Chapter 8: Variables and Expressions 103the 3 are connected by the conjunction +, and the verb, the action of the sentence, is the =. The
= says “is,” or “makes.”
The difference between a phrase and a sentence is whether or not you have a verb. Sentences
have verbs, phrases do not. x + 9 is a phrase. It has no equal sign or inequality sign. It sounds
like “a number increased by 9.” On the other hand, x + 9 > 21 is a sentence. The > is the verb “is
greater than.” It says “some number increased by 9 is greater than 21.”
When parentheses appear, it’s often easier to read if you refer to “the quantity.” The sentence
5(x + 7) = 45 can be read as “five times the quantity x plus 7 is 45.” The words “the quantity” tell
your listener that parentheses are grouping some symbols into one quantity.
The larger your vocabulary, the better able you are to say what you really mean, so let’s look at
some common language. That sentence 5(x + 7) = 45 could also be read as “five times the sum
of x and 7 is 45.” A sum is the result of an addition. If you change the plus sign to a minus sign,
5(x – 7) = 45 can be read as “five times the difference of x and 7 is 45.” A difference is the result
of a subtraction. Whenever you talk about a difference, you read the numbers in the order they
appear. The difference of x and 7 is x – 7. The difference of 7 and x is 7 – x.Idioms in Algebra
Idioms are phrases used in a language that just can’t translate word for word. If I tell you to give
me break, I’m not asking you to hurt me. I’m telling you to stop teasing me or trying to fool me.
“Give me a break” is an idiom.
Algebra has idioms, too. One in particular has to do with subtraction. The phrase “6 less than
some number” sounds as though it would begin with a 6 if you wrote it in symbols, but it actually
translates to x – 6. To see why, put a number in place of the words “some number.” If I say “6
less than 25,” you think of 25 – 6, or 19. You take 6 away from the number. So 9 less than some
number is t – 9, and 83 less than some number is y – 83.MATH TRAP
Don’t confuse “6 less than some number” with “6 is less than some number.” The word
is signals a verb. “6 less than some number” translates to x – 6, but “6 is less than some
number” would be 6 < x.If you want to read the phrase 7(x + 5), you could say “seven times the quantity x and 5,” or you
could say “the product of 7 and the quantity x plus 5.” A product is the result of multiplication.
When you want to say something about division, like x
5 11 , you can say “a number divided by 5
is 11,” or you can say “the quotient of x and 5 is 11.” A quotient is the result of division. The order
in which the numbers are named tells you which is the dividend and which is the divisor. The
quotient of x and 5 is x ÷ 5, but the quotient of 5 and x is 5 ÷ x.