Textbook

This chapter will focus on converting words to numbers. In other words, we will be taking a word problem and putting it into numerical terms. This is a key skill to understanding word problems. More often than not, the wording and details of a problem can cause students to make errors even when they understand the mathematical ideas perfectly. So, pay close attention to this chapter and you will be able to understand word problems simply and efficiently.

The following will list each mathematical operator and the words that are commonly used to express them in word problems:

There is not much else to this chapter other than the application of these terms, so we will do some practice. In the following examples, you will be given a word problem and tasked with turning the problem into an equation. It will be most beneficial to try each problem yourself before revealing the answer.

We will do the first one together:

A number is three less than four times a second number.

“A number” refers to a number we do not know. That makes it a variable. It will be $x$ in this case.

“Is” rewritten is “$=$”.

“Three less than” rewritten is “$−3$”.

“Four times” rewritten is “$4∗$”.

“Second number” is a new variable, $y$, since we already have used $x$.

Writing it all out, we get $x=4∗y−3$

$5$ times the original number is $2$ more than the new number.

(spoiler)

“$5$ times” rewritten is “$5∗$”

“The original number” rewritten is $x$

“Is” rewritten is “$=$”

“$2$ more” rewritten is “$+2$”

“The new number” rewritten is $y$

All together, $5∗x=y+2$

A second book is worth four more than two out of seven of the original book.

(spoiler)

“Second book” rewritten is $x$

“Is worth” rewritten is “$=$”

“Four more than” rewritten is “$+4$”

“Two out of seven” rewritten is “$2/7$”

“Original book” rewritten is $y$

All together, $x=(2/7)∗y+4$

When a car is driven off its dealership parking lot, its value becomes half its original value

(spoiler)

“Value” rewritten is $x$

“Is” rewritten is “$=$”

“Half its original value” rewritten is “$21 ∗y$”

All together, $x=21 ∗y$

There is an apartment in town that charges $$400$ as a down payment and $$600$ more for each month rented out. How much would it cost to rent the apartment for $6$ months?

(spoiler)

$$400$ is a base payment. It happens no matter how long the apartment is rented. We will rewrite this portion as “$+400$”

$$600$ is charged for “each month.” This means that we will multiply $$600$ by however many months we are renting. Rewritten, this is “$600∗$” the number of months, “$6$.”

All together, $x=400+600∗6=4,000$

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