do now 12/3/13 take out hw from last night. take out hw from last night. text page 116, #1-19 odds...
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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