Unit 2, Lesson 10
Navigating a Table of Equivalent Ratios
Accelerated 6
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Lin is paid \$90 for 5 hours of work. She used the table to calculate how much she would be paid at this rate for 8 hours of work.
A 2-column table with 5 rows of data. The first column is labeled "amount earned, in dollars" and the second column is labeled "time worked, in hours." Row 1: 90, 5; Row 2: 18, 1; Row 3: 144, 8; Row 4 and 5: blank. An arrow pointing from row 1 to row 2 is labeled "times one-fifth." Another arrow pointing from row 2 to row 3 is labeled "times 8."
At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work?
In 2022, 128 gigabytes (GB) of portable computer memory cost \$16.
One set of tick marks has already been drawn to show the result of multiplying 128 and 16 each by . Label the amount of memory and the cost for these tick marks.
Next, keep multiplying by and drawing and labeling new tick marks, until you can no longer clearly label each new tick mark with a number.
Here is a table that represents the situation. Find the cost of 1 gigabyte. You can use as many rows as you need.
| memory (gigabytes) | cost (dollars) |
|---|---|
| 128 | 16 |
Finding a row containing a “1” is often a good way to work with tables of equivalent ratios. For example, the price for 4 lbs of granola is \$5. At that rate, what would be the price for 62 lbs of granola?
Here are tables showing two different approaches to solving this problem. Both of these approaches are correct. However, one approach is more efficient.
Less efficient
More efficient
Notice how the more efficient approach starts by finding the price for 1 lb of granola.
Remember that dividing by a whole number is the same as multiplying by a unit fraction. In this example, we can divide by 4 or multiply by to find the unit price.