Exercise 4 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] 1/2to 1/4 & → & .1 /2./.1 /4. [1em] 8to 4 & → & 8/4 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] .1 /2./.1 /4. & 8/4 We need to simplify the above expressions. Let's start by simplifying the first fraction.

.1 /2./.1 /4.

DivFracByFracD

.a /b./.c /d.=a/b*d/c

1/2*4/1

MultFrac

Multiply fractions

4/2

ReduceFrac

a/b=.a / 2./.b / 2.

4÷ 2/2÷ 2

SimpQuot

Simplify quotient

2/1

Now, let's simplify the second fraction.

8/4

ReduceFrac

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

8÷ 4/4÷ 4

SimpQuot

Simplify quotient

2/1

Finally, we can compare the simplified rates. 2/1 = 2/1 Since the fractions are equivalent, the ratios are equivalent.