Math 6A (Period 2 & 5)

Ratios 5.1

A ratio is a comparison of two quantities. Ratios can be part -to -part, part – to -whole, or whole -to-part comparisons

The ratio of a to b can be written in three ways           

 a:b,                 a/b ,           and                           a to b.
Each of these is read “ a to b”

 Examples:

 2 red crayons  to 6 blue crayons
1 red crayon  for every 3 blue crayons
3 blue crayons for each red crayon
3 blue crayons per 1 red crayon
3 blue crayons out of every 4 crayons
2 red crayons out of 8 crayons

A tape diagram is a diagram that looks like a segment of tape. It shows the relationship between two quantities.

The ratio of your monthly allowance to your friend’s monthly allowance is 5:3 The monthly allowance totals $40. How much is each allowance?

To help visualize the problem, express the ration 5:3 using a tape diagram

You 

Your Friend

Because there are 8 parts, you know that one part represents 40÷8 = $5

5 parts represents 5 ∙5 = 25
3 parts represents 3 ∙5 = 15

Garlic bulbs- you separate 42 garlic bulbs into two groups: one for planting and one for cooking. You will plant 3 bulbs for every 4 bulbs that you will use for cooking. Each bulb has about 8 cloves. How many cloves will you plant?  To help visualize, express the ratio 3 for every 4 using tape diagram

Planting

Cooking

The seven parts represent 42 bulbs so each part represents 42÷ 7 = 6 bulbs

There are 3 ∙6 =18 bulbs for planting and 4 ∙6 = 24 bulbs for cooking.

The group of 18 bulbs has 18 ∙ 8 = 144 cloves. So you will plan 144 cloves of garlic.