Exercise 19 Page 65

One way to know if two ratios or rates are equivalent is by looking at their unit rates. We can check if the relationship between the two quantities is the same when we compare them as rates in their simplest form. Let's see if the given rates are equivalent! c|c Rosalinda & Rosalinda's sister [0.8em] $35/5weeks & $56/56days Let's notice that the first rate is in $

per week while the other in $ per day. We should make sure that rates are in the same units. Since there are 7 days in a week, we can change weeks into days in the first rate's denominator by multiplying their number by 7.

$35/5weeks

Substitute

5weeks= 5 * 7days

$35/5 * 7 days

Multiply

Multiply

$35/35days

So, we have the following rates to compare. c|c Rosalinda & Rosalinda's sister [0.8em] $35/35days & $56/56days We need to simplify the above expressions so that we can know the unit rates. Let's start by simplifying the first rate. To make the math a little bit simpler, we will only look at the numbers.

35/35

ReduceFrac

a/b=.a / 35./.b / 35.

35÷ 35/35÷ 35

SimpQuot

Simplify quotient

1/1

Let's now simplify the second rate

56/56

ReduceFrac

a/b=.a / 56./.b / 56.

56÷ 56/56÷ 56

SimpQuot

Simplify quotient

1/1

Finally, we can compare the simplified rates. 1/1 = 1/1 Since the given rates have the same unit rate, they are equivalent.