Mth 60 Module 2 Section Signed Numbers All numbers,, and

Transcription

1 Section Adding Signed Numbers Signed Numbers All numbers,, and The Number Line is used to display positive and negative numbers. Graph -7, 5, -3/4, and 1.5. Where are the positive numbers always located on a number line? Where are the negative numbers? The farther to the right on the number line, the the number is. The farther a number is to the left, the it is. The symbol > is read The symbol < is read 5 > 3 because it is -4 < -2 because it is Compare the following integers. 4 and 9 6 and -5-3 and and -4 The value is the distance a number is from zero. Identify which number has the greater absolute value, the more extreme number. -3 and and 3 Opposites and Notation for Opposites The opposite of 2 is -2, so -(-2), read the opposite of -2 is. Note: Zero, 0, is neither positive nor negative. The opposite of zero is. The opposite of 12 is. The opposite of -3 is. Find each value: - (-4) - [ - ( -1)] - { - [ - ( - 2)]} 1

2 Adding Signed Numbers Models Number Line Integer Tiles (-2) (-4) + (-2) Rules for Adding Integers (page 96) If TWO numbers have the SAME SIGN, ADD and KEEP the SIGN. If TWO numbers have DIFFERENT SIGNS, find the DIFFERENCE of the unsigned numbers and take the SIGN of the number FARTHER from ZERO (the more extreme number or the number with the greatest absolute value). Practice adding integers. (-1) + (-4) 4 + (-7) (-3) (-8) (-9.6) (-3) Summary of rule for adding signed numbers: When you add TWO POSITIVE numbers, the sum is always. When you add TWO NEGATIVE numbers, the sum is always. 2

3 When you add a POSITIVE number and a NEGATIVE number, the sign of the sum depends on which number is Section 2.2- Subtracting Signed Numbers Review. Find the following sums. Demonstrate that your answer is correct with a number line or integer tile drawing. a) 4 + (-5) = b) -3 + (-2) = c) = Choose a variable to represent the unknown quantity. Then translate the sentence into an equation and solve the equation, showing the process. Check the solution in two ways. When the total cost of a meal was divided five ways, each person s share was $ What was the total cost of the meal? Models for Subtraction Integer Related Number line Tiles Addition Problem (-3) 2 (-2) (-1) (-1) (-4) 3

4 In each case, to subtract a number is the same as So 5 8 is the same as See How to Subtract Signed Numbers on page 107. Rewrite each subtraction problem as an addition problem, then solve. Check your answers = -5 (-2) = 8 (-1) = 3 7 = 3.4 (-2.1) = = Simplify the following using the rules for addition and subtraction. 4 (-15) + (-10) (-2.7) Write a subtraction problem to represent the situation and use it to answer the question. John had $195 in his checking account before he wrote a check for $250 to pay his portion of the rent. His rent check was cashed before he could deposit his paycheck. If he was charged a $25 overdraft fee, what was his balance before he deposited his paycheck? 4

5 Section 2.3 Multiplying and Dividing Signed Numbers Review: 30 + (-5) = 30 (-5) = (-30) (-5) = Meaning of Multiplication 3 x 5 means because multiplication means repeated addition. What does 3 x (-5) mean? What does (-3) x (-5) mean? Rules for Multiplying Signed Numbers (page 120) When you multiply TWO NUMBERS with the SAME SIGN, the product is When you multiply TWO NUMBERS with OPPOSITE SIGNS, the product is When you multiply any number by ZERO (not positive or negative), the product is Meaning of Division 15 5 means because division means repeated subtraction. What does -15 (-5) mean? What does mean? Write the two related division sentences for each multiplication sentence. 3(5) = 15 3(-5) = -15 (-3)(-5) = 15 Rules for Dividing Signed Numbers (page 123) are the same as for When you divide TWO NUMBERS with the SAME SIGN, the quotient is When you divide TWO NUMBERS with OPPOSITE SIGNS, the quotient is 5

6 Since ZERO is neither positive nor negative, it has its own rules for division. Zero divided by a nonzero number is always Any number divided by zero is Multiplying or Dividing by -1 is the same as taking the of the number Simplify each expression. (-6)(-3) 3(-6) (-2)(0) (-30)(2)(-5) 2.7(-1.2) Use multiplication to check whether the following division problems were calculated correctly. State whether the answer is correct or incorrect and show the multiplication problem you did to check the answer. 18 (-2) =