Math OGT: Proportions

Janice had a 5-inch high by 3-inch wide photo enlarged to a 3.5-foot tall poster. What should be the approximate width of the poster?

2.1 feet First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (height on top and width on bottom!). Then, cross multiply and divide to solve. 3 x 3.5 = 10.5, 10.5/5 = 2.1

I am driving to my grandmas house, which is 900 miles away. I drove 11 hours at a speed of 60 miles per hour. How many miles do I still need to drive?

240 miles First, find out how many miles we drove in 11 hours if we went 60 miles per hour (per 1 hour). Set up a proportion and cross multiply and divide to solve. 60 x 11 = 660. 660 / 1 = 660. Then, if we traveled 660 miles and grandma's house is 900 miles away, we still have to drive 240 miles (900-660= 240).

Joel has a 50-meter roll of copper wire that weighs 7.5 kilograms. Approximately how many meters of wire will be in a new shipment that weighs 502.5 kilograms?

3,350 rolls of wire First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (rolls of wire on top and kilograms on bottom!). Then, cross multiply and divide to solve. 50 x 502.5 = 25,125. 25,125 / 7.5= 3,350

For his business, Gil has determined that the time it takes to finish a job varies inversely with the number of workers. This can be expressed as T = k/w where T = time, k is a constant, and w = number of workers. Gil's records show that 18 workers can finish a job in 6 days. How many days will it take 12 workers to do the same job?

4 days This problem has a lot of information that you do not need. Skip the first paragraph. The second paragraph tells us what we need to know and find out. First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (number of workers on top and days on bottom!). Then, cross multiply and divide to solve. 6 x 12 = 72. 72/18 = 4

Before her trip to Canada, Liz exchanged 300 U.S. dollars for Canadian dollars at a rate of 1 U.S. dollar to 1.35 Canadian dollars. Determine the amount of money in Canadian dollars that Liz received for her 300 U.S. dollars.

405 Canadian dollars First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (US dollars on top and Canadian dollars on bottom!). Then, cross multiply and divide to solve. 300 x 1.35 = 405 , 405 /1 = 405

25 rolls of tape weigh 200 pounds. How many pounds does 6 rolls of tape weigh?

480 pounds First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (rolls of tape on top and pounds on bottom!). Then, cross multiply and divide to solve. 200 x 6 = 1200. 1200/25= 480.

Alicia is 5 feet tall. She casts a shadow that measures 6.5 feet long at the same time that a sculpture in the park casts a shadow 12 feet long. What is the approximate height of the sculpture?

9.23 feet First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (actual height on top and shadow height on bottom!). Then, cross multiply and divide to solve. 5 x 12 = 60. 60/6.5 = 9.23

How can you identify a proportion problem?

A problem that can be solved by setting up a proportion often involves comparing two things. You're also usually given three numbers and asked to find the fourth.

What is the most important thing to remember when solving proportion problems?

Decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Students who get these problems wrong often had just put the numbers in the wrong spots. Take the exta 10 seconds to do this step.

If you have objects similar, can you find the length of a missing side using proportions?

Yes! When objects are similar, the lengths of their sides are proportional (and, by the way, the angles are equal!). If you know the length of the same side in both object (in this case, we know the length of the right side of each triangle), and the length of the side that is in the same spot as the side you're trying to find the length of, just set up a proportion. First, decide what's going to go in the top (numerator) and what's going to go in the bottom (denominator). Write it down. Then, plug in the numbers (right side on top and bottom in bottom). Then, cross multiply and divide to solve. 6 x 1 = 6. 6 / 3 = 2.

How do you cross multiply and divide?

You multiply the numbers across from each other (4 x 18 = 27). Then, you divide this by the other number (72 / 3 = 24).

I am driving to my grandmas house. I drove 11 hours at a speed of 60 miles per hour. In this proportion problem, what two things are we comparing?

miles and hours If you look at the numbers and their labels, it seems as though we're looking at miles and miles per hour. With this question, students often think one of the things we're looking at is speed. Think about miles per hour. What is this saying? If I drive 60 miles per hour, how long does it take me to drive 60 miles at this speed? One hour. 60 miles per hour is stating 60 miles per 1 hour. We could then find out how many miles we could drive (X) in 11 hours using a proportion.