Proportions By Mrs. Berg 7.RP.2

Yesterday… We learned about ratios. A ratio is the comparison of two quantities by division. What is the ratio of MSU Bulldogs to Ole Miss Black Bears written in simplest form three different ways?

We also… Learned about proportions. A proportion states that two ratios are equal (=) Today… We will review what we learned about proportions and we’ll take a closer look at how we can set up a proportion from scratch given a particular situation.

What do proportions have to do with food?

Catering PROPORT IONS Does it matter how many people are invited to a dinner when ordering food?

Too much? Not enough? Just right? PROPORT IONS Is this amount of food proportional for this family dinner?

Too much? Not enough? Just right? PROPORT IONS Is this amount of food proportional for this family dinner?

what are proportions in math? V O C A B U L R Y A Proportion states that 2 ratios are equal. ratio 1 ratio 2 Notice… simplified is .

Why learn about proportions? Proportions can help us solve many types of real world problems that deal with two different quantities. We will see examples of this in today’s lesson. Proportions can also help us find missing information from two figures that are similar.

Do the 2 ratios form a proportion? C R O S M U L T I P Y Two ratios form a proportion if their cross products are equal (=). Cross multiply to determine if each pair of ratios form a proportion: Example 1 Example 2

You Try! C R O S State whether the pair of ratios form a proportion: M L T I P Y State whether the pair of ratios form a proportion:

Solving a proportion that involves a variable. C R O S M U L T I P Y Flow Map = 12y = 240 12y = 240 y = 20 Step 1 Cross Multiply Step 2 Solve the one- step equation.

You Try! C R O S M U L T I P Y Solve the following proportion: =

Setting up a proportion IONS Important to Remember There is not just one correct way to set up a proportion. The key is to make sure you put “like units” across from each other. Inches inches miles miles feet feet Write a proportion for the situation: Swimming goggles are 12 for $84.36. At this rate, how much would it cost for 17 goggles? Example 1st Way: 2nd Way: Answer: $119.51 Answer: $119.51

Setting up a proportion IONS Remember, “like units” must be across from each other! Step 1 Take the information in the first sentence and make that your first ratio. Step 2 Take the information in the second sentence and set the second ratio up to where the “like units” are across from each other. Step 3 Cross multiply. Solve the one-step equation. Example Write a proportion for the situation. Then solve. A football player runs 25 yards in 2.5 seconds. How many seconds should it take the same football player to run 100 yards? = 25x = 250 x = 10

You Try! C R O S M U A) C) L T B) D) I P Y 1) Jim’s heartbeat is 142 beats per 2 minutes. Which proportion would give Jim’s heartbeat in 8 minutes? A) C) B) D) Both B and C Answer: D Answer x = $2.75 Write a proportion for the situation. Then solve. 3 ounces for $1.65; 5 ounces for x dollars. 2)

Closure = A proportion states that 2 ratios are equal. What do you do to determine if 2 ratios are equal? How do you solve a proportion with a variable? First you ________? = Then you solve the one-step ______? When setting up a proportion, it is important that the same units are _________? =