Solving Proportions 6.1.2.1 Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction 6.1.2.2 Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations

I can… Write proportions Solve proportions by using cross products Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

What are proportions? An equation in which two ratios are equivalent (equal) is called a proportion a = c_ b d 2 = 8_ 3 12 Ratio: 2 of 3 rows Ratio: 8 of 12 dots Proportion

The cross products of a proportion are EQUAL 6 x 5 = 3 x 10 30 = 30

Proportions Use cross products to decide if the following are proportions. 1) 2)

Proportions YES NO 3 x 60 = 5 x 36 4 x 15 = 8 x 8 180 = 180 60 64

Solving Proportions 4 = 24 y 30 4(30) = 24y 120 = 24y 24 24 5 = y 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Solving Proportions 10 = 5 y 8 10(8) = 5y 80 = 5y 5 5 16 = y 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Solving Proportions 2.1 = x 1.4 3 3(2.1) = 1.4x 6.3 = 1.4x 1.4 1.4 4.5 = x 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Your Turn… 3 = 12 n 28 3(28) = 12n 84 = 12n 12 12 7 = n 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Try Again… 6 = 12 z 24 6(24) = 12z 144 = 12z 12 12 12 = n 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Try Again… 22.5 = a 6 6 6(22.5) = 6a 135 = 6a 6 6 22 ½ or 22.5 = n 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Try Again… _h_ = _1_ 1.5 0.6 1(1.5) = 0.6a 1.5 = 0.6a 6 0.6 2.5 = n 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF

Word Problems 1 can = _c_ $2 $10 1(10) = 2c 10 = 2c 2 2 5 cans = c If you can buy one can of pineapple chunks for $2 then how many cans can you buy with $10? 1 can = _c_ $2 $10 1(10) = 2c 10 = 2c 2 2 5 cans = c 1. Set up the proportion 2. Solve for the variable. POOF

Your Turn… 1. Set up the proportion 2. Solve for the variable. You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? 1. Set up the proportion 2. Solve for the variable. 5 mi. = 20 mi_ 3 hr. t 3(20) = 5t 60 = 5t 5 5 12 hours = t POOF

Your Turn… 1. Set up the proportion 2. Solve for the variable. You are on a cruise. You have traveled 7 miles in 2 hours. At that same rate, how long will it take you to travel 28 miles? 1. Set up the proportion 2. Solve for the variable. 7 mi. = 28 mi_ 2 hr. t 2(28) = 7t 56 = 7t 7 7 8 hours = t POOF

Your Turn… Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall? 24 in wide = w _ 12 in tall 2 in tall 2(24) = 12w 48 = 12w 12 12 4 inches = w POOF

I can… Write proportions Solve proportions by using cross products Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Solve Using Cross Products 8.3 Notes Solve Using Cross Products 4 = 24 y 30 4(30) = 24y 120 = 24y 24 24 5 = y 1. Cross Multiply 2. Simplify 3. Solve for the variable. POOF