Algebra Demystified 2nd Ed

Chapter 1 FraCtions 9

6.^184 =^2322 ⋅⋅⋅^3 =⋅^22332 ⋅ = 29
7.^7
210

7

2357

71

7235

7

7

1

235

1

30

=

⋅⋅⋅

⋅ = or

⋅⋅⋅

=⋅

⋅⋅

=

8.^240
165

222235

3511

35 2222

3511

= ⋅⋅⋅⋅⋅

⋅⋅

= ⋅ ⋅⋅⋅⋅

⋅⋅

() =

()

335

35

2222

11

15

15

16

11

16

11

⋅

⋅

⋅ ⋅⋅⋅

=⋅=

9.^55
33

511

311

115

113

11

11

5

3

5

3

= ⋅

⋅

= ⋅

⋅

=⋅=

10.^150
30

2 355

235

2355

2351

235

23

= ⋅⋅⋅

⋅⋅

= ⋅⋅⋅

⋅⋅⋅

= ⋅⋅

⋅⋅

()

() 55

5

1

30

30

⋅= ⋅= 55

The Greatest Common Divisor

Fortunately there is a less tedious method for writing a fraction in its lowest

terms. We find the largest number that divides both the numerator and the

denominator. This number is called the greatest common divisor (GCD). We

factor the GCD from the numerator and denominator and then we rewrite

the fraction in the form:

GCD

GCD

Othernumeratorfactors

Otherdenominator

⋅

factors

In the previous practice problems, the product of the common primes was

the GCD.

EXAMPLES

Identify the GCD for the numerator and denominator and write the fraction

in lowest terms.

32

48

16 2

16 3

16

16

2

3

12

3

2

3

= ⋅

⋅

=⋅=⋅ =

45

60

15 3

15 4

15

15

3

4

1 3

4

3

4

= ⋅

⋅

=⋅=⋅ =

EXAMPLES

Identify the GCD for the numerator and denominator and write the fraction