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REVIEW OF NUMBER TERMS, FORMULAS, ETC

REVIEW OF NUMBER TERMS, FORMULAS, ETC. The SAT loves to throw around terminology about numbers. If you don’t know the terminology, you won’t know how to answer. Whole Numbers. The set of counting numbers, including zero {0, 1, 2, 3, . . .}

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REVIEW OF NUMBER TERMS, FORMULAS, ETC

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  1. REVIEW OF NUMBER TERMS, FORMULAS, ETC

  2. The SAT loves to throw around terminology about numbers. If you don’t know the terminology, you won’t know how to answer. • Whole Numbers.The set of counting numbers, including zero {0, 1, 2, 3, . . .} • Natural Numbers.The set of all whole positive numbers except zero {1, 2, 3. . .} • Integers. The set of all positive and negative whole numbers, including zero. Fractions and decimals are not included {. . . , –3, –2, –1, 0, 1, 2, 3, . . .}. • Rational Numbers. The set of all numbers that can be expressed as integers in fractions. That is, any number that can be expressed in the form m⁄n, where m and n are integers. • Irrational Numbers. The set of all numbers that cannot be expressed as integers in a fraction. Examples include π, , and 1.01001000100001000001. . . . A number must be either rational or irrational; no number can be both. • Real Numbers. Every number on the number line. The set of real numbers includes all rational and irrational numbers.

  3. Number Terms Practice • If x is an integer, what are the possible answers for x2 = 25 • Which of the following numbers is not rational? 33/99 164/258 -5/-15 • Which of the following is not a whole number? 5 0 -3 2 • Which of the following not a natural number? 6 3 198 0

  4. PEMDAS is an acronym for the order in which mathematical operations should be performed as you move from left to right through an expression or equation: Parentheses Exponents Multiplication Division Addition Subtraction “Please Excuse My Dear Aunt Sally”

  5. If an equation contains any or all of these PEDMAS elements, first carry out the math within the parentheses, then work out the exponents, then the multiplication, and the division. Addition and subtraction are actually a bit more complicated. When you have an equation to the point that it only contains addition and subtraction, perform each operation moving from left to right across the equation. 22

  6. Operations and Odd and Even Numbers If you know how odd and even numbers act when put through any of the four operations, you have a leg up in using the process of elimination. If the numbers in the answer choices are both odd and even, you should be able to use the rules of odd and even numbers to figure out if the answer you’re looking for is odd or even. So even if you don’t know the exact value of the answer you’re looking for, you should be able to eliminate half of the answers based on whether they’re odd or even.

  7. Odds & Evens Practice • EVEN • ODD • ODD • EVEN • EVEN • EVEN • ODD • 2859 + 4357 = odd or even • 345 + 276 = odd or even • 5392 – 237 = odd or even • 53 x 42 = odd or even • 224 - 16 = odd or even • 356 – 412 = odd or even • 45 x 57 = odd or even

  8. Multiplying and Dividing Negative Numbers When negative numbers are involved in multiplication and division, they affect whether the outcome is positive or negative. You should know these rules cold. Here’s a helpful trick when dealing with a series of multiplied or divided positive and negative numbers: If there’s an even number of negative numbers in the series, the outcome will be positive. If there’s an odd number, the outcome will be negative.

  9. Positive & Negative Practice • Positive • Negative • Positive • Negative • Positive • Positive • Negative • 2859 x 4357 = positive or negative • -34 x 34 = positive or negative • 5392 ÷ 237 = positive or negative • 53 x -42 = positive or negative • -224 ÷ - 16 = positive or negative • -356 x -412 = positive or negative • -45 x 57 = positive or negative

  10. Divisibility Rules The SAT sometimes tests whether you can determine if one number is divisible by another. To check divisibility, you could take the immense amount of time necessary to do the division by hand and see if the result is a whole number. Or you can give yourself a shortcut and memorize the list of divisibility rules Example: =z What are the possibilities for k?

  11. Divisibility Rules • All whole numbers are divisible by 1. • All numbers with a ones digit of 0, 2, 4, 6, or 8 are divisible by 2. • A number is divisible by 3 if its digits add up to a number divisible by 3. For example, 6,711 is divisible by 3 because 6 + 7 + 1 + 1 = 15, and 15 is divisible by 3. • A number is divisible by 4 if its last two digits are divisible by 4. For example, 80,744 is divisible by 4, but 7,850 is not. • A number is divisible by 5 if it ends in 0 or 5.

  12. Divisibility Rules • A number is divisible by 6 if it is even and also divisible by 3. • There are no rules for 7. It is a rebel. • A number is divisible by 8 if its last three digits are divisible by 8. For example, 905,256 is divisible by 8 because 256 is divisible by 8, and 74,513 is not divisible by 8 because 513 is not divisible by 8. • A number is divisible by 9 if its digits add up to a number divisible by 9. For example, 1,458 is divisible by 9 because 1 + 4 + 5 + 8 = 18 and 18 is divisible by 9. • A number is divisible by 10 if it ends in 0.

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