Rearranging Equations

Verbal Expressions

Sometimes you will be given a sentence, describing an expression or equation, and will be expected to write the expression or equation. Other times, you will be given an expression or equation, and be expected to write the sentence form of it.

Addition

A sentence or word problem may be asking you to add if you see these words:

Subtraction

A sentence or word problem may be asking you to add if you see these words:

A Note on Order

Due to the properties of addition, it doesn’t really matter the order you are adding the two terms. However, the order matters with subtraction. Write out the expression in the order the terms are given to you, with the exception of “less than.”

It is very to mix up “less” and “less than.” 13 less a number would be 13 - n, written in the order it was given. 13 less than a number would be n - 13, where you reverse the order.

Multiplication

Division

Exponents

Multi-Term Verbal Expressions

When creating an expression or equation from a sentence or word problem, there may be multiple operations being done.

Rearranging Equations

Rewriting Equations

Sometimes you may be asked to rewrite an equation in terms of a different variable than the original equation. To set an equation equal to a certain variable, we can rearrange the equation using our knowledge of basic algebraic principles.

Rewrite the following equation so that it gives y in terms of x.

"In terms of" refers to the fact that one variable is described by its relationship with another variable. y in terms of x means that one side of the equation will be set equal to y, while the other side of the equation will include the variable x.

Rewriting Equations with Multiple Variables

We can rearrange equations with more than two variables using the same process as above.

Practice Problems

Write the equation or expression based on the description.

1. 3 less twice a number j.
2. The quotient of q to the fifth power and 14 equals 8.
3. One third of d.
4. 3 multiplied by r decreased by 8.
5. The sum of 4 times f and 3 times g.

Write the description based on the equation or expression.

1. 
2. 
3. 
4. 
5. 

Answers

1. 3 - 2j
2. q⁵/14 = 8
3. (⅓)d
4. 3r - 8
5. 4f + 3g

 

1. 3 times a number minus 4 equals 6
2. v squared minus 5
3. 6 less the quotient of t and 3
4. 5 times a number y increased by 4 times a number z
5. Four fifths of a number