Presentation on theme: "Lesson 2 Operations with Rational and Irrational Numbers"— Presentation transcript:
1 Lesson 2 Operations with Rational and Irrational Numbers NCSCOS Obj.: 1.01; 1.02ObjectiveTLW State the coordinate of a point on a number lineTLW Graph integers on a number line.TLW Add and Subtract Rational numbers.TLW Multiply and Divide Rational numbers
3 SUBTRACT and use the sign of the larger number. Addition Rule1) When the signs are the same,ADD and keep the sign.(-2) + (-4) = -62) When the signs are different,SUBTRACT and use the sign of the larger number.(-2) + 4 = 22 + (-4) = -2
4 Karaoke Time!Addition Rule: Sung to the tune of “Row, row, row, your boat”Same signs add and keep, different signs subtract, keep the sign of the higher number, then it will be exact!
7 The additive inverses (or opposites) of two numbers add to equal zero. Example: The additive inverse of 3 is-3Proof: 3 + (-3) = 0We will use the additive inverses for subtraction problems.
8 What’s the difference between 7 - 3 and 7 + (-3) ? The only difference is that is a subtraction problem and 7 + (-3) is an addition problem.“SUBTRACTING IS THE SAME AS ADDING THE OPPOSITE.”(Keep-change-change)
9 When subtracting, change the subtraction to adding the opposite (keep-change-change) and then follow your addition rule.Example #1: (-7)- 4 + (+7)Diff. Signs --> Subtract and use larger sign.3Example #2:- 3 + (-7)Same Signs --> Add and keep the sign.-10
10 11b + (+2b) Same Signs --> Add and keep the sign. 13b Okay, here’s one with a variable!Example #3: 11b - (-2b)11b + (+2b)Same Signs --> Add and keep the sign.13b
11 Which is equivalent to -12 – (-3)? 12 + 312 - 3Answer Now
37 an easy way to determine the sign of the answer When you have an odd number of negatives, the answer is negative.When you have an even number of negatives, the answer is positive.4) (-2)(-8)(3)(-10)Do you have an even or odd number of negative signs?3 negative signs -> Odd -> answer is negative-480
38 Positive or negative answer? Positive - even # of negative signs (4) Last one!5)Positive or negative answer?Positive - even # of negative signs (4)Write all numbers as fractions and multiply.=12
39 What is the sign of the product of (-3)(-4)(-5)(0)(-1)(-6)(-91)? PositiveNegativeZeroHuh?Answer Now
40 Dividing Rules1) If the numbers have the same signs then the quotient is positive.-32 ÷ (-8 )= 42) If the numbers have different signs then the quotient is negative.81 ÷ (-9) = -9
41 When dividing two negative numbers, the quotient is positive. TrueFalseAnswer Now
42 When dividing a negative number and a positive number, use the sign of the larger number. TrueFalseAnswer Now
43 The reciprocal of a number is called its multiplicative inverse. The reciprocal of iswhere a and b 0.The reciprocal of a number is called its multiplicative inverse.A number multiplied by its reciprocal/multiplicative inverse is ALWAYS equal to 1.
44 Example #1The reciprocal of isExample #2The reciprocal of -3 is
45 Basically, you are flipping the fraction! We will use the multiplicative inversesfor dividing fractions.
46 Which statement is false about reciprocals? Reciprocals are also called additive inversesA number and its reciprocal have same signsIf you flip a number, you get the reciprocalThe product of a number and its reciprocal is 1Answer Now
47 Examples1)When dividing fractions, change division to multiplying by the reciprocal.