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Unit 1: Rational Numbers

Unit 1: Rational Numbers. Topic: Review of Integers. Math 9 Miss Wilkinson Monday, September 9. What is an Integer?. Integers : Includes all of the Whole Numbers (called Natural Numbers). Recall: Integers are positive and negative whole numbers including zero .

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Unit 1: Rational Numbers

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  1. Unit 1: Rational Numbers Topic: Review of Integers Math 9 Miss Wilkinson Monday, September 9

  2. What is an Integer? • Integers: Includes all of the Whole Numbers (called Natural Numbers). • Recall: Integers are positive and negative whole numbers including zero. • Never a fraction or decimal! • Integers are whole numbers that describe opposite ideas in mathematics.

  3. Positive Integers • right of zero • valued greater than zero. • Express ideas of up, a gain or a profit. • The sign for a positive integer is (+), however the sign is not always needed. • Meaning +3 is the same value as 3. Examples: Speed limits, time,golf scores.

  4. Negative Integers • left of zero • valued less than zero. • Express ideas of down or a lose. • The sign for a negative integer is (-). This sign is always needed. • Examples: thermometer, altitude, sports (+/-)

  5. Integers on a Number Line • Writing numbers down on a Number Line makes it easy to tell which numbers are bigger or smallerand how far they are away in relation to each other. • Ex: Plot 2, -6, 0 and-8 on a number line. Which number is larger?

  6. Comparing Integers Do we remember the symbols < and > ? • 1 < 3 means that 1 is LESS THAN 3 • 9 > 2 means that 9 is GREATER THAN 2 • 8 ___ 2 • 3 ___ 5 • -1 ___ -3 • -5 ____ 3

  7. Addition of Integers • Adding two positives results in a positive number. • Adding two negatives results in a negative number • Adding a negative is like subtracting a positive. Remember +(-n)=-n and –(+n)=-n where n is a number. • Math Term: SUM Examples: a) 15 + (-4) b) (+4) + (-15) c) (-8) + (-2)

  8. Subtraction of Integers • Subtracting a negative is like adding a positive. • Math Term: DIFFERENCE Examples: a) 8 – (-4) b) 8 – 4 c) -8 –4

  9. The Rules • Addition and Subtraction of integers can be put into two rules: Rule #1 Two like signs become a positive sign +(+) ex: 3+(+2) = 3 + 2 = 5 −(−)ex: 6−(−3) = 6 + 3 = 9 Rule #2 Two unlike signs become a negative sign +(−) ex: 7+(−2) = 7 − 2 = 5 −(+) ex: 8−(+2) = 8 − 2 = 6

  10. Multiplication of Integers In multiplication, we are trying to find the product of two integers. First step is to multiply the numbers like regular. Math Term: PRODUCT

  11. Understand So, why do two negatives make a positive? • If I say "Eat!" I am encouraging you to eat (positive) • But if I say "Do not eat!" I am saying the opposite (negative). • Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive).

  12. Examples • (3)(-4)= -12 c) (-4)(-1) WHY? 3 sets of 4 -4+-4+-4 = -8+-4 = -12 b) (7)(8)(-2) d) (6)(-3)(0)

  13. Division of Integers • Division of integers is the opposite of multiplying integers, but the rules are the same. • Do we remember how to long divide? • Math Term: QUOTIENT

  14. Examples: a)-20 ÷ -4 c) -12 ÷ 3 b) 64 ÷ -8 d) -156 ÷ 9

  15. Order of Operations • We now know how to add, subtract, multiply and divide integers • What happens when there is more than one of the above operations in the same problem? • When simplifying an expression that has more than one operation symbol, there is a special order you must follow. • Has anyone heard of BEDMAS?

  16. ÷ × • Brackets always come first. Solve what is inside the brackets • Exponents always come second. • D/M- when working with multiplication and division, you do whichever comes first as you work from left to right. If multiplication comes first, do it before dividing. • A/S-same as multiplication and division-when working with addition and subtraction, you do whichever comes first as you work from left to right.

  17. Examples • 8 x 2 -3 c) (5+2)(1-9) • 2x 4 -3 + 7 d) 22 + 7 x 2

  18. Assignment • I want to see where each and every one of your understanding is in regards to the review of integers and operations on integers (addition, subtraction, multiplication, division). • Please complete this short assignment at the end of class and hand it in to Miss Wilkinson.

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