Exercise 3 Page 196

Ratios form a proportion when they are equivalent. One way to know if two ratios or rates are equivalent is by writing them as fractions. ccc Ratio & & Fraction [0.8em] 4.5to 3 & → & 4.5/3 [1em] 6to 9 & → & 6/9 We can check if the relationship between the two quantities is the same when we compare these fractions in their simplest form. Let's see if the given rates are equivalent! c|c First Ratio & Second Ratio [0.8em] 4.5/3 & 6/9 We need to simplify the above expressions. Let's start by simplifying the first fraction.

4.5/3

ReduceFrac

a/b=.a / 1.5./.b / 1.5.

4.5÷ 1.5/3÷ 1.5

SimpQuot

Simplify quotient

3/2

Now, let's simplify the second fraction.

6/9

ReduceFrac

a/b=.a / 3./.b / 3.

6÷ 3/9÷ 3

SimpQuot

Simplify quotient

2/3

Finally, we can compare the simplified rates. 3/2 ≠ 2/3 Since the fractions are not equivalent, the ratios are not equivalent.