Page 208 - Basic College Mathematics with Early Integers

S E C T I O N 3.2 I FACTORS AND SIMPLEST FORM 185

In this text, we will write the factorization of a number from the smallest factor to
the largest factor.

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Concept Check True or false? The prime factorization of 117 is 9 13.
Explain your reasoning.
Objective Writing Fractions in Simplest Form

Fractions that represent the same portion of a whole or the same point on a number
line are called equivalent fractions. Study the table below to see two ways to visualize
equivalent fractions.

Equivalent Fractions
Figures Number Line

1 2 1 2
When we shade and on the same-sized figures, When we graph and on a number line,
3 6 3 6
1
3
2
0 6 1 2
a 2
6
1 2
1
2
notice that both and represent the same portion of a whole. notice that both and correspond to the same point.These fractions are
3 6 3 6
1 2 1 2
These fractions are called equivalent fractions and we write = . called equivalent fractions, and we write = .
3 6 3 6
1 2 1 2
Thus, = and and are equivalent.
3 6 3 6

s 4 8
6 12

2 4 8
For example, , , and all represent the same shaded portion of the rectangle’s
3 6 12
area, so they are equivalent fractions. To show that these fractions are equivalent, we
place an equal sign between them. In other words,

2 4 8
= =
3 6 12
There are many equivalent forms of a fraction. A special equivalent form of a
fraction is called simplest form.

Simplest Form of a Fraction
A fraction is written in simplest form or lowest terms when the numerator and
the denominator have no common factors other than 1.

2
For example, the fraction is in simplest form because 2 and 3 have no common
3
4 Concept Check Answer
factor other than 1.The fraction is not in simplest form because 4 and 6 both have
6 False; 9 is not prime