What is a ratio?

What is the difference between a ratio and a fraction?

What is a proportion?

Additive vs Multiplicative relationships

What is the meaning of? “proportional to”

Proportions A comparison of equal fractions A comparison of equal rates A comparison of equal ratios

Ratios and Rates If a : b = c : d, then a/b = c/d. Example: 35 boys : 50 girls = 7 boys : 10 girls 5 miles per gallon = 15 miles using 3 gallons

To determine proportional situations… Start easy: I can buy 3 candy bars for $2.00. So, at this rate, 6 candy bars should cost… 9 candy bars should cost… 30 candy bars should cost… 1 candy bar should cost… this is called a unit rate.

To determine proportional situations Here’s another. 7 small drinks cost as much as 5 large drinks. At this rate… How much should 14 small drinks cost? How much should 21 small drinks cost? How much should 15 large drinks cost?

Ratios are not the same as fractions The ratio of males to females is 3 : 2. That means 3/5 of the people are male, and 2/5 of the people are female. The mixture is 3 parts water and 1 part green dye. That means that 3/4 of the mixture is water and 1/4 of the mixture is green dye.

We can add fractions, but not ratios On the first test, I scored 85 out of 100 points. On the second test, I scored 90 out of 100 points. Do I add 85/100 + 90/100 as 175/200 or 175/100?

Exploration 6.3 Do the questions in part 1.

Some ratios or rates can’t be written as fractions I rode my skateboard 5 miles per hour. There is no “whole”, and so a fraction does not really make sense.

Reciprocal Unit Ratios Suppose I tell you that 4 doodads can be exchanged for 3 thingies. How much is one thingie worth? 4 doodads/3 thingies means 1 1/3 doodads per thingie. How much is one doodad worth? 3 thingies/4 doodads means 3/4 thingie per doodad.

To solve a proportion… If a/b = c/d, then ad = bc. This can be shown by using equivalent fractions. Let a/b = c/d. Then the LCD is bd. Write equivalent fractions: a/b = ad/bd and c/d = cb/db = bc/bd So, if a/b = c/d, then ad/bd = bc/bd.

To set up a proportion… I was driving behind a slow truck at 25 mph for 90 minutes. How far did I travel? Set up equal rates: miles/minute 25 miles/60 minutes = x miles/90 minutes. Solve: 25 • 90 = 60 • x; x = 37.5 miles.

Strange looking problems I see that 1/4 of the balloons are blue, and there are 6 more red balloons than blue. Let x = number of blue balloons, and so x + 6 = number of red balloons. Also, the ratio of blue to red balloons is 1 : 3 Proportion: x/x + 6 = 1/3 Alternate way to think about it. 2x + 6 = 4x x x + 6

Let’s look again at proportions Explain how you know which of the following rates are proportional? 6/10 mph 1/0.6 mph 2.1/3.5 mph 31.5/52.5 mph 240/400 mph 18.42/30.7 mph 60/100 mph