# 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.