Ratios

Ratios

I can...

• Describe a ratio relationship between two quantities.

• Write a ratio describing the relationship between two or more quantities when given in the same units.

• Write a ratio describing the relationship between two or more quantities when given in different units.

Standards

• 6.NS.8

  Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between two quantities. Use the following notations: a/b, a to b, a:b.

• 6.NS.9

  Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship.

Multiple Select

Review - Which fractions are equivalent to  $$\frac{8}{12}$$  ?

• $$\frac{2}{6}$$  

• $$\frac{2}{3}$$  

• $$\frac{4}{6}$$  

• $$\frac{16}{24}$$  

• $$\frac{3}{4}$$  

Ratios in Cooking

• Michael Ruhlman wrote this book Ratio explaining how recipes can just be broken down into ratios

• For instance cookies can be broken down into a 1:2:3 ratio - One Part sugar, two parts fat, and 3 parts flour

• Bread is a 3 to 5 ratio 3 parts water to 5 parts flour (+ yeast and salt).

What is a Ratio?

• A ratio compares two quantities

• You can compare the number of cars and trucks in a parking lot.

  You can compare the number of boys and girls in a library.

  You can compare the number of red and yellow flowers in a garden.

There are 3 Ways to write a ratio

• Use the word to in a sentence: There are 10 cars to every 3 trucks in the parking lot

• Use a fraction bar: The ratio is 5 girls
  4 boys in the library.

   $\frac{5\ girls}{4\ boys}$  

• Use a colon (:) between numbers: The ratio of red to yellow flowers is 2:4.

• Though a ratio is often shown like a fraction  $\left(\frac{7}{3}\right)$  
    it is not and you should never change them to proper fractions, or mixed numbers if they are improper.

• You can simplify them though.

A measurement ratio is 42in to 5ft

We need to get these to where they share the same units. How can we do that?

Multiple Choice

What is the greatest common factor of 42 and 60?

• 5

• 6

• 7

• 8

Multiple Select

LeMya has a collection of books. She has 6 historical fiction novels and 14 mystery novels. What is the ratio of mystery novels to historical fiction novels? Click all that apply

• $$\frac{14}{6}$$

• 14:6

• 14 to 6

• 12 to 3

Multiple Choice

What is the greatest common factor of 14 and 6?

• 2

• 3

• 6

• 7

For every 3 black cars in the parking lot, how many tan cars were in the parking lot?

• First write the ratio of black to tan cars

• simplify the fraction.

Multiple Select

What is the ratio of black to white cars?

• 8 to 12

• $$\frac{12}{10}$$

• 6:5

• $$\frac{8}{4}$$

Lots of ratios are comparing measurements

You can only simplify the if they are using the same measurements.

Multiple Choice

Choose the correctly simplified ratio shown with a fraction bar.

16yd to 24 yd

• $$\frac{16}{24}$$

• 8:12

• $$\frac{2}{3}$$

• $$\frac{8}{12}$$

Open Ended

Write and simplify the given ratio.

4 lb to 56 oz (1 lb = 16 oz)

What do you need to do first?

Open Ended

For a real -world problem, does a simplified ratio give you the same information as the original ratio?

Open Ended

Before you simplify a ratio that compares like measurements, what must be true about the measurements?

Poll

How do you feel about ratios?

• I like em

• I think I can figure them out.

• This makes no sense!