Illustrative Math Alignment: Grade 7 Unit 7

This is part of a collection of math examples that focus on linear function concepts.

This is part of a collection of math examples that focus on linear function concepts.

This is part of a collection of math examples that focus on linear function concepts.

This is part of a collection of math examples that focus on linear function concepts.

This is part of a collection of math examples that focus on linear function concepts.

This is part of a collection of math examples that focus on linear function concepts.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%.

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.

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%.

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.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "12 is what percent of 8?" The solution involves setting up the equation 8 * (x / 100) = 12, then solving for x to get x = 12 * (100 / 8), which equals 150%. This example demonstrates how to calculate a percentage when the first number is larger than the second, resulting in a percentage greater than 100%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "What is 7% of 9.5?" The solution involves converting 7% to its decimal equivalent, 0.07, and then multiplying it by 9.5 to obtain the result of 0.665. This example builds upon the previous one by introducing a decimal number as the base value.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "32 is what percent of 1.5?" The solution involves setting up the equation 1.5 * (x / 100) = 32, then solving for x to get x = 32 * (100 / 1.5), which equals 2133.3%. This example introduces a scenario where the resulting percentage is significantly larger than 100% and involves a decimal base number less than 1.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "48 is what percent of 55?" The solution involves setting up the equation 55 * (x / 100) = 48, then solving for x to get x = 48 * (100 / 55), which equals 87.27%. This example demonstrates how to calculate a percentage when the two numbers are relatively close in value, resulting in a percentage close to but less than 100%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "52.2 is what percent of 98.5?" The solution involves setting up the equation 98.5 * (x / 100) = 52.2, then solving for x to get x = 52.2 * (100 / 98.5), which is approximately 52.99%. This example introduces a scenario where both the numerator and denominator are decimal numbers, resulting in a percentage that is also close to the original numerator.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "68 is what percent of 320?" The solution involves setting up the equation 320 * (x / 100) = 68, then solving for x to get x = 68 * (100 / 320), which equals 21.25%. This example demonstrates how to calculate a percentage when dealing with whole numbers, resulting in a percentage that's less than 25%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "75.5 is what percent of 555.25?" The solution involves setting up the equation 555.25 * (x / 100) = 75.5, then solving for x to get x = 75.5 * (100 / 555.25), which is approximately 13.59%. This example introduces a scenario where both the numerator and denominator are decimal numbers, resulting in a percentage that's less than 15%.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "125 is what percent of 2?" The solution involves setting up the equation 2 * (x / 100) = 125, then solving for x to get x = 125 * (100 / 2), which equals 6250%. This example demonstrates how to calculate a percentage when the first number is significantly larger than the second, resulting in a percentage well over 100%.

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "300 is what percent of 3.5?" The solution involves setting up the equation 3.5 * (x / 100) = 300, then solving for x to get x = 300 * (100 / 3.5), which equals 8571.43%. This example introduces a scenario where the resulting percentage is extremely large, over 8000%, due to the first number being significantly larger than the small decimal base number.

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "278 is what percent of 99?" The solution involves setting up the equation 99 * (x / 100) = 278, then solving for x to get x = 278 * (100 / 99), which equals 280.80%. This example demonstrates how to calculate a percentage when the first number is significantly larger than the second, resulting in a percentage greater than 200%.