Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 4 Topic Linear Functions Description This example illustrates how to find the equation of a vertical line passing through the points (5, 3) and (5, 8). The slope is undefined because both x-coordinates are the same, resulting in division by zero when using the slope formula. This indicates a vertical line, and the equation is simply x = 5.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 5 Topic Linear Functions Description This example demonstrates how to find the equation of a line passing through the points (-6, 1) and (-2, 3). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 1/2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived and simplified to y = (1/2)x + 4.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 6 Topic Linear Functions Description This image shows a graph with two points (-8, 4) and (-4, 2). The slope is calculated as (y2 - y1) / (x2 - x1), resulting in a slope of -1/2. The equation of the line is derived using point-slope form and simplified to y = -(1/2)x. The slope is calculated as -1/2, and the line equation is determined using point-slope form: y = -(1/2)x.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 7 Topic Linear Functions Description This image shows a graph with two points (-7, 5) and (-1, 5). The slope is calculated as zero since the y-values are equal. The equation of the line is horizontal, simplified to y = 5. The slope is 0, indicating a horizontal line. The equation is y = 5.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 8 Topic Linear Functions Description This image shows a graph with two points (-5, 6) and (-5, 3). The slope is undefined because the x-values are equal. This results in a vertical line at x = -5. The slope is undefined, indicating a vertical line at x = -5.	Point-Slope Form and Slope-Intercept Form
Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9	Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 9 Topic Linear Functions Description The image shows a coordinate plane with two points (-5, -4) and (-4, -1) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-1 - (-4)) / (-4 - (-5)) = 3 / 1 = 3. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 1 = 3(x + 4), which simplifies to y = 3x + 11.	Point-Slope Form and Slope-Intercept Form
Math Example--Numerical Expressions--Dividing Integers: Example 1	Math Example--Numerical Expressions--Dividing Integers: Example 1 Topic Numerical Expressions Description This example demonstrates the division of two positive integers: 12 divided by 3. The solution shows that when dividing one integer by another, the result is a rational number. In this case, with two positive integers, the quotient is positive. The calculation is presented as 12 ÷ 3 = 12 / 3 = 4.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 10	Math Example--Numerical Expressions--Dividing Integers: Example 10 Topic Numerical Expressions Description This example demonstrates the division of three integers: (-144) ÷ 12 ÷ (-2). The solution shows that dividing three integers, two negative and one positive, results in a positive quotient. The calculation is presented step-by-step: (-144) ÷ 12 ÷ (-2) = -12 / -2 = 6.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 11	Math Example--Numerical Expressions--Dividing Integers: Example 11 Topic Numerical Expressions Description This example demonstrates the division of three integers: (-150) ÷ (-5) ÷ 3. The solution shows that dividing three integers, two negative and one positive, results in a positive quotient. The calculation is presented step-by-step: (-150) ÷ (-5) ÷ 3 = 30 / 3 = 10.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 12	Math Example--Numerical Expressions--Dividing Integers: Example 12 Topic Numerical Expressions Description This example illustrates the division of three negative integers: -108 ÷ (-2) ÷ (-6). The solution demonstrates that dividing three negative integers results in a negative quotient. The calculation is presented step-by-step: (-108 / -2) / -6 = 54 / -6 = -9.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 13	Math Example--Numerical Expressions--Dividing Integers: Example 13 Topic Numerical Expressions Description This example demonstrates the division of two positive integers: 12 ÷ 5. The solution shows that dividing two positive integers results in a positive quotient, which in this case is a mixed number. The calculation is presented as: 12 / 5 = 2 2/5.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 14	Math Example--Numerical Expressions--Dividing Integers: Example 14 Topic Numerical Expressions Description This example illustrates the division of a positive integer by a negative integer: 14 ÷ (-6). The solution demonstrates that dividing a positive by a negative results in a negative quotient, which in this case is a mixed number. The calculation is presented as: 14 / -6 = -2 1/3.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 15	Math Example--Numerical Expressions--Dividing Integers: Example 15 Topic Numerical Expressions Description This example demonstrates the division of a negative integer by a positive integer: -18 ÷ 4. The solution shows that dividing a negative by a positive results in a negative quotient, which in this case is a fraction. The calculation is presented as: -18 / 4 = -9/2 = -4 1/2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 16	Math Example--Numerical Expressions--Dividing Integers: Example 16 Topic Numerical Expressions Description This example illustrates the division of two negative integers: (-9) ÷ (-6). The solution demonstrates that dividing two negative integers results in a positive fraction. The calculation is presented step-by-step: (-9) ÷ (-6) = -9 / -6 = -3 / -2 = 1 1/2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 17	Math Example--Numerical Expressions--Dividing Integers: Example 17 Topic Numerical Expressions Description This example demonstrates the division of three positive integers: 20 ÷ 2 ÷ 4. The solution shows that dividing three positive integers results in a positive mixed number quotient. The calculation is presented step-by-step: 20 ÷ 2 ÷ 4 = 20 / 2 / 4 = 10 / 4 = 2 1/2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 18	Math Example--Numerical Expressions--Dividing Integers: Example 18 Topic Numerical Expressions Description This example illustrates the division of three integers: 48 ÷ 6 ÷ (-3). The solution demonstrates that dividing two positive integers and one negative integer results in a negative mixed number quotient. The calculation is presented step-by-step: 48 ÷ 6 ÷ (-3) = 48 / 6 / (-3) = 8 / (-3) = -2 2/3.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 19	Math Example--Numerical Expressions--Dividing Integers: Example 19 Topic Numerical Expressions Description This example demonstrates the division of three integers: 24 ÷ (-6) ÷ 2. The solution shows that dividing two positive integers and one negative integer results in a negative quotient. The calculation is presented step-by-step: 24 ÷ (-6) ÷ 2 = 24 / (-6) / (2) = -4 / 2 = -2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 2	Math Example--Numerical Expressions--Dividing Integers: Example 2 Topic Numerical Expressions Description This example illustrates the division of a positive integer by a negative integer: 14 divided by -7. The solution demonstrates that when dividing one integer by another, the result is a rational number. In this case, when dividing a positive integer by a negative integer, the quotient is negative. The calculation is presented as 14 ÷ (-7) = 14 / -7 = -2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 20	Math Example--Numerical Expressions--Dividing Integers: Example 20 Topic Numerical Expressions Description This example demonstrates the division of three integers: (-72) / 2 / 5. The solution shows that dividing a negative integer by two positive integers results in a negative mixed number quotient. The calculation is presented step-by-step: (-72) / 2 / 5 = -72 / (2 * 5) = -36 / 5 = -7 1/5.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 21	Math Example--Numerical Expressions--Dividing Integers: Example 21 Topic Numerical Expressions Description This example demonstrates the division of three integers: 125 / (-25) / (-2). The solution shows that dividing a positive integer by two negative integers results in a positive mixed number quotient. The calculation is presented step-by-step: 125 / (-25) / (-2) = 125 / (25 * -2) = -5 / -2 = 2 1/2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 22	Math Example--Numerical Expressions--Dividing Integers: Example 22 Topic Numerical Expressions Description This example illustrates the division of three integers: (-144) / 12 / (-5). The solution demonstrates that dividing a negative integer by a positive integer and then by a negative integer results in a positive fraction. The calculation is presented step-by-step: (-144) / 12 / (-5) = -144 / (12 * -5) = -12 / -5 = 2 2/5.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 23	Math Example--Numerical Expressions--Dividing Integers: Example 23 Topic Numerical Expressions Description This example demonstrates the division of three integers: (-150) / (-5) / 4. The solution shows that dividing a negative integer by a negative integer and then by a positive integer results in a positive mixed number quotient. The calculation is presented step-by-step: (-150) / (-5) / 4 = -150 / -5 / 4 = 30 / 4 = 7 1/2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 24	Math Example--Numerical Expressions--Dividing Integers: Example 24 Topic Numerical Expressions Description This example illustrates the division of three negative integers: (-108) ÷ (-2) ÷ (-7). The solution demonstrates that dividing three negative integers results in a negative mixed number quotient. The calculation is presented step-by-step: (-108) ÷ (-2) ÷ (-7) = -108 / -2 ÷ (-7) = 54 / -7 = -7 5/7.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 3	Math Example--Numerical Expressions--Dividing Integers: Example 3 Topic Numerical Expressions Description This example demonstrates the division of a negative integer by a positive integer: -18 divided by 6. The solution shows that when dividing one integer by another, the result is a rational number. In this case, when dividing a negative integer by a positive integer, the quotient is negative. The calculation is presented as (-18) ÷ 6 = -18 / 6 = -3.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 4	Math Example--Numerical Expressions--Dividing Integers: Example 4 Topic Numerical Expressions Description This example illustrates the division of two negative integers: -9 divided by -3. The solution demonstrates that when dividing one integer by another, the result is a rational number. In this case, when dividing two negative integers, the quotient is positive. The calculation is presented as (-9) ÷ (-3) = -9 / -3 = 3.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 5	Math Example--Numerical Expressions--Dividing Integers: Example 5 Topic Numerical Expressions Description This example demonstrates the division of three positive integers: 20 ÷ 2 ÷ 5. The solution shows that dividing three positive integers results in a positive quotient. The calculation is presented step-by-step: 20 ÷ 2 ÷ 5 = 20 / 2 ÷ 5 = 10 / 5 = 2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 6	Math Example--Numerical Expressions--Dividing Integers: Example 6 Topic Numerical Expressions Description This example demonstrates the division of three integers: 48 ÷ 6 ÷ (-4). The solution shows that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: 48 ÷ 6 ÷ (-4) = 48 / 6 ÷ (-4) = 8 / -4 = -2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 7	Math Example--Numerical Expressions--Dividing Integers: Example 7 Topic Numerical Expressions Description This example illustrates the division of three integers: 24 ÷ (-6) ÷ 2. The solution demonstrates that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: 24 ÷ (-6) ÷ 2 = -4 / 2 = -2.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 8	Math Example--Numerical Expressions--Dividing Integers: Example 8 Topic Numerical Expressions Description This example demonstrates the division of three integers: (-72) ÷ 2 ÷ 6. The solution shows that dividing three integers, two positive and one negative, results in a negative quotient. The calculation is presented step-by-step: (-72) ÷ 2 ÷ 6 = -72 / 2 ÷ 6 = -36 / 6 = -6.	Numerical Expressions
Math Example--Numerical Expressions--Dividing Integers: Example 9	Math Example--Numerical Expressions--Dividing Integers: Example 9 Topic Numerical Expressions Description This example illustrates the division of three integers: 125 ÷ (-25) ÷ (-5). The solution demonstrates that dividing three integers, two negative and one positive, results in a positive quotient. The calculation is presented step-by-step: 125 ÷ (-25) ÷ (-5) = -5 / -5 = 1.	Numerical Expressions
Math Example--Percents--Equations with Percents: Example 1	Math Example--Percents--Equations with Percents: Example 1 Topic Solving Equations Description This math example focuses on solving percent equations, specifically asking "What is 5% of 8?" The solution involves converting 5% to its decimal form, 0.05, and then multiplying it by 8 to get the result of 0.4. This straightforward approach demonstrates how to tackle basic percent calculations efficiently.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 10	Math Example--Percents--Equations with Percents: Example 10 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "What is 170% of 9.5?" The solution involves converting 170% to its decimal equivalent, 1.7, and then multiplying it by 9.5 to obtain the result of 16.15. This example combines a percentage greater than 100% with a decimal base number, further illustrating the versatility of the percent-to-decimal conversion method in complex scenarios.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 11	Math Example--Percents--Equations with Percents: Example 11 Topic Solving Equations Description This math example focuses on solving percent equations, specifically asking "What is 225.5% of 78?" The solution involves converting 225.5% to its decimal form, 2.255, and then multiplying it by 78 to arrive at the answer of 175.89. This example introduces a decimal percentage greater than 200% and a larger whole number as the base value, demonstrating the scalability and flexibility of the percent-to-decimal conversion method in complex scenarios.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 12	Math Example--Percents--Equations with Percents: Example 12 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "What is 400% of 92.8?" The solution involves converting 400% to its decimal equivalent, 4.0, and then multiplying it by 92.8 to obtain the result of 371.2. This example showcases how to handle percentages greater than 100% and their application to decimal numbers, illustrating the versatility of the percent-to-decimal conversion method in complex scenarios.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 13	Math Example--Percents--Equations with Percents: Example 13 Topic Solving Equations Description This math example focuses on solving percent equations by asking "5 is what percent of 9?" The solution involves setting up the equation 9 * (x / 100) = 5, then solving for x to get x = 5 * (100 / 9), which is approximately 55.56%. This example introduces a new type of percent problem where students must find the percentage given two known values.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 14	Math Example--Percents--Equations with Percents: Example 14 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "6 is what percent of 2.3?" The solution involves setting up the equation 2.3 * (x / 100) = 6, then solving for x to get x = 6 * (100 / 2.3), which is approximately 260.87%. This example introduces a scenario where the resulting percentage is greater than 100% and involves a decimal base number.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 15	Math Example--Percents--Equations with Percents: Example 15 Topic Solving Equations Description This math example focuses on solving percent equations by asking "9 is what percent of 38?" The solution involves setting up the equation 38 * (x / 100) = 9, then solving for x to get x = 9 * (100 / 38), which is approximately 23.68%. This example demonstrates how to calculate a percentage when the first number is smaller than the second, resulting in a percentage less than 100%.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 16	Math Example--Percents--Equations with Percents: Example 16 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "2 is what percent of 55.5?" The solution involves setting up the equation 55.5 * (x / 100) = 2, then solving for x to get x = 2 * (100 / 55.5), which is approximately 3.6036%. This example introduces a scenario where the resulting percentage is a small fraction, less than 5%, and involves a decimal base number.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 17	Math Example--Percents--Equations with Percents: Example 17 Topic Solving Equations Description This math example focuses on solving percent equations by asking "8 is what percent of 120?" The solution involves setting up the equation 120 * (x / 100) = 8, then solving for x to get x = 8 * (100 / 120), which is approximately 6.67%. This example demonstrates how to calculate a percentage when dealing with larger whole numbers, resulting in a percentage less than 10%.	Solving Percent Equations
Math Example--Percents--Equations with Percents: Example 18	Math Example--Percents--Equations with Percents: Example 18 Topic Solving Equations Description This math example demonstrates solving percent equations by asking "3.5 is what percent of 350?" The solution involves setting up the equation 350 * (x / 100) = 3.5, then solving for x to get x = 3.5 * (100 / 350), which equals 1%. This example introduces a scenario where the resulting percentage is a whole number (1%) and involves a decimal number as the first value.	Solving Percent Equations

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative Numbers

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