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### Percents and Proportions

• Percent represents a part of a whole. Remember to ask yourself if your answer makes sense. For example 50% of 120 means half of 120; 150% of 120 means over 120, in fact 120 plus an additional half.
• You can use a proportion to solve a percent problem. Set a ratio equal to an unknown out of 100.
• The number that follows the word “of” is the denominator.

### Percents and Proportions

Find 45% of 82.
• [x/82] = [45/100]
• 100x = 45 ×82
• 100x = 3690
• x = 3690 ÷100
x = 36.9
Find 60% of 29.
• 0.60 ×29 =
17.4
Find 48% of 102.
• [48/100] = [x/102]
• 100x = 8 ×102
• 100x = 4896
• x = 4896 ÷100
x = 48.96
What percent of 1030 is 845 to the nearest hundredth?
• [1030/845] =
• 1.2189 ×100% =
121.89%
What percent of 87 is 194 to the nearest hundredth?
• [87/194] =
• 0.4485 ×100%
44.85%
To the nearest hundredth, 10 is 45% of what number?
• [10/x] = [45/100]
• 45x = 1,000
x = 22.22
To the nearest hundredth, 94 is 85% of what number?
• [94/x] = [85/100]
• 85x = 9,400
x = 110.59
There are 800 students in the astronomy class at a university. This makes up 20% of the students at the school. How many students are at the university?
• [800/x] = [20/100]
• 17x = 80,000
x = 4000 students
Veronica used 75 feet of her roll of fabric. There is still 85% left of the roll. To the nearest hundredth, how long was the roll of fabric before Veronica used it?
• [75/x] = [85/100]
• 85x = 7,500
x = 88.24 feet
California is 163,969 square miles, which is about 4.3% the size of the United States. To the nearest square mile, how big is the United States?
• [163,696/x] = [4.3/100]
• 4.3x = 16,369,600
x = 3,806,883 square miles

*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.

### Percents and 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 0:23
• Proportion
• Cross Products
• Finding Part of a Whole 1:07
• Method 1: Find 50% of 36
• Method 2: Find 50% of 36
• Finding Part of a Whole, cont. 3:06
• Example: Find 65% of 143
• Finding the Whole Amount 3:44
• Example: How Many Students are in 8th Grade?
• Finding the Whole Amount, cont. 5:18
• Example: How Many Students are in the School?
• Finding a Percent 6:38
• Method 1: What Percent of 175 is 105
• Method 2: What Percent of 175 is 105
• Finding a Percent, cont. 9:57
• What Percent of 115 is 46?
• Extra Example 1: Find 8% of 48 11:09
• Extra Example 2: 9 is 25% of What Number? 11:34
• Extra Example 3: How Many Students are in the Class? 12:39
• Extra Example 4: 66 is What Percent of 55? 14:25