Sec 5-1D. Solve Proportions pg. 276 - 280

Definitions A Proportion is an equation stating that two ratios or rates are equivalent. 2 5 = 4 10 𝑎 𝑏 = 𝑐 𝑑 , 𝑏≠0, 𝑑 ≠0 Example, We sell 2 candy bars for $3.00 $3.00 2 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠 = $6.00 4 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠 = $12.00 8 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠 Equivalent ratios have the same value.

Cross Products We often use CROSS PRODUCTS to solve proportions. Consider, 𝑎 𝑏 = 𝑐 𝑑 Multiply both sides by bd (common denominator) 𝑏𝑑 𝑎 𝑏 = 𝑐 𝑑 𝑏𝑑 After cross-canceling we are left with ad =bc This is the cross product of the proportion This is the same as multiplying top by bottom across the equal sign…cross products!

Solve this proportion 4 13 = 𝑥 39 Use cross products (4)(39) = 13x 4 13 = 𝑥 39 Use cross products (4)(39) = 13x 156 = 13x 156 13 = 13𝑥 13 12 = x

Solve this proportion 18 eggs cost $3.50. How much would 10 eggs cost? 18 𝑒𝑔𝑔𝑠 $3.50 = 10 𝑒𝑔𝑔𝑠 𝑥 Use cross products 18x = ($3.50)(10) 18x = $35.00 18𝑥 18 = $35.00 18 x = $1.94 When setting up your proportion, make sure that like items are across from each other

Solve this proportion A certain vehicle can travel 23 miles on 1 tank of gas. How many gallons will it need to travel 700 miles. Round to the nearest tenth. Set up a proportion. 23 𝑚𝑖𝑙𝑒𝑠 1 𝑔𝑎𝑙𝑙𝑜𝑛 = 700 𝑚𝑖𝑙𝑒𝑠 𝑔 Use cross products 23g = 700 23𝑔 23 = 700 23 g = 30.4 gallons Miles on top Gallons on bottom