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Which three go together? Why do they go together?
Two binders cost \$14, and 5 binders cost \$35.
Complete the table to show the cost for 4 binders and 10 binders at that rate. Next, find the cost for a single binder in each case, and record those values in the third column.
| number of binders | cost (dollars) | unit price (dollars per binder) |
|---|---|---|
| 2 | 14 | |
| 4 | ||
| 5 | 35 | |
| 10 |
| number of notebooks | cost (dollars) | unit price (dollars per notebook) |
|---|---|---|
| 20 | 3 | |
| 50 | 3 | |
| 21 | 3 | |
| 84 | 3 | |
| 3 |
Clare makes bracelets at a constant speed.
Complete the table. Be prepared to explain your reasoning.
| time spent (hours) | number of bracelets | speed (bracelets per hour) |
|---|---|---|
| 2 | 6 | |
| 5 | 6 | |
| 42 | 6 | |
| 66 | 6 | |
| 90 | 6 | |
| 6 |
Noah and Lin each bought some bracelets that Clare made.
Noah bought 5 bracelets for dollars. How much did he pay per bracelet? Record it in the table.
| number of bracelets | cost (dollars) | unit price (dollars per bracelet) | |
|---|---|---|---|
| Noah | 5 | ||
| Lin |
Lin bought twice as many bracelets as Noah bought and paid twice the amount Noah paid. Complete the table to show her purchase.
Did Lin pay twice the unit price that Noah paid?
Pause here for a class discussion before moving on.
| number of bracelets | cost (dollars) | unit price (dollars per bracelet) | |
|---|---|---|---|
| Mai | |||
| Diego |
It takes 4 pounds of apples to make 6 cups of applesauce.
At this rate, how much applesauce can you make with:
7 pounds of apples?
10 pounds of apples?
How many pounds of apples would you need to make:
9 cups of applesauce?
20 cups of applesauce?
| pounds of apples | cups of applesauce |
|---|---|
| 4 | 6 |
| 7 | |
| 10 | |
| 9 | |
| 20 |
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 | |
| 8 | 20 | |
| 20 | 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 | |
| 8 | 20 | |
| 20 | 50 |
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 | quantity | unit rate 1 | unit rate 2 |
|---|---|---|---|