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SAT Math Word Problem Skills: Translating English Expressions Into Algebraic Expressions
SAT Math: Score high knowing how to translate from English into algebraic notation,
Part I: Translations Involving Only One Arithmetic Operation Students who score high in SAT math aren’t necessarily better at math or solving equations. What they do better is “problem translation”, the ability to translate English expressions into algebraic notation. The good news about problem translation is that all you need to do is memorize a set of rules. In the same way that by taking 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 less than a number” is written “x – 3” in algebraic notation.
Words indicating addition are plus, sum, total, greater than, increase, increased by, more than. Thus, “the sum of a number and 7” would be written “n + 7”. Note that we can use any letter as variable-x, n, w or w or any other letter we want.
In addition to recognizing words that indicate addition, recognize situations in which addition is logically implied. Generally, the idea of increase will imply an addition.
Subtraction is a little trickier because often – but not always – the word order of an English sentence indicating subtraction will be the reverse of the order of the algebraic expression. The words indicating subtraction are minus, difference and minus.
Here are some common phrases indicating subtraction and how the corresponding algebraic expressions are written: A number minus three n – 3 The difference between a number and 5 x – 5 3 less than a number x – 3 (Note the reversal of the order.) 7 is subtracted from a number x – 7 (note 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 are started from Cleveland. In algebra, you “started” from x, so the x must come first in this expression.
Also, when translating to algebra, even if the key words aren’t there, if the problem implies that a decrease has taken place, subtract. For example, if someone talks about losing money or the stock market going down, a downturn has taken place. Usually this will indicate subtraction.
Multiplication: Look for words like product and time. More importantly, examine 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 owns ten apartments and receives $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 not known. Suppose we reverse the information about the owner and know that he owns 10 apartments and earns $8,000 per month. If we assume that each apartment rents for the same amount, what is the rent for each apartment? In this case, we know a total amount and try 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 indicates addition. 8 greater than xx + 8 Is greater than indicates inequality 8 is greater than 5 8 > 5 How much greater than 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 indicates subtraction. 7 less than a number is x – 7.
Iit’s less than indicates inequality. 3 is less than 6 is 3 < 6.
How much less than indicates subtraction 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 ratio of a number and 20.
8. A number of cartons of milk are divided equally among 15 children.
9.. How much greater is 59 than a number.
10. The total profit is x items sold and generates a profit of $6 each.
3. 3/4(x) (three quarters times x)
4.x – 17
7. x / 20 (x divided by 20.)
8. x/ 15 (x divided by 15)
The next article in this series will focus on translations involving two or more arithmetic operations.
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