When comparing two objects of the same proportion... Proportional Relationships Proportion: a statement that two ratios are equal.

Definitions RATIO is two "things" (numbers or quantities) compared to each other. For example, "3 dollars per gallon" is a ratio. Or, "40 miles per 1 hour". Or, 15 girls versus 14 boys. Or, 569 words in 2 minutes. Or, 23 green balls to 41 blue balls, etc. Your math book might say it is a comparison of two numbers or quantities. A related term, RATE, is defined as a ratio where the two quantities have different units. Some people differentiate and say that the two things in a ratio have to have a same unit; some people don't differentiate and allow "3 dollars per gallon" to be called a ratio as well. PROPORTION is when you have two ratios set to be equal to each other. For example, "3 dollars per gallon" equals "6 dollars per two gallons". Or, 2 teachers per 20 kids equals 3 teachers per 30 kids.

What are proportions all about? Consider the problem: if 2 gallons (of something) costs this much, how much would 5 gallons cost? What is the general idea to solve this problem? Or, if car travels this much in 3 hours, how long could it travel in 4 hours? 6 hours? 7 hours? In proportion problems you have two things that both change at the same rate. For example, you have dollars and gallons as your two things. You know the dollars & gallons in one situation (e.g. 2 gallons costs $5.40), and you know either the dollars or the gallons of another situation, and are asked the missing one. For example, you are asked how much would 5 gallons cost. You know it is "5 gallons" and are asked the amount of dollars. You can make tables to organize your information: 2 gallons : $ miles : 3 hours 5 gallons : $X X miles : 4 hours In both examples, there are two things that both change at the same rate. In both examples, you have four numbers (two for one situation, two for the other situation), you are given three of them, and asked the fourth. So, how would we solve these types of problems?

Methods for solving Proportions 1) If 2 gallons is $5.40 and I'm asked how much is 5 gallons, since gallons increased 2.5-fold, I just multiply the dollars by 2.5 too. 2) If 2 gallons is $5.40, I figure first how much 1 gallon would be, and then how much 5 gallons. Okay, 1 gallons would be half of $5.40 or $2.70, and I'll go five times that. One good basic idea for solving proportion word problems is to think what would it be for 1 or for some other easy unit, and then multiply to get what is asked. For example: if car goes 110 miles in 3 hours, how far will it go in four hours? Figure out how far it gets in 1 hour, then multiply by 4.

Methods cont.... 3) I build a proportion and solve by cross multiplying: 2 gallons = 5 gallons $5.40 x 2X = 5 (5.40) X = / 2 X = ) I build a proportion but this way: (and it still works - you see, you can build the two fractions for your proportion in several different ways)build the two fractions for your proportion in several different ways 5.40 = 2 gallons X 5 gallons Let’s work it out and see!

Miles 4 Hour $ (dollars) 5 lb. (pound)

Proportion Example My families dinner plate is certain proportion of veggies. We all eat different quantities of food, but the proportions are equal...if our proportion of carrots to steak is 3 carrots to 1 oz. of steak and my daughter has 2 oz. of steak on her plate, how many carrots should be on her plate?

Setting up Proportions 3 = x 1 2 x(1) = 2(3) cross multiplication x = (2)(3)/1 x = 6 carrots!

Definitions RATIO is two "things" (numbers or quantities) compared to each other. For example, "3 dollars per gallon" is a ratio. Or, "40 miles per 1 hour". Or, 15 girls versus 14 boys. Or, 569 words in 2 minutes. Or, 23 green balls to 41 blue balls, etc. Your math book might say it is a comparison of two numbers or quantities. A related term, RATE, is defined as a ratio where the two quantities have different units. Some people differentiate and say that the two things in a ratio have to have a same unit; some people don't differentiate and allow "3 dollars per gallon" to be called a ratio as well. PROPORTION is when you have two ratios set to be equal to each other. For example, "3 dollars per gallon" equals "6 dollars per two gallons". Or, 2 teachers per 20 kids equals 3 teachers per 30 kids.

How does this apply to our Amateur Architect Project? A fraction is a ratio, it compares to numbers of the same unit 9/16th of an inch means: 9 equal parts of a whole (total 16 equal parts) inch 9:16 Let’s look at a proportional problem...

9/16ths of an 11” page? USE A PROPORTION TO FIND 9/16 OF 11. 9/16 MEANS 9 PARTS OUT OF A TOTAL 16 PARTS (OR A WHOLE) LET X = THE MEASUREMENT EQUAL TO 9/16 OF 11 9 = X (9) (11) = (x) (16) cross multiplication x = (9) (11) 16 x = ________”