Ratios, Rates, and Proportions

What are Ratios?

• A Ratio is a comparison of 2 numbers by division.
• There are 3 ways to show a ratio-
• You can use the word TO, or : and also a Fraction Bar.
• 3/4  ;  x:7 ;  7 to 12
• Ratios can be written part to part, part to whole, or whole to part.

Examples of Ratios

• I have 5 pieces of Homework.
• I have 2 pieces of S.S Homework.
• What's my ratio of S.S to Total?
• 2:5 - 2 to 5 - 2/5
• This is a Part to Whole Ratio.

What are Rates?

• Rates are comparing two different units.
• Rates show Part to Whole
• Unit Rates show 1 part of a whole.
• Rate-  60 miles/ 3 hours
• Unite Rate- 20 miles/ 1 hour

Examples of Rates

• I can type 360 words every hour
• The Rate is 360/ 60
• How many words can I type in the minute?
• Divide by 60 
• 1 min. / 6 words ---- 1/6 THAT'S SLOW!!!

What are Proportions?

•  A Proportion is a problem that states that 2 Ratios are equal.
• You use the equal sign to show.  
• They are just showing equivalent Fractions!
• 2/4 = 1/2

How to Solve a Proportion

• 8/12 = x/ 6
• Cross Multiply-- 8 * 6 = 12 * x
• Show Division --- 48/12 = 12x/12
• You have to get rid of 12 to make x alone!
• X= 4

Proportion Example

• I am baking cookies
• I use 3/4 cup of chocolate chips in one batch.
• I am making a triple batch
• How many cups of chocolate chips do I need?
• 0.75/1 = X/3               X = 2.25 or 2 1/4 cups

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