7th Grade Math

Chapter Study Guide and Review 193

Multiply and Divide Fractions (continued)

Divide Fractions (Lesson 3D)

Divide. Write in simplest form.

36. 
    

    53 ÷ 76 37. 4 ÷ (^) (- _^23 )

    
    


37. 
    

    2 43 ÷ 65 39. - 72 ÷ (^) (- 218 )

    
    


38. 
    

    MEASUREMENT How many ^18 -inch lengths
    are in 6 ^34 inches?

    
    

EXAMPLE 8 Find 2 _^4

5 ÷

_^7

10.

2 _^45 ÷ _ 107 = _^145 ÷ _ 107 Rename 2 _ 54.

2

/

2

= _^14 /

5 ·

_^10

7 Multiply by the reciprocal of

_^7

10.

1

/

1

/

= _^4

1

or 4 Simplify.

Lesson 3

Monomials

Multiply and Divide Monomials (Lesson 4A)

41. PHONE CALLS Mrs. Jones, as a
    telemarketer, made 3^3 phone calls on
    Monday. Suppose on Tuesday she made
    3 4 phone calls. How many times as
    many phone calls did she make on
    Tuesday than on Monday?

EXAMPLE 9 Find 3 · 35. Express using

exponents.

3 · 35 = 31 · 35 3 = 31

= 31 +^5 The common base is 3.

= 36 Add the exponents.

Negative Exponents (Lesson 4B)

Write each expression using a positive

exponent.

42. 6 -^3 43. 3 -^5 44. b-^4

Write each fraction as an expression using

a negative exponent other than -1.

45. ^1
    52
    46. 641 47. _^1
    x^4

EXAMPLE 10 Write m-^5 using a positive

exponent.

m-^5 = _^1

m^5

Definition of negative exponent

Scientific Notation (Lesson 4C)

Express each number in scientific notation.

48. 0.00027 49. 0.0000196


49. INSECTS The giant weta is the largest
    known insect, having a mass of about
    7.1 × 101 grams. Write this mass in
    standard form.

EXAMPLE 11 Write 3.06 × 106 in standard

form.

3.06 × 106 = 3,060,000

Move the decimal point

6 places.

EXAMPLE 12 Write 0.00016 in scientific

notation.

0.00016 = 16 × 0.0001 Move the decimal point 4 places.

= 1.6 × 10 -^4 Since 0exponent is negative. < 0.00016 < 1, the

Lesson 4

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