Do Now 2/1/10Do Now 2/1/10 Take out HW from FridayTake out HW from Friday

Text p. 258, #8-40 evens, & 11Text p. 258, #8-40 evens, & 11

Copy HW in your planner.Copy HW in your planner. Text p. 262, #2-34 evensText p. 262, #2-34 evens Chapter 5 TEST TuesdayChapter 5 TEST Tuesday

Be ready to copy Problem of the Week #1.Be ready to copy Problem of the Week #1.

HomeworkHomeworkText p. 258, #8-40 evens & Text p. 258, #8-40 evens &

#11#11 8) -0.08758) -0.0875 10) 4.0210) 4.02 11)11)

12) -1/312) -1/3 14) 3 1/314) 3 1/3 16) 3/816) 3/8 18) -9/3418) -9/34 20) 7 27/2820) 7 27/28

22) -1 1/322) -1 1/3 24) 2 5/1724) 2 5/17 26) 26)

28) 28) 30) -1 5/630) -1 5/6 32) 8 1/332) 8 1/3 34) -1 1/834) -1 1/8 36) 1/236) 1/2 38) 2/938) 2/9 40) -17/2140) -17/21

9

4a

5

4 7n20

95,

25

134,3.5,24.5,

25

263

ObjectiveObjective

SWBAT review writing fractions as SWBAT review writing fractions as decimals and vice versa, adding and decimals and vice versa, adding and subtracting like and unlike fractions, subtracting like and unlike fractions, multiplying fractions, dividing multiplying fractions, dividing fractions, and solving equations and fractions, and solving equations and inequalities with rational numbers.inequalities with rational numbers.

Section 5.1, “Rational Section 5.1, “Rational Numbers”Numbers”

A A RATIONAL NUMBERRATIONAL NUMBER is a number is a number that can be written as a quotient of two that can be written as a quotient of two integers (a fraction). Numbers that cannot integers (a fraction). Numbers that cannot be written as a fraction are called be written as a fraction are called IRRATIONALIRRATIONAL..

Writing Decimals as FractionsWriting Decimals as Fractions Decimal numbers can be one of the Decimal numbers can be one of the

following: following: 1) terminating1) terminating

2) repeating 2) repeating (follows a pattern)(follows a pattern)

3) nonrepeating 3) nonrepeating (goes on forever without a (goes on forever without a pattern)pattern)

5...92360679774.2

11

545.0...454545.0

8

3375.0

rationalrational

rationalrational

irrationalirrational

Writing Decimals as Writing Decimals as FractionsFractions

Write the following decimal as fraction.Write the following decimal as fraction.

0.450.45 How do you say this?How do you say this?

““Forty-five hundredths”Forty-five hundredths”

SimplifySimplify

100

45

5522

533

20

9

Writing Decimal Numbers As Mixed Writing Decimal Numbers As Mixed NumbersNumbers

Rewrite the decimal number as a sum.Rewrite the decimal number as a sum. Write the decimal as a fraction. Write the decimal as a fraction.

11

““Three hundred Three hundred seventy-five seventy-five thousandths”thousandths”

.375.37511 ++

3388++11

3388

SimplifySimplify

1000

375

1258

1253

8

3

Writing Decimals as Writing Decimals as FractionsFractions

Write the following decimal as a fraction.Write the following decimal as a fraction.

0.090.09 For repeating decimals use the following strategy: For repeating decimals use the following strategy:

Simplify, if Simplify, if possiblepossible

99

09

1133

33

11

1

If there are two repeating digits in the decimal, place the digits over 99. If there are two repeating digits in the decimal, place the digits over 99.

0.090909…0.090909…

If there is one repeating digit in the decimal, place the digit over 9. If there is one repeating digit in the decimal, place the digit over 9.

If there are three repeating digits in the decimal, place the digits over 999. If there are three repeating digits in the decimal, place the digits over 999.

Writing Fractions as Decimals Writing Fractions as Decimals

8

7Rewrite the fraction as a Rewrite the fraction as a decimal.decimal.

8

7 This means 7 divided by 8.This means 7 divided by 8.

A fraction is the quotient of two integersA fraction is the quotient of two integersRemember

87

780

64 6

87

Finished

.00

56 4

05

40

Section 5.2 “Adding and Subtracting Like Section 5.2 “Adding and Subtracting Like Fractions”Fractions”

Adding Fractions with Common Denominators

To ADD fractions with common denominators, add their numerators together.

7

3

7

2

7

5

7

3

7

2

Add the numerators

c

ba

c

b

c

a

Section 5.2 “Adding and Subtracting Like Section 5.2 “Adding and Subtracting Like Fractions”Fractions”

Subtracting Fractions with Common DenominatorsSubtracting Fractions with Common Denominators

To SUBTRACT fractions with common denominators, subtract their numerators.

6

1

6

5

3

2

6

4

Subtract the numerators

c

ba

c

b

c

a

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. 1. Rewrite the fractions using a common Rewrite the fractions using a common denominatordenominator. .

2. 2. Add or subtract the numeratorsAdd or subtract the numerators. .

7

1

5

2 35

14

75

72

5

2

35

5

57

51

7

1

What is the common

denominator?

35

19

35

5

35

14

Section 5.3 “Adding and Subtracting Section 5.3 “Adding and Subtracting Unlike Fractions”Unlike Fractions”

““Adding and Subtracting Mixed Adding and Subtracting Mixed Numbers”Numbers”

Mixed Numbers with Different Mixed Numbers with Different DenominatorsDenominators

To To ADDADD & & SUBTRACT SUBTRACT mixed numbers do the mixed numbers do the following:following:

1. Write the fractions as improper fractions1. Write the fractions as improper fractions

2. Write fractions using the LCD.2. Write fractions using the LCD.

3. Add or subtract the numerators3. Add or subtract the numerators

4. Simplify if necessary4. Simplify if necessary

Try It OutTry It Out

8

31

4

14

2.2. Write fractions using LCD.Write fractions using LCD.

8

11

8

34

8

72

8

233. Simplify3. Simplify

8

11

4

17

1.1. Improper fractionsImproper fractions

Simplify the Simplify the Expression.Expression. 9

7

12

5 ww

Find the LCD for 12 and 9. Find the LCD for 12 and 9. LCD = 36

Rewrite equivalent fractions using the LCD. Rewrite equivalent fractions using the LCD.

36

?

12

5

w

36

?

9

7

w

36

15

312

35

12

5 www

36

28

49

47

9

7 www

36

13

36

28

36

15 www

Section 5.4, “Multiplying Section 5.4, “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

Section 5.5, “Dividing Section 5.5, “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

Section 5.6, “Using Section 5.6, “Using Multiplicative Inverses to Multiplicative Inverses to

Solve Equations” Solve Equations”

Multiplicative Inverse PropertyMultiplicative Inverse Property

To solve an equation that has a To solve an equation that has a fractional coefficient, you can multiply fractional coefficient, you can multiply each side of the equation by the each side of the equation by the fraction’s multiplicative inverse. fraction’s multiplicative inverse.

MULTIPLICATIVEMULTIPLICATIVEINVERSEINVERSE

RECIPROCALRECIPROCAL==

127

4x

127

4x

21x41

7121

x

Solve for x.Solve for x.

Multiply each side of the equation Multiply each side of the equation by the by the MULTIPLICATIVE INVERSEMULTIPLICATIVE INVERSE of 4/7 of 4/7

Divide (cancel) common factorsDivide (cancel) common factors

11

-3-3

4

7121x

MultiplyMultiply

4

7

4

7

Section 5.7, “Equations and Section 5.7, “Equations and Inequalities with Rational Inequalities with Rational

Numbers” Numbers”

Another way to solve an equation Another way to solve an equation with fractions is to clear fractions by with fractions is to clear fractions by multiplying the multiplying the WHOLE EQUATIONWHOLE EQUATION by by the LCD of the fractions. the LCD of the fractions.

The resulting equation is equivalent to The resulting equation is equivalent to the original equation WITHOUT fractions. the original equation WITHOUT fractions.

3

1

5

4

15

11 x

3

1

5

4

15

11 x

11

7

11

11

x

Two-step equation. Solve for x.Two-step equation. Solve for x.

15

15

3

1

5

4

15

11x

Find LCD of all fractions in the Find LCD of all fractions in the equation, then multiply the whole equation, then multiply the whole equation by the LCD.equation by the LCD.

Solving Equations by Clearing Solving Equations by Clearing FractionsFractions

Use distributive property and simplify Use distributive property and simplify each termeach term of the equation. of the equation. 15 15

125121211 x

711 x

11

7x

x11 512

m8.014.53.2

m8.014.53.2

80

80

80

284 m

Two-step equation. Solve for m.Two-step equation. Solve for m.

100

100

m8.014.53.2

Look for the greatest number of decimal Look for the greatest number of decimal places. Then multiply the WHOLE places. Then multiply the WHOLE EQUATION by that power of 10.EQUATION by that power of 10.

Solving Equations by Clearing Solving Equations by Clearing DecimalsDecimals

Use distributive property and Use distributive property and simplify simplify each termeach term of the equation. of the equation.

100 100

m80514514)514(230

m80284

55.3m

230 m80514

BLUFF!BLUFF!

HomeworkHomework

Chapter 5 TEST tomorrow!!Chapter 5 TEST tomorrow!!

Text p. Text p. 262, #2-34 evens262, #2-34 evens