Illustrative Math Alignment: Grade 6 Unit 3
Unit Rates and Percentages
Lesson 14: Solving Percentage Problems
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 3TopicRatios, Proportions, and Percents DescriptionThis example demonstrates solving for b in a proportion where a = 8, c = 4, and d = 3. We set up the proportion 8 / b = 4 / 3 and solve for b, resulting in b = 6. This problem shows how to find an unknown value in the denominator of a proportion. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 30TopicRatios, Proportions, and Percents DescriptionThis example illustrates how to determine if two triangles are not similar using proportions. Two triangles are shown, both with a 75° angle. The first triangle has sides of 15 and 9, while the second has sides of 28 and 18. The problem requires setting up a proportion to check for similarity: 15 / 9 = 28 / 18. After simplifying, the ratios are not equal (5 / 3 ≠ 14 / 9), concluding that the triangles are not similar. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 31TopicRatios, Proportions, and Percents DescriptionThis example demonstrates how to determine if two right triangles are similar using proportions. Two right triangles are shown, one with legs of length 4 and 3, and the other with legs of length 10 and 7.5. The problem requires setting up a proportion to check for similarity: 4 / 3 = 10 / 7.5. After simplifying, both ratios are equal (4 / 3 = 4 / 3), confirming that the triangles are indeed similar. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 32TopicRatios, Proportions, and Percents DescriptionThis example illustrates how to determine if two right triangles are not similar using proportions. Two right triangles are shown, one with legs of length 12 and 5, and the other with legs of length 35 and 15. The problem requires setting up a proportion to check for similarity: 12 / 5 = 35 / 15. After simplifying, the ratios are not equal (12 / 5 ≠ 7 / 3), concluding that the triangles are not similar. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 33TopicRatios, Proportions, and Percents DescriptionThis example demonstrates how to determine if two rectangles are similar using proportions. Two rectangles are shown, with the first having dimensions 3 and 8, and the second having dimensions 9 and 24. The problem requires setting up a proportion to check for similarity: 3 / 8 = 9 / 24. After simplifying, the ratios are equal, confirming that the rectangles are indeed similar. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 34TopicRatios, Proportions, and Percents DescriptionThis example illustrates how to determine if two rectangles are similar using proportions with algebraic expressions. Two rectangles are shown, with the first having dimensions 11.5 and 23, and the second having dimensions 23x and 46x. The problem requires setting up a proportion to check for similarity: 11.5 / 23 = 23x / 46x. After simplifying, the ratios are equal, confirming that the rectangles are indeed similar for any value of x. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 35 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 35TopicRatios, Proportions, and Percents DescriptionThis example demonstrates how to determine if two parallelograms are similar using proportions. Two parallelograms are shown, with the first having dimensions 6 and 9, and the second having dimensions 15 and 22.5. The problem requires setting up a proportion to check for similarity: 6 / 9 = 15 / 22.5. After simplifying, the ratios are equal, confirming that the parallelograms are indeed similar. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 36 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 36TopicRatios, Proportions, and Percents DescriptionThis example demonstrates how to determine if two parallelograms are not similar using proportions. Two parallelograms are shown, with the first having dimensions 9 and 28, and the second having dimensions 18 and 54. The problem requires setting up a proportion to check for similarity: 9 / 18 ≠ 28 / 54. After simplifying, the ratios are not equal, concluding that the parallelograms are not similar. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 37 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 37TopicRatios, Proportions, and Percents DescriptionThis example illustrates solving a proportion problem using similar triangles with algebraic expressions. Two triangles are shown, one with side lengths 9 and 18, and the other with expressions 6x and 10x + 6. The problem requires setting up a proportion to determine the value of x for which the triangles are similar: 9 / 18 = 6x / (10x + 6). Solving this equation leads to x = 3. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 38 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 38TopicRatios, Proportions, and Percents DescriptionThis example demonstrates solving a proportion problem using similar right triangles with algebraic expressions. Two right triangles are shown, one with side lengths 4 and 3, and the other with expressions 3x and 2x + 1. The problem requires setting up a proportion to determine the value of x for which the triangles are similar: 4 / 3 = 3x / (2x + 1). Solving this equation leads to x = 4. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 39 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 39TopicRatios, Proportions, and Percents DescriptionThis example illustrates solving a proportion problem using similar rectangles with an unknown side length. Two rectangles are shown, one with side lengths of 4 and x, and the other with side lengths of 15 and 4. The problem requires setting up a proportion to determine the value of x for which the rectangles are similar: 4 / 15 = x / 4. Solving this equation leads to x = 16/15. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 4 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 4TopicRatios, Proportions, and Percents DescriptionThis example illustrates solving for b in a proportion where a is expressed as x + 2, and c and d are given constants (c = 5, d = 2). We set up the equation (x + 2) / b = 5 / 2 and solve for b, resulting in the expression b = (2(x + 2)) / 5. This problem demonstrates how to handle algebraic expressions in proportions. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 40 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 40TopicRatios, Proportions, and Percents DescriptionThis example demonstrates solving a proportion problem using similar parallelograms with algebraic expressions. Two parallelograms are shown, one with side lengths of 6 and x, and the other with expressions of 3x + 2 and 22. The problem requires setting up a proportion to determine the value of x for which the parallelograms are similar: 6 / 22 = x / (3x + 2). Solving this equation leads to x = 3. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 5TopicRatios, Proportions, and Percents DescriptionThis example demonstrates solving for c in a proportion where a = 9, b = 4, and d = 12. We set up the proportion 9 / 4 = c / 12 and solve for c, resulting in c = 27. This problem shows how to find an unknown value in the numerator of a proportion. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 6TopicRatios, Proportions, and Percents DescriptionThis example illustrates solving for c in a proportion where a = 8, b = 3, and d is expressed as x + 3. We set up the equation 8 / 3 = c / (x + 3) and solve for c, resulting in the expression c = (8(x + 3)) / 3. This problem demonstrates how to handle algebraic expressions in the denominator of a proportion. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 7TopicRatios, Proportions, and Percents DescriptionThis example demonstrates solving for d in a proportion where a = 12, b = 5, and c = 48. We set up the proportion 12 / 5 = 48 / d and solve for d, resulting in d = 20. This problem shows how to find an unknown value in the denominator of a proportion when all other values are known. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 8TopicRatios, Proportions, and Percents DescriptionThis example illustrates solving for d in a proportion where a = 11, b = 5, and c is expressed as x - 4. We set up the equation 11 / 5 = (x - 4) / d and solve for d, resulting in the expression d = (5(x - 4)) / 11. This problem demonstrates how to handle algebraic expressions in the numerator of a proportion. |
Proportions |
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Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9 | Math Example--Ratios, Proportions, and Percents--Solving Proportions: Example 9TopicRatios, Proportions, and Percents DescriptionThis example demonstrates solving a proportion problem using similar triangles. Two triangles are shown, with one having sides of 3 and 4, and the other having sides of 6 and x. The problem requires finding the length of side x by setting up a proportion based on the similar triangles: 3 / 4 = 6 / x. Solving this equation leads to x = 8. |
Proportions |
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Math Example: Percents with Double Number Lines: Example 1 | Math Example: Percents with Double Number Lines: Example 1TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to find 50% of 250 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 250. By aligning 50% on the percentage line with its corresponding value on the numerical line, we can see that 50% of 250 is 125. This method visually represents the concept that 50% is equivalent to one-half of a quantity. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 10 | Math Example: Percents with Double Number Lines: Example 10TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to determine an unknown value using a double number line when given a part and its corresponding percentage, involving a decimal percentage. The image shows two number lines: one ranging from 0 to 100% and another from 0 to an unknown number x. The position 70 is marked on the second line, visually illustrating the process of finding x when 70 is 12.5% of x. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 11 | Math Example: Percents with Double Number Lines: Example 11TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 75, with 25 marked as an intermediate point. This visual representation helps students understand the relationship between the part (25) and the whole (75) in percentage terms. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 12 | Math Example: Percents with Double Number Lines: Example 12TopicRatios, Proportions, Percents DescriptionThis example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 220, with 55 marked as an intermediate point. This visual representation helps students understand the relationship between the part (55) and the whole (220) in percentage terms. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 13 | Math Example: Percents with Double Number Lines: Example 13TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to determine what percent one number is of another using a double number line. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 495, with 99 marked as an intermediate point. This visual representation helps students understand the relationship between the part (99) and the whole (495) in percentage terms. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 14 | Math Example: Percents with Double Number Lines: Example 14TopicRatios, Proportions, Percents DescriptionThis example illustrates how to calculate what percent one number is of another using a double number line. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to 396, with 198 marked at the midpoint. This visual representation helps students understand the relationship between the part (198) and the whole (396) in percentage terms. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 15 | Math Example: Percents with Double Number Lines: Example 15TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to determine what percent one number is of another using a double number line, particularly when dealing with more complex ratios. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to 856, with 107 marked at an eighth of the way. This visual representation helps students understand the relationship between the part (107) and the whole (856) in percentage terms. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 2 | Math Example: Percents with Double Number Lines: Example 2TopicRatios, Proportions, Percents DescriptionThis example illustrates how to calculate 25% of 180 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 180. By aligning 25% on the percentage line with its corresponding value on the numerical line, we can determine that 25% of 180 is 45. This method visually demonstrates that 25% is equivalent to one-quarter of a quantity. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 3 | Math Example: Percents with Double Number Lines: Example 3TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to find 33 1/3% of 240 using a double number line. The solution displays two parallel number lines: one ranging from 0 to 100% and the other from 0 to 240. By aligning 33 1/3% on the percentage line with its corresponding value on the numerical line, we can see that 33 1/3% of 240 is 80. This method visually represents the concept that 33 1/3% is equivalent to one-third of a quantity. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 4 | Math Example: Percents with Double Number Lines: Example 4TopicRatios, Proportions, Percents DescriptionThis example illustrates how to calculate 40% of 105 using a double number line. The solution presents two parallel number lines: one spanning from 0 to 100% and the other from 0 to 105. By aligning 40% on the percentage line with its corresponding value on the numerical line, we can determine that 40% of 105 is 42. This method visually demonstrates that 40% is equivalent to two-fifths of a quantity. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 5 | Math Example: Percents with Double Number Lines: Example 5TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to find 12.5% of 88 using a double number line. The solution shows two parallel number lines: one ranging from 0 to 100% and the other from 0 to 88. By aligning 12.5% on the percentage line with its corresponding value on the numerical line, we can see that 12.5% of 88 is 11. This method visually represents the concept that 12.5% is equivalent to one-eighth of a quantity. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 6 | Math Example: Percents with Double Number Lines: Example 6TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to solve for an unknown value using a double number line when given a percentage. The image features two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 75 is 50% of x. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 7 | Math Example: Percents with Double Number Lines: Example 7TopicRatios, Proportions, Percents DescriptionThis example illustrates how to determine an unknown value using a double number line when given a part and its corresponding percentage. The image depicts two parallel number lines: one spanning from 0 to 100% and another from 0 to an unknown value x. It visually demonstrates the process of finding x when 120 is 25% of x. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 8 | Math Example: Percents with Double Number Lines: Example 8TopicRatios, Proportions, Percents DescriptionThis example demonstrates how to find an unknown value using a double number line when given a part and its corresponding percentage, involving a fractional percentage. The image shows two parallel number lines: one ranging from 0 to 100% and another from 0 to an unknown value x. It visually illustrates the process of determining x when 125 is 33 1/3% of x. |
Ratios and Rates |
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Math Example: Percents with Double Number Lines: Example 9 | Math Example: Percents with Double Number Lines: Example 9TopicRatios, Proportions, Percents DescriptionThis example illustrates how to solve for an unknown value using a double number line when given a part and its corresponding percentage. The image shows two horizontal number lines: the top line ranges from 0 to 100%, and the bottom line ranges from 0 to an unknown number x. The 40% mark on the top line aligns with 220 on the bottom line, visually demonstrating the process of finding x when 220 is 40% of x. |
Ratios and Rates |
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MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents | MATH EXAMPLES--Teacher's Guide: Solving Equations with Percents
What Are Percents?Percents Are a Type of Fraction |
Solving Percent Equations |
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Math in the News: Issue 100--Late Night TV Ratings | Math in the News: Issue 100--Late Night TV Ratings
July 2014. In this issue of Math in the News we look at the mathematics of the Nielsen Ratings. This provides an excellent application of ratios, proportions, and percents. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 21--Why Does Washington Spend So Much? | Math in the News: Issue 21--Why Does Washington Spend So Much?
8/8/11. In this issue we look at federal spending and the growth of such spending. Looking at data provided by the government, we calculate the annual rate of growth. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis and Percents |
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Math in the News: Issue 96--The California Drought | Math in the News: Issue 96--The California Drought
July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents and Proportions |
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Math in the News: Issue 96--The California Drought | Math in the News: Issue 96--The California Drought
July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents and Proportions |
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Paper-and-Pencil Quiz: Equations with Percents (Easy) | Paper-and-Pencil Quiz: Equations with Percents (Easy)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Hard) | Paper-and-Pencil Quiz: Equations with Percents (Hard)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Paper-and-Pencil Quiz: Equations with Percents (Medium) | Paper-and-Pencil Quiz: Equations with Percents (Medium)
This is part of a collection of math quizzes on the topic of Equations with Percents. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key).Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Quiz LibraryTo see the complete collection of Quizzes, click on this link.ary">click on this link. |
Solving Percent Equations |
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Video Definition 26--Fraction Concepts--Percent | Video Definition 26--Fraction Concepts--Percent
This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video. |
Fractions and Mixed Numbers |
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Video Definition 27--Fraction Concepts--Percent Error | Video Definition 27--Fraction Concepts--Percent Error
This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video. |
Fractions and Mixed Numbers |
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Video Definition 28--Fraction Concepts--Percentage | Video Definition 28--Fraction Concepts--Percentage
This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video. |
Fractions and Mixed Numbers |
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Video Definition 29--Fraction Concepts--Percentage Decrease | Video Definition 29--Fraction Concepts--Percentage Decrease
This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video. |
Fractions and Mixed Numbers |
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Video Definition 30--Fraction Concepts--Percentage Increase | Video Definition 30--Fraction Concepts--Percentage Increase
This is part of a collection of math video definitions related to to the topic of fractions. Note: The download is an MP4 video. |
Fractions and Mixed Numbers |
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Video Transcript: Application of Ratios: Roofs and Ramps | Video Transcript: Application of Ratios: Roofs and Ramps
What Are Ratios?A ratio is the relationship between two or more quantities among a group of items. |
Applications of Ratios, Proportions, and Percents |
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Video Transcript: Percents: Applications of Percent -- Grade | Video Transcript: Percents: Applications of Percent -- Grade
This is the transcript that goes with the video segment entitled Video: Percents: Applications of Percent -- Grade. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents |
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Video Transcript: Percents: Calculating Commissions and Tips | Video Transcript: Percents: Calculating Commissions and Tips
This is the transcript that goes with the video segment entitled Video: Percents: Calculating Commissions and Tips. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents |
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Video Transcript: Percents: Calculating Tax | Video Transcript: Percents: Calculating Tax
This is the transcript that goes with the video segment entitled Video: Percents: Calculating Tax. This is part of a collection of video transcripts for the video tutorial series on Percents. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript LibraryTo see the complete collection of video transcriptsy, click on this link. Video LibraryTo see the complete collection of videos in the Video Library, click on this link. |
Percents |
