Question

1.Think about what you know about reach fill in each Box use words numbers and pictures show as many ideas as you can2. What to rates can you write for the ratios showing by the double number lines what do tell you

Answer 1

A rate is a constant value that relates two proportional variables, like miles and gallons, pounds and days, etc.

In the case of units rates, the second variable has a value of one unit.

Some examples are:

• 100 cars pass by in 2 hours. The unit rate is 100/2=50 cars per hour.

• You can paint 3 boards in half an hour. The unit rate is 3/0.5=6 boards per hour.

• 200 sausages were eaten by 50 people. The unit rate is 200/50=4 sausages per person.

For any 2 variables, we can write 2 ratios, being one the inverse of the other.

For example, for the graph of miles and gallons, we can see that 1 gallon corresponds to 30 miles.

We then can write a ratio as:

`k_1=\frac{30\text{ miles}}{1\text{ gallon}}=30\text{ miles per gallon}`

This is a unit rate, as the second variable (gallons) have a value of 1 unit.

We can also write a second ratio as:

`k_2=\frac{1\text{ gallon}}{30\text{ miles}}=(1)/(30)\text{gallons per mile}\approx0.033\text{ gallons per mile}=(1)/(k_1)`

This second ratio is the inverse of the first one.