in common applications.

Any quantity expressed as a numerator (the value above the bar) and a denominator (the value below the bar).

Line separating the numerator from the denominator.

Plotted figure in a plane.

Largest possible value that evenly divides each term of an expression containing two or more terms.

Parentheses, brackets, and braces that can affect the order of operations. Terms and operations within the grouping symbol take precedence.

Terms and operations within grouping symbols.

Longest side of right triangle.

A fraction whose numerator is larger than the denominator.

Relationship between two unequal values.

Without end; uncountable, as in a repeating decimal

A positive or negative whole number or zero; numbers starting with zero and going up or down in increments of one.

Point where a graph crosses the x-axis or y-axis.

Point shared by two lines.

Number with no fractional equivalent whose decimal never repeats or terminates.

All the points in the coordinate plane that satisfy a linear equation.

Adjective describing expression or equation in which the highest power of any variable is one. Constants can be higher powers. For example, x + y = 4 is linear.

Status of a fraction whose numerator and denominator cannot be divided evenly by the same number. A fraction with a numerator of 12 and a denominator of 25 is in lowest terms.

Improper fraction written as a whole number alongside a fraction.

An expression with only one term.

A number evenly divisible by a specific factor. Example, 14 and 21 are multiples of 7.

Rule stating if the product of two numbers is zero, then one of the numbers must be zero.

An integer multiplied with both the numerator and denominator of a fraction.

Values starting with 1 and increasing by 1.

Any quantity that is less than zero; usually preceded by a minus sign.

Two numbers, one positive and one negative, whose product is negative one.

When two or more grouping symbols are inside one another, such as {32[4 × 2(2 + 5)]}.

A set of numbers.

The top number in a fraction.

A whole number that is not evenly divided by 2.

Mathematical process, such as addition, subtraction, multiplication, and division, performed on one or more quantities.

Two values inside parentheses and separated by a comma that indicate the position of a point in the coordinate plane.

Point of intersection of the x-axis and y-axis in a coordinate plane.

Lines that never intersect and are always the same distance apart.

Fractions with a denominator of 100. The percentage is the numerator of the fraction — how many out of 100.

Total distance around the outside of a region or area.

Counting method that determines the number of ordered arrangements there are when a certain number of objects are selected from a given set.

Lines that form a 90-degree angle at their intersection.

The letter (π) from the Greek alphabet refers to the ratio of the circumference of a circle to its diameter, which is approximately 3.14 or 22/7.

Expression with one or more terms.

Any quantity greater than zero.

Any number raised to the power of zero equals 1 as long as the base number isn’t zero.

A prime number that evenly divides the number you’re working on.

Process of finding the prime numbers that, when multiplied together, produce a given composite number.

Whole number larger than the number 1 that can be divided evenly only by itself and 1.

Positive number that when multiplied by itself produces a given positive number. For example, the square roots of 25 are 5 and −5, but the principal square root of 25 is only 5.

The result of multiplication.

Fraction whose value is less than 1. The numerator is always smaller than the denominator.

Equation showing that two ratios are equal to one another.

Formula specific to right triangles stating that the hypotenuse (c) squared is equal to the sum of the squares of the remaining sides (a and b): a2 + b2 = c2.

One of four regions in a coordinate plane defined by the x-axis and the y-axis.

Also known as second degree, expression or equation in which the highest power is 2. The degree is 2.

Result of division.

Symbol for the operation to find a square root.

Distance from the center of a circle to its outer edge; half its diameter.

Multiplying a base number the number of times indicated by the exponent. For example, 5 is being raised to the power of 3 in expression 53.

Quantity, positive or negative, that can be written as a fraction; its decimal equivalent terminates or repeats.

Any rational or irrational number.

1. Two numbers whose product is always 1, such as 3 × 1/3 and 0.25 × 4. 2. Either one of the two numbers in a reciprocal. Example: 3 is the reciprocal of 1/3; and 1/3 is the reciprocal of 3.

Four-sided plane figure with all right angles; its opposite sides are equal to one another in length.

Process in which a common factor of the numerator and denominator of a fraction is divided out, leaving an equivalent fraction.

Two numbers that have no factors in common other than the number 1.

Value that is left over when one number is divided by another.

A decimal in which beyond a certain point a digit or set of digits repeats indefinitely. (Example: 3.3333… and 3.1787878…) Rounding off results in an estimated or approximate value.

90-degree angle.

Three-sided plane figure with a 90-degree angle (right angle).

Value that multiplied by itself a number of times results in the value or number wanted, such as 2 is the root of 4, because 2 multiplied by itself produces 4.

Approximating the value to the nearest digit or decimal place, such as rounding 14.9 up to 15.

A standard way of writing very large and very small numbers as the product of two values — a number between 1 and 19 and a power of 10. Scientific notation follows the form N × 10a where N is a number from 1 up to 10, but not 10 itself, and a is an integer (positive or negative number).

Half the perimeter.

Symbol indicating whether a value is positive (+) or negative (−).

A fraction in which both the numerator and the denominator are whole numbers.

To combine all that can be combined and put an expression in its most easily understandable form.

Number indicating the measure of a line’s steepness or slant and whether it rises or falls.

Value(s) of the variable that make the equation a true statement.

Find the answer or what number the variable stands for.

1. Product of another number times itself. 2. Value with an exponent of 2.

Value resulting in a given value when multiplied by itself. For example, the square root of 4 is 2, because 2 ×2 = 4, which is a perfect square.

Method of replacing a value with its equivalent.

Result of addition.

Characteristic of equations that allows for the exchange of the value(s) on one side of the equal sign with the value(s) on the other side (quantities on the right go to the left; quantities on the left go to the right) without changing the truth of the equation: If x = y, then y = x.

Short-cut division process in which only the coefficients of the terms in an expression are used. The answer is obtained by multiplying and adding.

Group of number(s) and/or variable(s) connected to one another by multiplication or division and separated from other terms by addition or subtraction.

Expression with three terms. Each term is separated from the others by addition or subtraction.

To factor a trinomial into two binomials

A numeric equivalence or worth of an expression or variable.

Letter representing an unknown number or what you’re solving for in an algebra problem.

Corner of a figure; where two sides intersect to form an angle.

Measurement of the amount of space within a three-dimensional solid figure.

All natural numbers plus zero. Start with zero and add one repeatedly to find the whole number spectrum (0, 1, 2, 3 . . . ).