Proportions/Ratios Audrey & Kourtney

Proportions – Definition A proportions is a part, share, or number considered in comparative relation to a whole.

For example.. A bag of flour cost $4.65. You want to buy four bags of flour. How much would four bags of flour cost? Let’s find out.

The problem To set up the problem, you write is over of. In this case, it would look like this. Is = 1 bag of flour ^Is ^Of Of = The price of one bag Now let’s find out the other side of the proportion. 1/4.65

1/4.65 = 4/x The Other Proportion Since you have is/of, you need to find the other proportion to find the price of four bags. To do this, you have to cross multiply. 1/4.65 = 4/x

Finding X X is the variable in the problem. It is the denominator of the 4/x proportion. To find X, you cross multiply. You want to multiply the two available numbers. In this case, it’s 4 and 4.65. So you multiply 4 and 4.65. 1/4.65 = 4/x

The Solution 4 * 4.65 = ? The answer is 18.6. Since we know the answer, we divide it by the other number in the proportion. 1 is the other numerator, so we divide it by 1. 18.6 / 1 = 18.6

The Answer The answer to this proportion is $18.60. You will have to pay $18.60 for four bags of flour. This is how you solve a proportion. Now we will work on ratios.

Problem You are at a swimming party and you have to pay for a slice of pizza. One slice of pizza is $1.50. You want to buy 4 pieces for you and three other friends. How much will it cost to buy 4 slices of pizza? Hint: Cross – multiply, is/of

Answer It will cost 6 dollars.

Another Example You are in a club that picks up trash on the side of the road. You earn $10 per hour. You earn $5.15 per 75 pieces of trash. You work from 8:00 A.M. to 5:00 P.M. and you pick up 945 pieces of trash. What is the ratio of money you earned through hours and money you earned through pieces of trash? Let’s find out.

The Money. $ So if you work from 8:00 A.M. to 5:00 P.M., you work how many hours? 9 hours. And you earn $10 per hour. 9 * 10 = 90 You earned $90 in the hours you worked.

The Trash. If you pick up 945 pieces of trash, and every 75 pieces you earn $5.15, how much did you earn picking up trash? 945 / 75 = 12.6 12.6 * 5.15 = 64.89 You earn $64.89 by picking up trash.

Comparing. You earned $90 per hour and $64.89 per 75 pieces of trash. Now make a ratio of it. 90 : 64.89 That’s the ratio.

Constructed Response You’re at a school book fair and you want to buy 3 new books. Red Wall is $4.00, 20 Boy Summer is $7.50, and Baby Sitters Club is $6.00. You have $20. Make a ratio of the money you have and the money you need to buy all 3 books with 9.5% tax.

The Answer $19.16

One more problem You have 86% (450 points) in your English class. How many possible points can you have? Hint: 450/x = 86/100

Answer You can have a total of 523 points.

Thanks! We’re done. (: