Do Now 12/2/13Do Now 12/2/13

Copy HW in your planner.Copy HW in your planner. Text p. 116, #1-19 oddsText p. 116, #1-19 odds Benchmark Test Chapters 1,2,3, & 11 Wednesday and Benchmark Test Chapters 1,2,3, & 11 Wednesday and

Thursday.Thursday.

ObjectiveObjective

SWBAT review adding, subtracting, SWBAT review adding, subtracting, multiplying, and dividing decimalsmultiplying, and dividing decimals

ADDITION & ADDITION &

SUBTRACTION SUBTRACTION

REVIEWREVIEW

|35| = 35|35| = 35

35 + 1835 + 18

Adding Two Integers with SAME signs

To add two integers with the SAME signs, add the absolute values of the numbers. The answer will have the same sign.

|18| = 18|18| = 18

35 + 18 35 + 18 = 53 = 53

Section 2.2 “Adding Integers” Section 2.2 “Adding Integers”

|-35| = 35|-35| = 35

-35 + (-18)-35 + (-18)

|-18| = 18|-18| = 18

35 + 18 35 + 18 = 53 = 53 - -

Remember this?

|-35| = 35|-35| = 35

-35 + 18-35 + 18

Adding Two Integers with DIFFERENT signs

To add two integers with DIFFERENT signs, subtract the smaller absolute value from the greater absolute value and write the sign of the integer with the greater absolute value.

|18| = 18|18| = 18

35 – 18 35 – 18 = 17 = 17 - - Because 35 has a greaterBecause 35 has a greaterabsolute value than 18 the absolute value than 18 the answer is “negative”.answer is “negative”.

Section 2.2 “Adding Integers”Section 2.2 “Adding Integers”Remember this?

Section 2.3 Section 2.3 “Subtracting Integers” “Subtracting Integers”

When subtracting two integers, When subtracting two integers, ADD ADD the OPPOSITEthe OPPOSITE of the second of the second number to the first. number to the first.

8 – 5 = 8 – 5 =

Instead of subtracting ADD Instead of subtracting ADD the OPPOSITE!! the OPPOSITE!!

8 8 + (-5)+ (-5) = =ADD the OPPOSITE ADD the OPPOSITE

33Do the “OPP-OPP”Do the “OPP-OPP”““Opposite-Opposite”Opposite-Opposite”

Remember this?

Section 3-1Section 3-1Adding & Subtracting DecimalsAdding & Subtracting Decimals

Add & subtract decimal numbers Add & subtract decimal numbers

by lining up the decimal point. by lining up the decimal point.

1.2 +0.87

2.07HUNDREDTH

s

TENTH

S

One

s

1.2 + 0.871.2 + 0.87

0 Use a zero as a placeholder so that both numbers are in the same place value

62.82 – 32.7

30.12HUNDREDTH

s

TENTH

S

One

s

32.7 + (-62.82)32.7 + (-62.82)

Use a zero as a placeholder so that both numbers are in the same place value.

Tens

|32.7| = 32.7|32.7| = 32.7 |-62.82| = 62.82|-62.82| = 62.82

62.82 – 32.7 62.82 – 32.7

- - Because 62.82 has a greaterBecause 62.82 has a greaterabsolute value than 32.7 the absolute value than 32.7 the answer is “negative”.answer is “negative”.

0

5.23 + 9.1

14.33HUNDREDTH

s

TENTH

S

One

s

-5.23 – 9.1-5.23 – 9.1

Use a zero as a

placeholder so that

both numbers are in the

same place value.- -

0

-5.23 + (-9.1)-5.23 + (-9.1)Add the Opposite !!!Add the Opposite !!!

To add two integers To add two integers with the SAME signs, with the SAME signs, find the sum of their find the sum of their absolute values. Use absolute values. Use the sign of the two the sign of the two integersintegers

““Real-Life”Real-Life”During one month in the United During one month in the United

States, 492.23 million commuter trips were States, 492.23 million commuter trips were taken on buses, and 26.331 million taken on buses, and 26.331 million commuter trips were taken on light rail. commuter trips were taken on light rail. How many more trips were taken on buses How many more trips were taken on buses than on light rail? than on light rail?

492.23492.2300 – – 26.33126.331

465.899465.899million more trips were million more trips were taken on buses than on taken on buses than on light raillight rail

MULTIPLICATIONMULTIPLICATION

REVIEWREVIEW

““Multiplying Integers”Multiplying Integers”Rule #1Rule #1 The product of two integers with the same The product of two integers with the same

sign is always POSITIVE!sign is always POSITIVE!8 x 3 = 24 -8 · (-7) = 568 x 3 = 24 -8 · (-7) = 56

Rule #2Rule #2 The product of two integers with different The product of two integers with different

signs is always NEGATIVE!signs is always NEGATIVE! -6 x 3 = -18 8(-4) = -32-6 x 3 = -18 8(-4) = -32

Remember this?

To multiply decimals, multiply as you To multiply decimals, multiply as you would integers. To place the decimal point would integers. To place the decimal point in the product count the number of decimal in the product count the number of decimal places in each factor. The product will places in each factor. The product will have the same number of decimal places have the same number of decimal places as the sum of the decimal places in the as the sum of the decimal places in the factors.factors.

Section 3-2Section 3-2Multiplying DecimalsMultiplying Decimals

Find the product. -2.78 · 0.8Find the product. -2.78 · 0.8

-2.-2.7878 x 0.x 0.88

How many How many decimal places decimal places are in are in each number? each number?

2 decimal places2 decimal places

1 decimal place1 decimal place

-2224-2224 How many How many decimal places decimal places are in the sum ofare in the sum ofboth numbers? both numbers?

3 decimal places will then be in the product!3 decimal places will then be in the product!

-2.-2.224224

Find the product. -16 x 0.014Find the product. -16 x 0.014

0.0.014014

00840084x -16x -16

How many How many decimal places decimal places are in are in each number? each number?

3 decimal places3 decimal places

0 decimal places0 decimal places

+0140+0140-0224-0224

How many How many decimal places decimal places are in the sum ofare in the sum ofboth numbers? both numbers?

3 decimal places will then be in the product!3 decimal places will then be in the product!-0.-0.224224

““Real-Life”Real-Life”The average snowfall in Howell, NJ is The average snowfall in Howell, NJ is

18.55 inches per winter. What is the total 18.55 inches per winter. What is the total amount of snowfall in inches expected over amount of snowfall in inches expected over the next 2.5 years? the next 2.5 years?

18.5518.55x 2.5x 2.5

46.37546.375 Inches of snowfall expected in the Inches of snowfall expected in the next 2.5 yearsnext 2.5 years

92759275 3710037100

DIVISIONDIVISION

REVIEWREVIEW

Section 3-3 “Dividing Decimals”Section 3-3 “Dividing Decimals”

By multiplying both numbers by the same power By multiplying both numbers by the same power of ten, you can make the of ten, you can make the divisordivisor an integer. an integer. Dividing by an integer is much easier than Dividing by an integer is much easier than dividing by a decimal.dividing by a decimal.

How do you divide two decimal numbers

0.6 ÷ 0.6 ÷ 0.30.3 0.30.3 0.6 0.6divisordivisor

oror

0.30.3 0.6 0.6 33 6 6Multiply both Multiply both numbers by 10numbers by 10

22

Find the quotient of -0.875 ÷ (-0.25)Find the quotient of -0.875 ÷ (-0.25)

33

757512 12

55

125125FinishedFinished

..87 87 2525Move the decimal point Move the decimal point straight up, then divide as straight up, then divide as you normally would.you normally would.

0.250.25 0.875 0.875 2525 87.5 87.5Multiply both numbers Multiply both numbers

by 100 to make the by 100 to make the divisor an integerdivisor an integer

55The quotient of two The quotient of two

integers with the same integers with the same sign is always sign is always

POSITIVE!POSITIVE!

““Real-Life”Real-Life”If Sandy and her family used 14.95 If Sandy and her family used 14.95

gallons of gas to drive 358.8 miles, how gallons of gas to drive 358.8 miles, how many miles per gallon did the car get? many miles per gallon did the car get?

The car got 24 miles per The car got 24 miles per gallongallon

14.9514.95 358.8 358.8

14951495 35880 35880

Multiply both numbers

Multiply both numbers by 100 to make the

by 100 to make the divisor an integer

divisor an integer

2424

2424

HomeworkHomework

Text p. 116, #1-19 oddText p. 116, #1-19 odd

Joey is in the process of buying a new vehicle. He Joey is in the process of buying a new vehicle. He

has narrowed his options down to 2 choices. Which has narrowed his options down to 2 choices. Which vehicle gets better gas mileage (mpg) vehicle gets better gas mileage (mpg)

and by how much?and by how much?

2.5 gallons of gas 2.5 gallons of gas can go 48.5 milescan go 48.5 miles

6.8 gallons of gas 6.8 gallons of gas can go 164.9 can go 164.9

milesmiles

2.5 48.52.5 48.5 6.8 164.96.8 164.919.419.4 24.2524.25

– – 19.419.424.2524.25

4.854.8500

miles per gallon miles per gallon

The car gets 4.85 The car gets 4.85 more miles per gallon more miles per gallon of gasoline than the of gasoline than the SUV.SUV.