1. Sec 5-1D. Solve Proportionspg

2. 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
$ 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠 = $ 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠 = $ 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠
Equivalent ratios have the same value.

3. 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!

4. 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
= 13𝑥 13
12 = x

5. 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 = $
x = $1.94
When setting up your proportion, make sure that like items are across from each other

6. 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 =
g = 30.4 gallons
Miles on top
Gallons on bottom