Exercise 19 Page 287

We want to complete a table. We can use the portion where both values are known to find the missing values.

Miles	25		125
Gallons		3	5	12

We know that we can travel 125 miles with 5 gallons of gas. Let's write this as a rate. 125miles/5gallons or 125/5

We will use this rate to find the missing values.

First Value

We can find an equivalent rate with a numerator of 25 to find how many gallons we need to travel 25 miles.

125/5

ReduceFrac

a/b=.a / 5./.b / 5.

125/ 5/5/ 5

CalcQuot

Calculate quotient

25/1

We need 1 gallon to travel 25 miles.

Miles	25		125
Gallons	1	3	5	12

Second Value

Now we want to find how many miles we can travel with 3 gallons. It is better to use the unit rate 251 to find this missing value, because we cannot easily multiply to make a denominator of 5 into a denominator of 3. 125/5=& /3 ⇒ 5* ? = 3 [0.8em] 25/1=& /3 ⇒ 1* ? = 3 We need to get an equivalent rate with a denominator of 3.

25/1

ExpandFrac

a/b=a * 3/b * 3

25* 3/1* 3

Multiply

Multiply

75/3

We can travel 75 miles with 3 gallons.

Miles	25	75	125
Gallons	1	3	5	12

Third Value

To find the last value, we use the unit rate 251 again. This time we need an equivalent rate with a denominator of 12.

25/1

ExpandFrac

a/b=a * 12/b * 12

25* 12/1* 12

Multiply

Multiply

300/12

We can travel 300 miles with 12 gallons.

Miles	25	75	125	300
Gallons	1	3	5	12