Exercise 10 Page 231

One way to know if two ratios or rates are equivalent is by writing them as fractions. 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] 12cups of soda/54cups of juice & 8cups of soda/36cups of juice We need to simplify the above expressions. Let's start by simplifying the first rate. To make the math a little bit simpler, we will only look at the numbers.

12/54

ReduceFrac

a/b=.a / 6./.b / 6.

12÷ 6/54÷ 6

SimpQuot

Simplify quotient

2/9

Let's now simplify the second rate.

8/36

ReduceFrac

a/b=.a / 4./.b / 4.

8÷ 4/36÷ 4

SimpQuot

Simplify quotient

2/9

Finally, we can compare the simplified rates. 2/9 = 2/9 Since the fractions are equivalent, the ratios are equivalent.