Do Now 12/3/13Do Now 12/3/13

Take out HW from last night.Take out HW from last night. Text page 116, #1-19 oddsText page 116, #1-19 odds

Copy HW in your planner.Copy HW in your planner. Text p. 134, #1-15 odds & #10Text p. 134, #1-15 odds & #10 Benchmark Test Chapters 1, 2, 3, & 11 Benchmark Test Chapters 1, 2, 3, & 11

Wednesday Wednesday

HomeworkHomework Text p. 116, #1-19 odds Text p. 116, #1-19 odds

1) 34.411) 34.41 3) 15.223) 15.22 5) 32.645) 32.64 7) 0.427) 0.42 9) 12.299) 12.29

11) 28.111) 28.1 13) 4013) 40 15) 7.515) 7.5 17) 24.8417) 24.84 19) $21.9219) $21.92

ObjectiveObjective

SWBAT review adding, subtracting, SWBAT review adding, subtracting, multiplying, and dividing fractions multiplying, and dividing fractions and mixed numbers.and mixed numbers.

Mixed Numbers to Improper Mixed Numbers to Improper FractionFraction

5

18

5

418 x 5 = 408 x 5 = 40

40 + 1 = 4140 + 1 = 41

Remember this???

MultiplyMultiply

AddAdd

ADDITION & ADDITION &

SUBTRACTION SUBTRACTION

REVIEWREVIEW

Section 3-5 “Adding and Subtracting Section 3-5 “Adding and Subtracting Fractions”Fractions”

Adding Fractions and Mixed Numbers Adding Fractions and Mixed Numbers with Common Denominatorswith Common Denominators

To To ADD/SUBTRACTADD/SUBTRACT fractions with common fractions with common denominators:denominators:

1)1)Rewrite as improper fractions (if necessary)Rewrite as improper fractions (if necessary)

2)2)Add/subtract their numerators.Add/subtract their numerators.

3)3)Simplify if necessary.Simplify if necessary.

7

3

7

2

7

5

7

3

7

2

6

1

6

5

3

2

6

4

Fractions with Different DenominatorsFractions with Different Denominators

To To ADDADD or or SUBTRACTSUBTRACT fractions with fractions with different denominators follow these steps:different denominators follow these steps:

1). Rewrite as improper fractions (if necessary)1). Rewrite as improper fractions (if necessary)

2). 2). Rewrite the fractions using a common Rewrite the fractions using a common denominatordenominator. .

3). 3). Add or subtract the numeratorsAdd or subtract the numerators. .

7

1

5

2 35

?

5

2

55: 5, 10, 15, 20, 25, 30, : 5, 10, 15, 20, 25, 30, 3535, 40, 4077: 7, 14, 21, 28, : 7, 14, 21, 28, 3535, 42, 42

35

?

7

1

What is the common denominator?

35

19

35

5

35

14

35

14

7

7

5

2

35

5

5

5

7

1

Equivalent fractions

8

31

4

14

2. Common denominators

8

11

8

34

8

72

8

23

3. Subtract numerators

8

11

4

17

1. Improper fractions

Mixed Number PracticeMixed Number Practice

24

336

Simplify

4

338

4

14

4

17

Subtract numerators

“Opp-Opp”

)2(4

336

4

33)2(6

Commutative property

4

15

4

32

Subtract numerators

MULTIPLICATIOMULTIPLICATIONN

REVIEWREVIEW

Section 3-6, “Multiplying Section 3-6, “Multiplying Fractions” Fractions”

Multiplying FractionsMultiplying Fractions

To multiply fractions:To multiply fractions:

1. Rewrite fractions as improper fractions 1. Rewrite fractions as improper fractions (when necessary)(when necessary)

2. Multiply the numerators and 2. Multiply the numerators and denominators.denominators.

3. Simplify if necessary.3. Simplify if necessary.

bd

ac

d

c

b

a

35

12

7

4

5

3

5

13

4

32

5

16

4

11

51

)4(11

54

)16(11

MultiplyMultiply

Rewrite as improper fractions and assign Rewrite as improper fractions and assign negative to numerator.negative to numerator.

Divide (cancel) common factorsDivide (cancel) common factors

MultiplyMultiply11

44

5

44

5

48

SimplifySimplify

Mixed Number times Mixed Number times Mixed NumberMixed Number

Word ProblemWord Problem

Who ran farther Sally Jo or Sally Sue? Who ran farther Sally Jo or Sally Sue?

Sally Jo ran 4 ½ times around a ½ mi. track.Sally Jo ran 4 ½ times around a ½ mi. track.Sally Sue ran 3 ¼ times around a 5/6mi. trackSally Sue ran 3 ¼ times around a 5/6mi. track

6

5

4

13

2

1

2

14

2

1

2

9

6

5

4

13

4

12

4

9

24

172

24

65

24

62

4

12

Sally SueSally Sueran farther!!ran farther!!

3

236

1

36

11

212

31

)2(36

MultiplyMultiply

Divide (cancel) common Divide (cancel) common factors if possiblefactors if possible

MultiplyMultiply

1

24 24

SimplifySimplify

Rewrite a Rewrite a whole number whole number with a with a denominator denominator of 1.of 1.

3

2

Whole Number times Whole Number times FractionFraction

Word ProblemWord Problem

There are 36 students in your class. 2/3 of them went on the class trip. How many students went on the trip?

11

1212

DIVISIONDIVISION

REVIEWREVIEW

Section 3-7, “Dividing Section 3-7, “Dividing Fractions” Fractions”

Dividing FractionsDividing Fractions

To divide fractions:To divide fractions:

1. Rewrite fractions as improper fractions 1. Rewrite fractions as improper fractions (when necessary)(when necessary)

2. Write the reciprocal of the second 2. Write the reciprocal of the second fraction.fraction.

3. Multiply the numerators and 3. Multiply the numerators and denominators.denominators.

4. Simplify if necessary.4. Simplify if necessary.

bc

ad

c

d

b

a

d

c

b

a

20

11

20

21

4

7

5

3

7

4

5

3

RECIPROCALRECIPROCAL – –

two nonzero numbers whose two nonzero numbers whose product is 1. product is 1.

3

21

6

6

2

3

7

41

28

28

4

7

RECIPROCAL = MULTIPLICATIVE RECIPROCAL = MULTIPLICATIVE

INVERSEINVERSE

22

4

10

7

4

22

10

7

20

77

45

)11(7

410

)22(7

DivideDivide

Multiply by the RECIPROCALMultiply by the RECIPROCAL

Divide (cancel) common factorsDivide (cancel) common factors

MultiplyMultiply55

-11-11

20

173

4

22

10

7 Assign negative sign to the numeratorAssign negative sign to the numerator

A recipe that yields 2 loaves of A recipe that yields 2 loaves of bread requires 3½ cups of sugar. bread requires 3½ cups of sugar.

You have a bag of sugar that You have a bag of sugar that contains 14¼ cups. How many contains 14¼ cups. How many cups of sugar will be left in the cups of sugar will be left in the

bag if you make 8 loaves of bread?bag if you make 8 loaves of bread?

8 loaves ÷ 2 loaves per batch = 4 batches8 loaves ÷ 2 loaves per batch = 4 batches

4 batches ∙ 3 ½ cups of sugar = 14 cups4 batches ∙ 3 ½ cups of sugar = 14 cups

14¼ cups – 14 cups for recipe = ¼ cup left over.14¼ cups – 14 cups for recipe = ¼ cup left over.

Benchmark ReviewBenchmark Review

Chapter 1 - Chapter 1 - Simplifying variable expressionsSimplifying variable expressions

a + b; when ‘a’ = -12 and ‘b’ = 7 a + b; when ‘a’ = -12 and ‘b’ = 7

PropertiesProperties Commutative - 2 + 3 = 3 + 2 Commutative - 2 + 3 = 3 + 2 Associative - Associative -

Identity - 2 + 0 = 2Identity - 2 + 0 = 2 Distributive - 2(n + 4) = 2n + 8 Distributive - 2(n + 4) = 2n + 8

5

3

5

12

5

3

5

12

5

3

5

12

BenchmarkBenchmark

Chapter 2 - Chapter 2 - IntegersIntegers

Chapter 11 - Chapter 11 - EquationsEquations