Illustrative Math Alignment: Grade 6 Unit 3

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, and Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

Topic

Ratios, Proportions, Percents

Description

This 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.

What Are Percents?

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.

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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.

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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.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

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.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

This is part of a collection of math quizzes on the topic of Equations with Percents.

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This is part of a collection of math quizzes on the topic of Equations with Percents.

Related Resources

Quiz Library

ary">click on this link.

This is part of a collection of math quizzes on the topic of Equations with Percents.

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Quiz Library

ary">click on this link.

Topic

Fractions

Description

The term Percent represents a fraction with a denominator of 100, showing a proportion out of 100. Examples include 1% = 1/100, 5% = 5/100, and 25% = 25/100. Percentages are a real-world application of fractions and decimals, often used in data analysis, finance, and everyday calculations.

Topic

Fractions

Description

The term Percent Error describes the difference between an estimated value and the actual value, expressed as a percentage of the actual value. The example provided shows an estimated value of 100 versus an actual value of 107, resulting in a percent error of approximately 6.54%. This concept links fractions, percentages, and error analysis, which are important in measurement and data accuracy.

Topic

Fractions

Description

The term Percentage refers to converting fractions and decimals into their equivalent percentages. Examples include 1/2 = 50%, 0.4 = 40%, and 1/3 ≈ 33.3%. This concept connects fractions, decimals, and percentages, emphasizing their equivalence and usage in various contexts.

Topic

Fractions

Description

The term Percentage Decrease refers to the reduction in value expressed as a percentage of the original value. The example shows a decrease from 75 to 50, calculated as (75 - 50) / 75 * 100%, which equals 33.3%. This term applies percentages to real-world contexts like discounts and data analysis, building on fraction concepts.

Topic

Fractions

Description

The term Percentage Increase refers to the increase in value expressed as a percentage of the original value. The example shows an increase from 25 to 40, calculated as (40 - 25) / 25 * 100%, which equals 60%. This term reinforces the application of percentages and fractions in scenarios like profit and growth analysis.

What Are Ratios?

A ratio is the relationship between two or more quantities among a group of items.

This is the transcript that goes with the video segment entitled Video: Percents: Applications of Percent -- Grade.

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This is the transcript that goes with the video segment entitled Video: Percents: Calculating Commissions and Tips.

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This is the transcript that goes with the video segment entitled Video: Percents: Calculating Tax.

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