SAT Math: Score Higher by Being aware of How to Translate From English Into Algebraic Notation,
Portion I: Translations Involving Only 1 Arithmetic Operation Students who rating large in the SAT Math are not always much better at computation or equation resolving. What they are better at is “dilemma translation,” the capability to translate English expressions into algebraic notation. The good news about problem translation is that small a lot more is required than the memorization of a established of rules. In the very same way that, when getting a foreign language, you memorize the truth that “property” is “Haus” in German, “maison” in French, or “casa” in Spanish, you memorize the fact that “three less than a amount” is written as “x – 3” in algebraic notation.
Words and phrases indicating addition are plus, sum, overall, higher than, enhance, elevated by, far more than. As a result, “the sum of a quantity and seven” would be created as “n + 7.” Discover that we can use any letter as a variable-x, n, w, or w or any other letter we choose.
In addition to recognizing the words and phrases that point out addition, identify the situations in which addition is logically implied. Normally, the idea of increase will suggest addition.
Subtraction is a little trickier because often — but not usually — the term order of an English phrase indicating subtraction will be the reverse of order of the algebraic expression. Words and phrases indicating subtraction are minus, difference, and considerably less.
Listed here are some widespread phrases indicating subtraction and how the corresponding algebraic expressions are prepared: A quantity minus 3 n – three The variation between a number and five x – five three much less than a number x – 3 (Notice the reversal of the buy.) seven is subtracted from a amount x – seven (Observe that the phrase “from” signifies a commencing stage. If you say, for case in point, that you traveled to New York from Cleveland, that phrase suggests that you started from Cleveland. In algebra, you “began” from x. Hence, the x should come 1st in this expression.
Also, when translating into algebra, even if the important phrases are not there, if the problem implies that a reduce has taken location, subtract. For instance, if somebody talks about getting rid of money or the inventory industry likely down, a lower has taken area. Generally, that will indicate subtraction.
Multiplication: Seem for phrases like solution and occasions. Far more importantly, seem at the underlying logic of the dilemma. If the very same thing is taking place more than and more than once again and you are trying to locate a overall quantity, believe about multiplying. Recognize that the term “of” when accompanying a fraction or decimal implies multiplication. For illustration, if a landlord owns ten residences and collects $800 from every single tenant, his total revenue is 10(800) = $eight,000.
Division: Look for terms like divide and ratio. Far more importantly, look for situations in which the complete is acknowledged but the dimensions of every specific component is not recognized. Suppose we reverse the data about the landlord and we know that he has 10 residences and earns $eight,000 for each month. If we believe that every single condominium rents for the same volume, how significantly is the lease for each apartment? In yoursite.com , we know a complete volume and are making an attempt to discover the dimension of every equivalent element-in this circumstance, a rent payment. For that reason, we divide.
Important Position: Distinguish among the meanings of “greater than,” “is higher than,” and “how much higher than.” Increased than implies addition. eight better than x x + 8 Is increased than implies an inequality eight is better than five eight > 5 How considerably increased than implies subtraction. “How considerably greater than 5 is x” would be written as
x — 5. In the same way, distinguish amongst “significantly less than,” “is much less than” and “how a lot less.”
Significantly less than indicates subtraction. seven less than a amount is x – seven.
Is much less than signifies an inequality. 3 is much 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 milk cartons is divided evenly among 15 children.
9.. How much greater is 59 than a number.
10. Total profit is x items are sold and earn $6 profit each.
Answers:
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
10. 6x
The next article in this series will focus on translations involving two or more arithmetic operations.