SAT Math: Score Large by Knowing How to Translate From English Into Algebraic Notation,
Part I: Translations Involving Only One Arithmetic Operation Pupils who score substantial in the SAT Math are not essentially better at computation or equation solving. What they are greater at is “problem translation,” the potential to translate English expressions into algebraic notation. The good information about problem translation is that small a lot more is essential than the memorization of a established of policies. In the very same way that, when having a overseas language, you memorize the reality that “home” is “Haus” in German, “maison” in French, or “casa” in Spanish, you memorize the reality that “a few much less than a amount” is prepared as “x – 3” in algebraic notation.
Terms indicating addition are plus, sum, complete, increased than, improve, improved by, more than. As a result, “the sum of a number and seven” would be written as “n + seven.” Observe 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 phrases that indicate addition, recognize the circumstances in which addition is logically implied. Typically, the thought of improve will suggest addition.
Subtraction is a minor trickier due to the fact typically — but not constantly — the phrase purchase of an English phrase indicating subtraction will be the reverse of purchase of the algebraic expression. Adding 3 digit numbers with regrouping indicating subtraction are minus, big difference, and significantly less.
Below are some common phrases indicating subtraction and how the corresponding algebraic expressions are written: A quantity minus 3 n – three The variation between a variety and 5 x – five three much less than a variety x – three (Notice the reversal of the get.) seven is subtracted from a amount x – seven (Discover that the phrase “from” implies a beginning point. If you say, for case in point, that you traveled to New York from Cleveland, that phrase implies that you started from Cleveland. In algebra, you “started out” from x. Consequently, the x ought to come very first in this expression.
Also, when translating into algebra, even if the essential phrases are not there, if the issue indicates that a decrease has taken place, subtract. For instance, if someone talks about getting rid of money or the inventory market place going down, a lessen has taken location. Normally, that will reveal subtraction.
Multiplication: Search for words like solution and instances. Much more importantly, look at the underlying logic of the issue. If the exact same thing is happening in excess of and in excess of once more and you are making an attempt to find a whole sum, think about multiplying. Understand that the term “of” when accompanying a fraction or decimal indicates multiplication. For case in point, if a landlord owns ten flats and collects $800 from each and every tenant, his overall revenue is ten(800) = $eight,000.
Division: Look for phrases like divide and ratio. Far more importantly, look for circumstances in which the whole is recognized but the size of every individual element is not recognized. Suppose we reverse the info about the landlord and we know that he has ten apartments and earns $eight,000 for every month. If we suppose that each condominium rents for the same sum, how considerably is the hire for each condominium? In this case, we know a whole sum and are attempting to uncover the size of each equivalent element-in this situation, a rent payment. For that reason, we divide.
Critical Stage: Distinguish amongst the meanings of “higher than,” “is increased than,” and “how significantly greater than.” Better than signifies addition. eight better than x x + 8 Is greater than suggests an inequality eight is greater than five 8 > 5 How much better than signifies subtraction. “How significantly greater than 5 is x” would be created as
x — five. In the same way, distinguish among “much less than,” “is considerably less than” and “how considerably much less.”
Considerably less than indicates subtraction. 7 considerably less than a variety is x – seven.
Is much less than implies an inequality. three is much less than six 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.
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.