Section 3.5 1

Multiplicative Identity for Fractions

When we multiply a number by 1, we get the same number:

1 . a a an

an

Section 3.5 2

A fraction is in simplest form when it has the smallest numerator and the smallest denominator. That is, the numerator and denominator have no common factor other than 1.

Section 3.5 3

ReducingReducing is a shortcut you may have when working with fraction notation.Reducing may be done only when there are common factors in numerators and denominators.

The difficulty with reducing is that it is often applied incorrectly in situations like the following:

The correct answers are:

CAUTION!

2 3

2

43;

1

4

1 15;

22

5

1

44

2 3 5 4 1 5 15 5; ;

2 2 4 2 6 54 18

Section 3.5 4

A Test for EqualityTo test if two fractions are really equivalent to each other, we can use a process called cross multiplication.

We multiply these two We multiply these twonumbers: 3 4 numbers 6 2.

We call 3 4 and 6 2 cross products. Since the cross products are the same 3 4 = 6 2 we know that

3 2

6 4

Section 3.5 5

Section 3.5 6

Homework:Problems 9, 11 – copy the problem, find ? = ______. Explain in words (or by showing work) how you found your answer.

Problems 17, 23, 25, 31, 33 – copy the problem, given the answer below. Explain in words (or by showing work) how you found your answer.

Problems 43, 47 – coy the problem, then use cross multiplication to determine the answer, state the answer.

Problem 49 – copy the words, give the answer and justify in word or by showing work how you got your final/simplified answer.