translate each mathematical phrase into an English phrase.m2 +2n
Answers
Step-by-step explanation:
The expressions we'll be translating are very straightforward. For example, the phrase "3 more than an unknown number" becomes the mathematical expression "x + 3." Because the unknown number has no explicitly stated value, we label it with a variable x. To get a value three more than x, simply add 3 to it. If this is tricky to you, just think in terms of a real number example. Ask yourself "What is 3 more than the number 7?" Clearly the answer is 10, and you get that answer via the expression "7 + 3 = 10." So, to get 3 more than an unknown number, replace the known number 7 with the unknown number x.
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In this translation problem, the key words were "more than," because they clued you in that addition will be necessary. Each operation has its own cue words, and I've listed them here, with an example for each:
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Addition
Kelley's Cautions
Since subtraction is not commutative, be careful to get the order of the numbers right. Notice that "5 less a number" and "5 less than a number" mean completely different things.
More than/greater than: "11 greater than a number" means "x + 11"
Sum: "The sum of a number and 6" means "x + 6"
Subtraction
Critical Point
If no symbol is written between two things, multiplication is implied. Thus, 5y means "5 times y" and 2(x + 1) means "2 times the whole expression (x + 1)." Also, from this point forward, I will usually use the symbol "·" to indicate multiplication, because it's too easy to mix up the other multiplication symbol, —, with the variable x.
Fewer than/less than: "7 fewer than a number" means "x - 7"
Less: "17 less a number" means "17 - x"
Difference: "The difference of a number and 6" means "x - 6"
Multiplication
You've Got Problems
Problem 1: Translate into a mathematical expression: 5 less than one third of a number.
Product: "The product of a number and 3" means "x · 3", also written "3x" (since multiplication is commutative, the order in which you write the numbers doesn't matter)
Of: "Half of 20" means " 1�„2 · 20"
Division
Quotient: "The quotient of 10 and a number" means "10 · x"
Fractions: Don't forget that any expression written as a fraction is technically a division problem in disguise.
Example 1: Translate into mathematical expressions.
(a) The sum of 6 and twice a number
Solution: The phrase "twice a number" translates into two times the number, or 2x. (Think about it€”twice the number 8 would be 2 · 8 = 16.) The word "sum" indicates that you should add 6 and 2x together to get a final answer of 6 + 2x.
(b) The product of 2 and 3 more than a number
Solution: You may be tempted to give an answer of 2 · x + 3, but that equals 2x + 3, or "3 more than 2 times a number." You need to use parentheses to keep the x + 3 together like so: 2(x + 3). Now, the 2 is multiplied by the entire x + 3, not just the x.
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