The table shows different amounts of apples selling at the same rate. This means that all of the ratios of weight (in pounds) to price (in dollars) are equivalent.
We can find the unit price in dollars per pound by dividing the price (in dollars) by the weight of apples (in pounds).
In each case, the unit price is always the same. Whether we buy 4 pounds of apples for 10 dollars or 8 pounds of apples for 20 dollars, the apples cost 2.50 dollars per pound.
| weight of apples (pounds) |
price (dollars) |
unit price (dollars per pound) |
|---|---|---|
| 4 | 10 | 10÷4=2.50 |
| 8 | 20 | 20÷8=2.50 |
| 20 | 50 | 50÷20=2.50 |
We can also find the number of pounds of apples we can buy per dollar by dividing the weight of apples (in pounds) by the price (in dollars).
| weight of apples (pounds) |
price (dollars) |
pounds per dollar |
|---|---|---|
| 4 | 10 | 4÷10=0.4 |
| 8 | 20 | 8÷20=0.4 |
| 20 | 50 | 20÷50=0.4 |
The number of pounds we can buy for a dollar is the same as well! Whether we buy 4 pounds of apples for 10 dollars or 8 pounds of apples for 20 dollars, we are getting 0.4 pound per dollar.
This is true in all situations: When two ratios are equivalent, their unit rates will be equal.
| quantity x | quantity y | unit rate 1 | unit rate 2 |
|---|---|---|---|
| a | b | ba | ab |
| 5⋅a | 5⋅b | 5⋅b5⋅a=ba | 5⋅a5⋅b=ab |
| s⋅a | s⋅b | s⋅bs⋅a=ba | s⋅as⋅b=ab |