1 of 11. Adding Signed Numbers. MAT001 Chapter 9 Signed Numbers. Section 9.1. The Number Line. Ordering Numbers. CQ9-01. Replace? with < or >.

Transcription

1 Sectin 9 Adding Signed Numbers The Number Line A number line is a line n which each pint is assciated with a number 0 Negative numbers Psitive numbers f The set f psitive numbers, negative numbers, and zer is the set f signed numbers f Ordering Numbers Signed numbers are named in rder n the number line Smaller numbers are n the left CQ9-0 Replace? with < r > 9? less than 0 < Replace the? with r > > > greater than? Since lies t the right f, we knw that > f f CQ9-0 Replace? with < r >? CQ9-0 Replace? with < r >? f f f

2 CQ9-0 Replace? with < r >? 9 Abslute Value The abslute value f a number is the distance between that number and zer n a number line Symbl fr abslute value = Distance f Distance f = f f CQ9-0 CQ f f Adding Tw Numbers with Same Signs CQ9-07 9) Additin Rule fr Tw Numbers with the Same Sign T add tw numbers with the same sign: Add the abslute value f the numbers Use the cmmn sign in the answer Add ) + ) + We add the abslute values f the numbers and A negative sign is used because we added tw negative numbers f f f

3 Adding Tw Numbers with Different Signs Adding Tw Numbers with Different Signs Additin Rule fr Tw Numbers with Different Signs T add tw numbers with different signs: Subtract the abslute value f the numbers Use the sign f the number with the larger abslute value Add + 9) + 9 We subtract the abslute values f the numbers and 9 A negative sign is used because the sign f the larger number is negative f Add ) + ) + We subtract the abslute values f the numbers and The answer is psitive because the sign f the larger number is psitive Add ) + + f Adding Tw Numbers with Different Signs CQ Cmmutative Prperty f Additin Fr any real numbers a and b, a + b = b + a This mrning, the temperature in Alaska was F This afternn, the temperature rse F What was the new temperature? + Because additin is cmmutative, we culd als have added the temperatures this way: + f f CQ ) CQ f f f

4 Adding Three r Mre Signed Numbers CQ9-7 0) Add ) + + ) Because additin is cmmutative, the numbers can be added in any way ) + + ) 0 + ) r ) + ) f f Adding Three r Mre Signed Numbers Assciative Prperty f Additin Fr any real numbers a, b, and c, a + b) + c = a + b + c) The fllwing table represents the prfit and lss fr the past five mnths at Sally s Butique Find the verall prfit Mnth Prfit/Lss Jan,90 Feb, Mar,0 Apr,7 May 7 It is usually easier t add the psitive numbers and the negative numbers separately,90,0 +,7,07, + 7 $,00 prfit,070 f CQ ) f Oppsite Numbers Sectin 9 The ppsite f a psitive number is a negative number with the same abslute value The ppsite f is Subtracting Signed Numbers 0 + ) = 0 The sum f a number and its ppsite is zer 0 = 0 + ) = f = 7 + ) = 7 = 0 + ) = 0 Subtracting is the same as adding the ppsite f f

5 Subtractin f Signed Numbers Subtractin f Signed Numbers T subtract signed numbers, add the ppsite f the secnd number t the first number a b = a + b) Subtract + ) 0 The ppsite f is Change the subtractin t additin Perfrm the additin f the tw negative numbers f Subtractin f Signed Numbers Subtract ) + ) The ppsite f is Change the subtractin t additin Perfrm the additin Remember when subtracting tw signed numbers: The first number des nt change The subtractin sign is changed t additin Write the ppsite f the secnd number Find the result f the additin prblem f CQ9-79 ) CQ f f CQ9- CQ9- ) f f f

6 CQ9-7 ) CQ9- f f CQ9-9 9 Applied Prblems with Signed Numbers Find the difference in altitude between a muntain feet high and a grge 0 feet belw sea level Sea level feet Difference in altitude feet 0 feet ) = 97 feet 0) = + 0 = f f 0 feet CQ9-0 The rm temperature is F nw After an hur, it drps F One mre hur later, it rises 0 F What is the rm temperature after hurs? F F 7 F 7 F CQ9- The rm temperature is F nw After an hur, it rises F One mre hur later, it drps F What is the rm temperature after hurs? F F F F f f f

7 Multiplicatin with Different Signs Sectin 9 Ntice the fllwing pattern when multiplying numbers with different signs Multiplying and Dividing Signed Numbers This number decreases by each time ) = ) = ) = 0) = 0 ) = ) = ) = This number decreases by each time The pattern suggests that when we multiply a psitive number by a negative number, we get a negative number 7 f f Multiplicatin with Different Signs CQ9-0) Multiplicatin f Signed Numbers with Different Signs T multiply tw numbers with different signs, multiply the abslute value The result is negative Multiply ) ) = Multiply 9) 9) = 0 The result will always be negative f f CQ9- ) Divisin with Different Signs 0 0 Divisin f Signed Numbers with Different Signs T divide tw numbers with different signs, divide the abslute value The result is negative Divide = 9 Divide 00 0) 00 0) = The result will always be negative f f 7 f

8 CQ CQ ) f f Multiplicatin with Same Signs Ntice the fllwing pattern when multiplying tw negative numbers This number decreases by each time ) = ) = ) = 0 ) = 0 ) = ) = ) = This number decreases by each time The pattern suggests that when we multiply tw negative numbers, we get a psitive number The same is true fr divisin f signed numbers with the same sign) f Multiplicatin with Same Signs Multiplicatin and Divisin f Signed Numbers with the Same Signs T multiply r divide tw numbers with the same sign, multiply r divide the abslute values The result is psitive Divide 7 ) Multiply 7 ) = The result will always be psitive f CQ9- ) ) CQ9-7 9) f f f

9 CQ9-0 0) ) Multiplying Three r Mre Signed Numbers Multiply )) )) = ) First multiply ) = Perfrm the peratins = Then multiply ) = T divide the first tw fractins, invert and multiply the secnd fractin f 0f Order f Operatins Sectin 9 Order f Operatins with Signed Numbers f Order f Operatins fr Signed Numbers With gruping symbls: D first Perfrm peratins inside any parentheses Simplify any expressins with expnents and square rts Multiply r divide frm left t right D last Add r subtract frm left t right Perfrm the peratins in the prper rder + ) = + ) Divide = Add f Order f Operatins If a fractin has peratins in the numeratr, in the denminatr, r bth, these peratins must be dne first Then the fractin may be simplified r the divisin carried ut Perfrm the peratins in the prper rder ) ) ) Perfrm the multiplicatin in ) the numeratr and the divisin in the denminatr 9 Perfrm the divisin in the numeratr Perfrm the additin in the numeratr f Order f Operatins Perfrm the peratins in the prper rder + ) = + 9 ) = + ) = + = = 9 Simplify the expnent inside the parentheses Perfrm the subtractin inside the parentheses Simplify the expnent Add Subtract f 9 f

10 CQ9-9 CQ9-0 0 ) 0 0 f f CQ9- ) CQ9- ) ) f f CQ9- ) CQ f f f

11 CQ9- ) CQ9- ) 0 0 f f f