7.1 Ratios and Proportions

7.1 Ratios and Proportions

Ratio Reminders

• Don't forget to reduce your fractions!

• We will typically use fractions when discussing ratios and proportions.

• Double check to make sure you're in the same unit measure!!!

Multiple Choice

A cabinet measures 5 feet by 30 inches. What is the dimension ratio?

•  $\frac{2}{1}$  

•  $\frac{60}{30}$  

•  $\frac{5}{30}$  

•  $\frac{30}{5}$  

Proportions

• When two or more ratios are equivalent

• "Proportional" means that both ratios should reduce to the same fraction

Solving Proportions

• Notice that once you are done, the ratios reduce to the same fraction and the cross-products are equal (18=18)

Multiple Choice

Some proportion problems are easy and can be solved using basic mental math. For example: A cookie recipe calls for 1 cup of brown sugar and 2.5 cups of flour. If I use 5 cups of flour, how much brown sugar should I use?

• 2 cups

• 5 cups

• 1 cup

• 3 cups

Proportions

Other problems can be a bit more difficult to think about so we can use proportions to solve them. Review the picture before moving onto the next slide

Multiple Choice

Solve the proportion then check your answer by looking at their cross-products

• c = 4

• c = 8

• c = 14

• c = 10

Multiple Choice

Try another: Solve for x

• x = 16

• x = 28

• x = 135

• x = 26

Multiple Choice

Find a. Don't forget to distribute when cross-multiplying!

• 29/12

• 41/12

• 107/12

• 13

Multiple Choice

A 6-ounce package of fruit snacks contains 45 pieces. How many pieces would you expect in a 10-ounce package? What is a correct way to setup the proportion?

• 
  

  $\frac{6}{45}=\frac{10}{x}$

• $\frac{10}{45}=\frac{6}{x}$
  

Multiple Choice

A shop produces 39 wetsuits every 2 weeks. How long will it take the shop to produce 429 wetsuits? Setup then solve a proportion.

• 18 wk

• 20 wk

• 22 wk

• 24 wk

Extended Ratios

• When a ratio involves three or more quantities

• Notice how we setup a problem like this

Open Ended

A triangles sides have an extended ratio of 3:5:6. The perimeter is 98. What is the correct setup?

Multiple Choice

You should have a setup of 3x+5x+6x=98. Now solve for x and find the shortest side

• 21

• 35

• 42

• 180

Poll

How confident are you working with ratios and proportions?

• Dude, this is so easy!

• I can do it with a little guidance

• I'm struggling a bit but I will keep trying!

• I need to meet during office hours