- The expression translates to 7 + −4.
Reminder: The AND keyword translates to mean “plus” because the leading keyword is SUM OF. With other leading keywords (discussed in the following sections), AND can mean other things. Also notice that you do not simplify the expression and get “3” for the answer because you are just translating words into symbols and not performing the math.
Two other keywords on the addition keyword list, PLUS and INCREASED BY, can be correctly translated by the direct translation strategy. In the direct translation strategy, you translate each word into its corresponding algebraic symbol, one at a time, in the same order as written, as shown in Example 4.
Example 4: Translate the following: a number increased by twenty‐four
- The expression translates to x + 24.
Some additional keywords, such as GAIN, MORE, INCREASE OF, and RAISE, are commonly found in story problems, as in Example 5.
Example 5: Translate the following story problem into a mathematical expression about the weight of the linebacker: The defensive linebacker weighed two hundred twenty‐two pounds at the beginning of spring training. He had a gain of seventeen pounds after working out with the team for four weeks.
- The expression translates to 222 + 17.
Note: Not all numbers mentioned in a word problem should be included in the mathematical expression. The number “four” is just interesting fact, but it is not information you need in order to write an expression about the linebacker's weight.
You may also be wondering why the answer isn't 239 pounds. That's because the question asks you to translate the story problem into a mathematical expression, not to evaluate the expression.
Example 6: Translate the following word problem into a mathematical expression about the cashier's current hourly wage: A cashier at the corner grocery was earning $6.25 an hour. He received a raise of 25 cents an hour.
- The expression translates to 6.25 + 0.25.
Note: The hourly wage is stated in dollars, and the raise is stated in cents. Any time you are adding two numbers that have units, make sure both numbers are measured with the same units; if they aren't, convert one of the numbers to the same units as the other. Having both numbers measured with the same units is called homogeneous units. In this example, you convert his raise, the 25 cents, to $0.25 because his hourly wage is measured in dollars, not cents, so the raise must also be in dollars.
Subtraction keywords also include leading keywords, keywords that can be translated one word at a time, and keywords that are found in story problems. Look at the following list of subtraction keywords:
- DIFFERENCE BETWEEN _____ AND _____
One subtraction keyword (DIFFERENCE BETWEEN) is a two‐part expression that begins with a leading keyword that defines the corresponding AND. You can use the same methods of underlining and circling the keywords shown in the preceding section to translate these expressions.
Example 7: Translate the following: the difference between four and six
Here is how you translate Example 7: