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EOP Math

EOP Math. Lesson 1 Ms. Lindsay July 8, 2013. Real Numbers. Natural Numbers are 1,2,3,4… Integers consists of the natural numbers together with their negatives and …-3,-2,-1,0,1,2,3… Rational Numbers are constructed by taking ratios of integers

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EOP Math

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  1. EOP Math Lesson 1 Ms. Lindsay July 8, 2013

  2. Real Numbers • Natural Numbers are • 1,2,3,4… • Integers consists of the natural numbers together with their negatives and • …-3,-2,-1,0,1,2,3… • Rational Numbers are constructed by taking ratios of integers • r=m/n where m and n are integers and n is not 0 • Irrational numbers- numbers that can not be expressed as a ratio of a ratio • Sgrt(2)

  3. Properties of Real Numbers • Commutative Property – When we add or multiply two numbers, order doesn’t matter • a+b=b+aab=ba • Associative Property- When we add or multiply three numbers, it doesn’t matter which two we add first • (a+b) + c = a + (b+c) (ab)c = a(bc) • Distributive Property – When we multiply a number by a sum of two numbers, we get the same result as multiplying the number by each of the terms and then adding the results • a(b+c) = ab + ac • (b+c)a= ab+ ac

  4. Check for Understanding • Is -4 • A Rational Number • An Irrational Number Is 2/3 • A Rational Number • An Irrational Number Is 3^1/3 • A Rational Number • An Irrational Number

  5. Properties of Negatives Property Example (-1)a = -a -(-a) = a (-a)b=a(-b) = -(ab) (-a)(-b) = ab -(a+b) = -a – b -(a-b) = b-a (-1)5 = -5 -(-5) = 5 (-5)7 = 5(-7) = -(5*7) (-4)(-3) = 4*3 -(3+5) = -3-5 -(5-8) = 8-5

  6. Check for Understanding -5*2 =? 5*2=? 5*-2=?

  7. Properties of Fractions Property Description a/b * c/d = ac/bd a/b / c/d = a/b * d/c a/c + b/c = a+b/c To multiply fractions, multiply numerators and denominators To divide fractions, invert (flip) and multiply To add fractions with different denominators, add the numerators

  8. Properties of Fractions Property Description a/b + c/d=(ad + bc)/bd ac/bc = a/b If a/b + c/d then ad=bc To add fractions with different denom. Find a common denom. Then Add the numerators Cancel numbers that are common facts in numerator & denom. Cross multiply

  9. Exponents • If a is any real number and n is a positive integer, then the nth power of a is • a^3 = a*a*a • The number a is called the base and n is called the exponent

  10. Check for Understanding A*A*A = ? B*B*B*B*B*B= ? C*C= D=

  11. Square Roots Roots (or radicals) are the opposite operation of applying exponents you can "undo" a power with a radical, and a radical can "undo" a power The symbol is called the radical symbol To simplify a square root, you "take out" anything that is a "perfect square"; that is, you take out front anything that has two copies of the same factor:

  12. Check for Understanding Sqrt (144) = ? Sqrt (64) =? Sqrt (16) = ?

  13. Perfect Squares

  14. Why Perfect Squares?

  15. Check for Understanding Now with the person sitting next to you. Write down all of the perfect squares you can remember. You have 20 seconds!

  16. Law of Exponents

  17. Fractions, Decimals and Percents Fractions and decimals represent the same things: numbers that are not whole numbers.

  18. Examples of Converting Fractions to Decimals

  19. Converting Decimal to Percentages To convert from decimal to percentage, just multiply the decimal by 100, but remember to put the "%" sign so people know it is per 100.

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