1. 3.4 Ratios & Proportions

2. 3.4 - Ratios & Proportions Goals / “I can…”  Find ratios and rates  Solve proportions

3. 3.4 - Ratios & Proportions A ratio is a comparison of two numbers with the same unit by division. 3 roses = 3 7 roses 7

4. What do Ratios look like? Ratios can be written in three different ways: a to b a:b Because a ratio is a fraction, b can not be zero Ratios are expressed in simplest form

5. How to Use Ratios? The ratio of boys and girls in the class is 12 to18. 4cm 1cm This means, for every 12 boys you can find 11 girls to match. There could be just 12 boys, 11 girls. There could be 24 boys, 22 girls. There could be 120 boys, 110 girls…a huge class What is the ratio if the rectangle is 8cm long and 2cm wide? Still 4 to 1, because for every 4cm, you can find 1cm to match The ratio of length and width of this rectangle is 4 to 1.. The ratio of cats and dogs at my home is 2 to 1 How many dogs and cats do I have? We don’t know, all we know is if they’d start a fight, each dog has to fight 2 cats.

6. How to simplify ratios? The ratios we saw on last slide were all simplified. How was it done? Ratios can be expressed in fraction form… This allows us to do math on them. The ratio of boys and girls in the class is The ratio of the rectangle is The ratio of cats and dogs in my house is

7. How to simplify ratios? Now I tell you I have 12 dogs and 6 cats. Can you simplify the ratio of cats and dogs to 2 to 1? == Divide both numerator and denominator by their Greatest Common Factor 6.

8. 3.4 - Ratios & Proportions A rate is a comparison of two numbers with different units by division. 25 miles $7.25 2000 revolutions 1 hour hr 5 min

9. 3.4 - Ratios & Proportions A unit rate is a rate with a denominator of 1.

10. 3.4 - Ratios & Proportions Example: A brand of apple juice costs $1.56 for 48 ounces. Find the unit rate.

11. 3.4 - Ratios & Proportions Converting rates: To convert rates you must find a conversion factor. Example:  Approximately how many seconds have you been alive?

12. Now you know enough about properties, let’s solve the Mysterious problems! If your car gets 30 miles/gallon, how many gallons of gas do you need to commute to school everyday? 5 miles to school 5 miles to home Let x be the number gallons we need for a day: Can you solve it from here? x = Gal

13. Now, on to proportions! What is a proportion? A proportion is an equation that equates two ratios The ratio of dogs and cats was 3/2 The ratio of dogs and cats now is 6/4=3/2 So we have a proportion :

14. 3.4 - Ratios & Proportions Solving using Cross Products (Multiplying) PROPERTY  IF, then ad = bc.

15. Properties of a proportion? 2x6=12 3x4 = 12 3x4 = 2x6 Cross Product Property

16. How about an example? Solve for x: 7(6) = 2x 42 = 2x 21 = x Cross Product Property

17. 3.4 - Ratios & Proportions Example:

18. Can you solve this one? Solve for x: 7x = (x-1)3 7x = 3x – 3 4x = -3 x = Cross Product Property

19. 3.4 - Ratios & Proportions Example