Math 6A ( Period 2 & 5)

Ratio Tables 5-2

Essential Question:  How can you find two ratios that describe the same relationship?

We looked at a recipe or mixture of lemonade and iced tea.

the one from the book called for 1 cup of lemonade for every 3 cups of iced tea

We created a table and thought of various combinations that still kept that same relationship

C. of Lemonade	1	2	3	5	8	10
C. of Iced tea	3	6	9	15	24	30
Total Cups	4	8	12	20	32	40

A mixture contains 13 cups of lemonade, how could we determine how many cups of iced tea would be required? How could we use the given table to find that answer? 
1) we saw that the relationship was 1:3 so we could multiply 3 (cups of iced tea) by 13 to get 39 cups of iced tea.
2) we could use the existing information in the table. We know that 5 + 8 = 13 so if we just add the information for iced tea in those columns ( 15 + 24 =39) we would get 39 cups of iced tea as well.

Two ratios that describe the same relationship are equivalent ratios. You can find equivalent ratios by:

·        adding or subtracting quantities in equivalent ratios

·        multiplying or dividing each quantity in a ratio by the same number.

You can find and organize ratios in a ratio table.

Pens	1	2
Pencils	3		9

using repeated addition:

Pens	1	2	3
Pencils	3	6	9

The equivalent ratios are 1:3; 2:6 and 3:9

Dogs	4		24
Cats	6	12

You can use multiplication to find the missing values

Dogs	4	8	24
Cats	6	12	36

The equivalent ratios are 4:6; 8:12 and 24:36

We discussed how they are all equivalent to 2:3 as well

Using a Ratio Table in a word problem

The nutrition fact labeled on a box of crackers shows that there are 240 milligrams of sodium in every 36 crackers.

You eat 15 crackers. How much sodium do you consume?

The ratio of sodium to crackers is 240 to 36. Create a ratio table to find equivalent ratios with 15 crackers.

Sodium (mg)	240	120	20	100
Crackers	36	18	3	15

The ratio 100 to 15 is equivalent to 240 to 36.

So, you consumed 100 milligrams of sodium.

You eat 21 crackers. How much sodium do you consume?

Notice, you can add the two middle columns in the table above to find the solution to that question.

Since 18 + 3 = 21 120 + 20 = 140   140 milligrams of sodium in in 21 crackers.
You could also use the ratio 20:3 and multiply both by 7 and you will arrive at 140:21 or 140 milligrams of sodium