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Determine if and where Will and Pedro will meet if they start driving from the same intersection. Pedro travels 2 blocks east, 2 blocks south, 2 blocks east, and 2 blocks north. Will starts traveling 2 blocks north, 4 blocks east, and 2 blocks south.

Yes, they will meet 4 blocks east.

LESSON 3-1Estimating with Fractions and Mixed Numbers

Problem of the Day

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Questions about homework?

34. An astronomical unit (AU is approximately 9.3 X 107 mi. Pluto is about 39 AU from the sun. Write the distance in miles using both scientific notation and standard form.

(39 AU)(9.3 x 107 mi/AU)

= 362.7 x 107 distributive property

= 3.627 x 109 move the decimal point 2 places to the left, so add 2 to exponent

Scientific notation: 3.627 x 109

Standard notation: 3,627,000,000

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More on exponents

23 = 2•2•2 = 822 = 2•2 = 421 = 2What is the pattern so far?Dividing the product by 2 (which is the base)20 = 1What if I want to divide by 2 again?

½What would the exponent be then? (See pattern above)2-1 = ½

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More on exponents

Now try it yourself with 3 as the base33 = 3•3•3 = 2732 = 3•3 = 931 = 330 = 13-1 = 1/3

Exponent Rules:1) If an exponent is zero,

the answer is 1.2) If an exponent is negative,

the answer is a fraction (NOT a negative number)

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LESSON 3-1

(For help, go to Lesson 1-1.)

Estimating with Fractions and Mixed Numbers

Check Skills You’ll Need

1. Vocabulary Review How is estimating with compatible numbers different from estimating by rounding?

Use compatible numbers to estimate each quotient.

2. 49.8 ÷ 6.8 3. 21.05 ÷ 5.29 4. 25.27 ÷ 2.99

5. 52.6 ÷ 8.8 6. 19.4 ÷ 10.1

Check Skills You’ll Need

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LESSON 3-1Estimating with Fractions and Mixed Numbers

Solutions

1. When you estimate by rounding, you round the number to the nearest unit. When you use compatible numbers, you look for numbers that are easy to compute mentally.

2. 7 3. 4 4. 8 5. 6 6. 2

Check Skills You’ll Need

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LESSON 3-1Estimating with Fractions and Mixed Numbers

Quick Check

Definition

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We use benchmarks to estimate fractions.

It is a convenient number used to replace fractions less than 1. We use 0, ½ or 1 to estimate fractions.

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LESSON 3-1

Use benchmarks to estimate + .47

45

47

45+

Use benchmarks to estimate each fraction. Then add.

12

12

+ 1 = 1

Estimating with Fractions and Mixed Numbers

Quick Check

Additional Examples

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LESSON 3-1

5 – 3 = 2 Round each mixed number. Then subtract.

Estimate 5 – 2 .19

56

5 – 219

56

Estimating with Fractions and Mixed Numbers

Quick Check

Additional Examples

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LESSON 3-1

Estimate 6 • 6 .18

58

6 • 7 = 42 Round each mixed number. Then multiply.

6 • 618

58

Estimating with Fractions and Mixed Numbers

Quick Check

Additional Examples

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LESSON 3-1

Estimate 26 ÷ 8 .14

23

26 ÷ 814

23

27 ÷ 9 = 3 Use compatible numbers. Use 27 for 26 anduse 9 for 8 .

142

3

Estimating with Fractions and Mixed Numbers

Quick Check

Additional Examples

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Estimate.

1. + 2. 4 – 1

3. 2 • 6 4. 43 ÷ 10

35

12

LESSON 3-1

18

34

23

3

56

1 10

78

13

18 4

Estimating with Fractions and Mixed Numbers

Lesson Quiz

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Adding and Subtracting FractionsLesson 3-2

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LESSON 3-2

(For help, go to Lesson 2-3.)

Find each missing number.

2. = 3. = 4. = ?8

4?

816

?10

45

16

Adding and Subtracting Fractions

Check Skills You’ll Need

1. Vocabulary Review Two fractions that name the same amount are called ? .

Check Skills You’ll Need

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LESSON 3-2

2. = = 3. = = 4. = =45

4 x 25 x 2

810

816

8 ÷ 2 16 ÷ 2

48

16

1 x 46 x 4

424

Adding and Subtracting Fractions

Solutions

1. equivalent

Check Skills You’ll Need

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When adding and subtracting fractions, the first step is to check that the denominators of all the addends are the same.

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LESSON 3-2

Find + .27

37

Keep the denominator the same.27

37

+ = 2 + 37

Add the numerators. The answer is close to the estimate.

57=

27

37+ 1

412

34+ , orEstimate

Adding and Subtracting Fractions

Quick Check

Additional Examples

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When adding and subtracting fractions, the first step is to check that the denominators of all the addends are the same.

What if the denominators are not the same?

(Hint: equivalent fractions)

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LESSON 3-2

Find + .59

16

59

16+ 1

212+ 0 , orEstimate

The LCD is 18.59

5 • 29 • 2

= = 1018

16

1 • 36 • 3

318

The LCD is 18. + = = +

1318

Add the numerators. The answer is close to the estimate.

Adding and Subtracting Fractions

Quick Check

Additional Examples

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LESSON 3-2

34

The LCD is 16.34

3 • 44 • 4

= = 1216

34

1 16

34

34– – 0 , orEstimate

1 16

1 16

116

– – = = –

1116

Subtract the numerators.

The board is now in. thick1116

Check for Reasonableness  The answer, , is close to the estimate, . The answer is reasonable.

1116

34

A carpenter begins with a board that is in. thick. She removes in. from its thickness. How thick is the board now? 1

16

Adding and Subtracting Fractions

Quick CheckAdditional Examples

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Find each sum or difference.

1. +

2. –

3. +

4. –

35

LESSON 3-2

45

1112

1012

56

34

23

78

251

112

7121

524

Adding and Subtracting Fractions

Lesson Quiz

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Homework:

•Lesson 3-1: pp. 122 – 123, #s 1, 2, 12 - 44 evens•Lesson 3-2: pp. 128-129, #s 26-46 evens

•Get quiz signed (Lesson 2-1 to 2-4)

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