Exercise 35 Page 201

Rates form a proportion when they are equivalent. 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 Rate & Second Rate [0.8em] .3 /4.pound/5gallons & .4 /5.pound/5 13gallons 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.

34/5

DivFracD

a/c/b= a/b* c

3/4* 5

Multiply

Multiply

3/20

Let's now simplify the second rate.

45/5 13

MixedToFrac

a bc=a* c+b/c

45/5* 3+ 13

▼

Simplify

Multiply

Multiply

45/15+ 13

AddTerms

Add terms

45/163

DivFracByFracD

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

4/5 * 3/16

MultFrac

Multiply fractions

4* 3/5* 16

Multiply

Multiply

12/80

ReduceFrac

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

12÷ 4/80÷ 4

CalcQuot

Calculate quotient

3/20

Finally, we can compare the simplified rates. 3/20 = 3/20 Since the fractions are equivalent, the rates form a proportion.