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SAT Math Word Problem Skills: Translating English Expressions Into Algebraic Expressions
SAT Math: high score for being able to translate from English to algebraic notation,
Part I: Translations Involving Only One Arithmetic Operation Students who score high on the SAT Math are not necessarily better at calculus or solving equations. What they do best is “problem translation,” the ability to translate English expressions into algebraic notation. The good news about translating problems is that it requires little more than memorizing a set of rules. In the same way that, when learning a foreign language, you memorize the fact that “house” is “Haus” in German, “maison” in French or “casa” in Spanish, you memorize the fact that “three minus d ‘a number’ is written as ‘x – 3’ in algebraic notation.
Words that indicate sum are more, sum, total, greater than, increase, increased by, more than. So “the sum of a number and 7” would be written as “n + 7”. Note that we can use any letter as a variable-x, n, wowo any other letter we choose.
In addition to recognizing words that indicate addition, recognize situations in which addition is logically involved. Generally, the idea of increase will imply addition.
Subtraction is a bit trickier because often, but not always, the order of the words in an English sentence indicating subtraction will be the opposite of the order of the algebraic expression. Words that indicate subtraction are less, difference, and less.
Here are some common phrases that indicate subtraction and how to write the corresponding algebraic expressions: A number minus three n – 3 The difference between a number and 5 x – 5 3 less than a number x – 3 (Note the inversion of the order). 7 is subtracted from a number x – 7 (notice that the word “from” indicates a starting point. If you say, for example, that you traveled to New York from Cleveland, this sentence indicates that you started from Cleveland. In algebra, you “started” at x, so x should come first in this expression.
Also, when translating to algebra, even if the keywords aren’t there, if the problem implies that a decrease has occurred, subtract. For example, if someone talks about losing money or the stock market going down, a decline has occurred. This will usually indicate the remainder.
Multiplication: Look for words like product and time. More importantly, look at the underlying logic of the problem. If the same thing happens over and over and you’re trying to find a total amount, consider multiplying. Recognize that the word “of” when accompanying a fraction or decimal indicates multiplication. For example, if a landlord has ten apartments and charges $800 from each tenant, his total income is 10(800) = $8,000.
Division: Look for words like divide and ratio. More importantly, look for situations where the total is known but the size of each individual part is unknown. Let’s say we invest in the information about the owner and know that he owns 10 apartments and earns $8,000 a month. Assuming that each apartment rents for the same amount, how much is the rent for each apartment? In this case, we know a total amount and are trying to find the size of each equal part, in this case, a rent payment. Therefore, we divide.
Important point: Distinguish between the meanings of “greater than,” “is greater than,” and “how much greater than.” Greater than addition indicates. 8 greater than xx + 8 It is greater that indicates an inequality 8 is greater than 5 8 > 5 The greater that indicates subtraction. “How much greater than 5 is x” would be written as
x — 5. Similarly, distinguish between “less than”, “is less than” and “how much less”.
Less than indicate the remainder. 7 less than a number is x – 7.
mes less than indicates an inequality. 3 is less than 6 is 3 < 6.
How much less than state the remainder How much less than 8 is x 8 – x
Practice the following translation exercises: Use x to represent an unknown number.
1. A number increased by 11.
2. The sum of a number and 13
3. 3/4 of a number
4.. A number minus 17
5. 12 less than a number.
6. 15 is subtracted from a number
7. The relationship between a number and 20.
8. A number of cartons of milk are divided equally among 15 children.
9.. How much bigger is 59 than a number.
10. The total profit is x items that are sold and earn $6 each.
1. x + 11
2. x + 13
3. 3/4(x) (three-fourths times x)
4. x – 17
5. x — 12
6. x — 15
7. x / 20 (x divided by 20.)
8. x/ 15 (x divided by 15)
9. 59 — x
The next article in this series will focus on translations involving two or more arithmetic operations.
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