Writing Algebraic Expressions

Turning Sentences into Equations

In math class you will often need to write equations or expressions based on a scenario to perform some math and solve the question. You will want to express unknown terms using variables. Look for terms like "a number" which can be represented with a variable like \(x\). Then you will need to add operators (+, -, *, /). Look for terms like "increase", "decrease", "double", "triple", "half". Finally, if you need to write an equation (=) look for terms like "is" or "equals". See the summary table below.

Part of Equation Example Keywords
Variables \(x, y\) "A number"
Operators \(+ - * /\) "increase", "decrease", "double", "triple", "half", "more", "less"
Equal Sign \(=\) "is", "equals"

If we had to write an expression for the phrase "double a number is 14", the number would be represented by \(x\), we need to multiply it by \(2\) since it says "double" and the term is equal to 14 because it says "is":

\( 2x = 14 \)

Write an expression for the phrase 'a number decreased by 6 is 5'.

Sometimes there are several unknowns. Use separate variables to represent each one. It is also good practice to write out what each variable represents. Here is an example question:

Elmer earns $5 per hour when they babysits 1 child. They earn $8 per hour when they babysits 4 children. Write an expression to represent their earnings.

Let \(E\) represent Elmer's earnings in dollars ($).

Let \(x\) represent the number of hours they babysit 1 child.

Let \(y\) represent the number of hours they babysit 4 child.

Elmer's earnings is the sum of the money earned from babysitting 1 child and 4 child. The earnings from babysitting 1 child is \(5x\) because they earm $5/hr and \(x\) is the number of hours worked. Similarly, the earnings from babysitting 4 child is \(8y\) because they earm $8/hr and \(y\) is the number of hours worked. The total earnings are:

\( E = 5x + 8y\)

Writing Equations for Word Problems

Writing equations is very important for solving word problems! Use what we have learned to solve the question below. Remember, each unknown is represented with a variable.

The length of a rectangle is 2 times the width of the rectangle. Let \(x\) represent the width of the rectangle.

Write an expression to represent the length of the rectangle.


Write a simplified expression for the perimeter of the rectangle.


Suppose the width is \(6 \; [cm]\). Find the perimeter of the rectangle.


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