Mathematics 4 Life and Beyond: Solving Equations Containing Decimals (3-5)

Solving Equations Containing Decimals

Vocabulary

Integers - A set of whole numbers and their opposites.

Divisor - The quantity by which another quantity is to be divided (the number outside).

Dividend - A quantity to be divided (the number inside).

Quotient - The result (answer) of the division of one quantity by another.

Reciprocal - Two numbers that have the product of 1.

Coefficient - A number used to multiply a variable.

Inverse Operation - The operation that is the opposite of another (i.e. multiplication = division)

Variable - A symbol, usually a letter, that can stand for a variable quantity.

Linear equation - An equation whose graph in a coordinate grid is a straight line.

A linear equation is an algebraic equation in which the variable(s) are multiplied by numbers or added to numbers, with nothing more complicated than that.
A solution to an equation is a number that can be plugged in for the variable to make a true number statement.
Some linear equations can be solved with a single operation. For this type of equation, use the inverse operation to solve. Inverse operations "undo" each other. The easiest type involves only an addition or a subtraction.

Example:

Solve:
p + 4.5 = 9.3
The inverse operation of addition is subtraction. So, subtract –4.5 from both sides.
p + 4.5 – 4.5 = 9.3 – 4.5
Simplify.
p = 4.8

We can also solve linear equations when multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of 1.

Example 1:

Solve: