1. RATIOS are just Comparisons You can write ratios three different ways. The Fraction Way a b The Colon Way a:b The Written Way a to b “a” is the first object you are comparing and “b” is the second object you are comparing the first to. WORK IT: The table shows the number of pizzas sold during a week. Use the information to find the ratios. Write the ratios 3 different ways. a) Small pizzas to large pizzas. b) Medium pizzas to large pizzas. c) Large pizzas to all pizzas. WORK IT: You can use ratios to find rates. To find the Rate, Compare the Distance to the Time with a ratio. SizeSmallMediumLarge Pizzas96144240 Distance 5m10m30m Time (in Seconds) 10s20s60s NAME______________________PERIOD____

2. We can compare TWO ratios to find missing information by Writing an equation that puts the two ratios equal to each other. This is called a PROPORTION. Still confused? Look below. Distance 5m10m ? m Time (in Seconds) 10s20s 80s We can use the rate from the last problem to write a proportion to find the missing distance. 1 x 2 80 = 10 1 20 2 = Step 1: Multiply each side by 80 to “get the variable alone on one side” Step 2: Divide 80 by 2 Step 3: x=40 so the missing distance is 40m WORK IT: Proportions are also very useful for making science conversions. Finish the chart to find out how many seconds are in a day and then a week. Seconds 360sec ? sec Time1 hour 24 hours168 hours

3. Solve some easy proportions. Try to simplify fractions when possible, before solving. 2 x c 11 5 3 8 4 5 t d 80 8 24 5 100 = = = = Write the four you just solved in sentence form: Example: 3 x write “3 is to 8 as x is to 32” 8 32 = 1._________________________________________ 2._________________________________________ 3._________________________________________ 4._________________________________________

4. BUT WAIT! WHAT IF THE VARIABLE IS IN THE DENOMINATOR? 8 6 x 15 Step 1: Multiply the right numerator by x and multiply the left numerator by the 15. This is what you think of when you “cross multiply” Notice that it is ONLY only only! done when you have two fractions equal to each other. 8 ● 15 = 6 ● x 120 = 6xStep 3: Divide both sides by 6. 20 = x Step 2: Simplify = Solve some easy proportions where the variable is in the Denominator. 24 13 52 3x 6 z ==