Notes

One way to create a ratio table is by using addition. Let's start with the given ratio 3:12. You can begin by first making a table and creating some empty spaces that you know you will have to fill in later. Your table can be horizontal or vertical–it does not matter.

Horizontal Table

Number of subs 3
Bag of chips 12 One way to create a ratio table is by using addition. Let's start with the given ratio 3:12. You can begin by first making a table and creating some empty spaces that you know you will have to fill in later. Your table can be horizontal or vertical–it does not matter.

Horizontal Table

Number of subs 3
Bag of chips 12
Vertical Table

Number of subs Bags of chips
3 12



Next, you create a pattern through addition. So continue to add 3 to the number of subs and continue to add 12 to the bags of chips. Continuing this pattern will create the ratio table of equivalent ratios.

Let's see equivalent ratios
First row says Number of subs 3 6 9 12 with an arrow labeled plus 3 between each number. Second row says Bag of chips 12 24 36 48 with an arrow labeled plus 12 between each number.
Notice that to find each value, you do something different in each row.

Number of subs: The pattern is to add 3 each time, because that is the first term of the ratio.

3 + 3 = 6; 6 + 3 = 9; 9 + 3 = 12

Bags of chips: The pattern is to add 12 each time, because that is the second term of the ratio.

12 + 12 = 24; 24 + 12 = 36; 36 + 12 = 48

This shows that the ratios 3:12, 6:24, 9:36, and 12:48 are all equivalent.

This creates equivalent ratios because they express the same relationship. So if you are changing the ratio by adding the ratio terms, you are really just adding the same relationship to itself, which will produce the same relationship. You can also subtract the same relationship, as long as you do not reduce it to 0.


Caution
Be careful that you do not make these mistakes using the addition method.

Both of these are big mistakes. These are not correct tables.

First row says Number of subs 3 15 27 39 with an arrow labeled plus 12 between each number. Second row says Bag of chips 12 15 18 21 with an arrow labeled plus 3 between each number. Entire table crossed out.
Here the ratio numbers were reversed. You must add the same number to itself.

First row says Number of subs 3 10 17 24 with an arrow labeled plus 7 between each number. Second row says Bag of chips 12 17 22 27 with an arrow labeled plus 5 between each number. Entire table crossed out.
Here a completely different relationship was added. The ratio 7:5 is not the same as 3:12, so adding 7s and 5s will not create a ratio table equivalent to 3:12.
Vertical Table

Number of subs Bags of chips
3 12
From the slider, you were able to see that the ratio 2:8 can be scaled up to 8:32. While scaling up, you were able to see some of the other ratios in between.

Equivalent ratios:
Ratios that have the same simplest form and express the same relationship between two quantities.

The ratios 2:8, 4:16, 6:24, and 8:32 are examples of equivalent ratios. Equivalent ratios are ratios that express the same relationship between two quantities. By understanding the equivalent ratios, you will be able to see how Ellie can make different quantities of the athletic drink, while ensuring that the taste is the same.

Ratios that are equivalent have the same simplest form. The simplest form for these ratios is 1:4.


Next, you create a pattern through addition. So continue to add 3 to the number of subs and continue to add 12 to the bags of chips. Continuing this pattern will create the ratio table of equivalent ratios.