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For more information, please see full course syllabus of Pre Algebra

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### Proportions

• Ratios that are equal form a proportion.
• The Cross Products Property is true because of the Multiplication Property of Equality.
• There are two ways to solve a proportion. You may be able to create an equivalent proportion by finding equivalent ratios by multiplying or dividing the numerator and denominator by the same number. The second way, the preferred method, is to use cross products and then solve for the missing number by using division.

### Proportions

[9/x] = [45/10]
• 45x = 9 ×10
• 45x = 90
• x = 90 ÷45
x = 2
[7/35] = [x/20]
• 35x = 20 ×7
• 35x = 140
• x = 140 ÷35
x = 4
[2/x] = [5/15]
• 5x = 2 ×15
• 5x = 30
• x = 30 ÷5
x = 6
[x/20] = [6/30]
• 30x = 6 ×20
• 30x = 120
• x = 120 ÷30
x = 4
[7/13] = [14/x]
• 7x = 13 ×14
• 7x = 182
• x = 182 ÷7
x = 26
[8/x] = [16/7]
• 16x = 8 ×7
• 16x = 56
• x = 56 ÷16
x = 3[1/2]
You exchange \$ 235 for 1501.97 Chinese Yuan. Find the unit rate of exchange to the nearest hundredth.
• [\$ 235/1501.97] = [\$ 1/e]
• 235e = 1501.97
• e = 1501.97 ÷235
e = 6.39
Does this ratio form a proportion? Explain.
[65/25], [13/5]
• [(65 ÷5)/(25 ÷5)] = [13/5]
Yes. You can create an equivalent ratio by dividing.
A car can travel 155 miles on 5 gallons of gas. How far can the car travel on 7 gallons of gas?
• [155/5] = [x/7]
• 5x = 155 ×7
• 5x = 1085
• x = 1085 ÷5
x = 217 miles
You are making a map of the state of Colorado that is to scale. Colorado is approximately 380 miles long and 280 miles wide in real life. If the Colorado on your map is going to be 14 inches wide, how long will it be?
• [380 mi long/280 mi wide] = [(x in long)/14 in wide]
• 280x = 380 ×14
• 280x = 5320
• x = 5320 ÷280
x = 19 in

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Proportions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:16
• Proportion
• Cross Products
• Identifying a Proportion 11:28
• Example: Do the Ratios Form a Proportion?
• Solving Proportions Using Two Methods 2:47
• Example: x/4 = 12/21
• Example: 20/y = 15/9
• Solving Proportions in Word Problems 5:56
• Example: Find the Unit Rate of Exchange
• Extra Example 1: Does the Ratio Form a Proportion? 9:55
• Extra Example 2: Solving Proportions 10:53
• Extra Example 3: Find the Length of the Photo 11:33
• Extra Example 4: Distance 12:59