Illustrative Math Alignment: Grade 7 Unit 5

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of multiplying integers. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

Topic

Numerical Expressions

Description

Example 1 demonstrates the multiplication of two positive integers: 3 × 5. The solution shows that when multiplying two positive numbers, the result is always positive. In this case, 3 × 5 = 15.

Numerical expressions are fundamental in mathematics, representing values through various operations like addition, subtraction, multiplication, and division. This collection of examples illustrates different scenarios of integer multiplication, helping students recognize patterns and develop strategies for solving numerical problems effectively.

Topic

Numerical Expressions

Description

Example 10 illustrates the multiplication of three integers: -5, 4, and -6. The solution demonstrates that when multiplying three integers with two negative numbers and one positive number, the result is positive. In this case, (-5) × 4 × (-6) = 120.

Topic

Numerical Expressions

Description

Example 11 shows the multiplication of three integers: -7, -5, and 8. The solution demonstrates that when multiplying three integers with two negative numbers and one positive number, the result is positive. In this case, (-7) × (-5) × 8 = 280.

Topic

Numerical Expressions

Description

Example 12 demonstrates the multiplication of three negative integers: -6, -2, and -8. The solution shows that when multiplying three negative numbers, the result is negative. In this case, (-6) × (-2) × (-8) = -96.

This collection of examples covers various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations of negative integers, students can recognize patterns and develop a solid foundation for more complex mathematical operations.

Topic

Numerical Expressions

Description

Example 2 illustrates the multiplication of a positive integer by a negative integer: 4 × (-6). The solution demonstrates that when multiplying a positive number by a negative number, the result is always negative. In this case, 4 × (-6) = -24.

This collection of examples covers various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, students can recognize patterns and develop a solid foundation for more complex mathematical operations.

Topic

Numerical Expressions

Description

Example 3 demonstrates the multiplication of a negative integer by a positive integer: (-7) × 6. The solution shows that when multiplying a negative number by a positive number, the result is always negative. In this case, (-7) × 6 = -42.

This collection of examples explores various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, students can recognize patterns and develop a solid foundation for more complex mathematical operations.

Topic

Numerical Expressions

Description

Example 4 shows the multiplication of two negative integers: (-8) × (-3). The solution demonstrates that when multiplying two negative numbers, the result is always positive. In this case, (-8) × (-3) = 24.

This collection of examples covers various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, students can recognize patterns and develop a solid foundation for more complex mathematical operations.

Topic

Numerical Expressions

Description

Example 5 illustrates the multiplication of three positive integers: 2 × 4 × 5. The solution demonstrates that when multiplying multiple positive numbers, the result remains positive. In this case, 2 × 4 × 5 = 40.

This collection of examples explores various scenarios of integer multiplication, helping students understand the rules governing the multiplication of positive and negative numbers. By presenting different combinations, including multiple factors, students can recognize patterns and develop a solid foundation for more complex mathematical operations.

Topic

Numerical Expressions

Description

Example 6 demonstrates the multiplication of three integers, including a negative number: 3 × 6 × (-4). The solution shows that when multiplying multiple numbers with one negative factor, the result is negative. In this case, 3 × 6 × (-4) = -72.

Topic

Numerical Expressions

Description

Example 7 presents the multiplication of three integers with a negative number in the middle: 2 × (-5) × 6. The solution demonstrates that the position of the negative number doesn't affect the result, which is negative when there's an odd number of negative factors. In this case, 2 × (-5) × 6 = -60.

Topic

Numerical Expressions

Description

Example 8 depicts the multiplication of three integers with a negative number at the beginning: (-6) × 3 × 5. The solution shows that the position of the negative number doesn't affect the result, which is negative when there's an odd number of negative factors. In this case, (-6) × 3 × 5 = -90.

Topic

Numerical Expressions

Description

Example 9 demonstrates the multiplication of three integers: 9, -3, and -4. The solution shows that when multiplying three integers with two negative numbers and one positive number, the result is positive. In this case, 9 × (-3) × (-4) = 108.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/2 + 1/3. The solution involves finding a common denominator, which is 6, and then adding the fractions to get 5/6. To solve this, we multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3/3) + (1 * 2/2) = 3/6 + 2/6. Then, we add the numerators while keeping the common denominator: (3 + 2)/6 = 5/6.

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(8x) - 1/(3x). The solution involves finding a common denominator, which is 24x, and then subtracting the fractions to get -5/(24x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 3)/(8x * 3) - (1 * 8)/(3x * 8) = 3/(24x) - 8/(24x). Then, we subtract the numerators while keeping the common denominator: (3 - 8)/(24x) = -5/(24x).

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 2/(3x) + 4/(5x). The solution involves finding a common denominator, which is 15x, and then adding the fractions to get 22/(15x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (2 * 5)/(3x * 5) + (4 * 3)/(5x * 3) = 10/(15x) + 12/(15x). Then, we add the numerators while keeping the common denominator: (10 + 12)/(15x) = 22/(15x).

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 4/(7x) - 3/(8x). The solution involves finding a common denominator, which is 56x, and then subtracting the fractions to get 11/(56x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (4 * 8)/(7x * 8) - (3 * 7)/(8x * 7) = 32/(56x) - 21/(56x). Then, we subtract the numerators while keeping the common denominator: (32 - 21)/(56x) = 11/(56x).

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(x + 1) + 1/3. The solution involves finding a common denominator, which is 3(x + 1), and then adding the fractions to get (x + 4)/(3(x + 1)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3)/(x + 1) * 3 + (1 * (x + 1))/(3 * (x + 1)) = 3/(3(x + 1)) + (x + 1)/(3(x + 1)). Then, we add the numerators while keeping the common denominator: (3 + x + 1)/(3(x + 1)) = (x + 4)/(3(x + 1)).

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(x + 3) - 1/4. The solution involves finding a common denominator, which is 4(x + 3), and then subtracting the fractions to get (-x + 1)/(4(x + 3)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 4)/(x + 3) * 4 - (1 * (x + 3))/(4 * (x + 3)) = 4/(4(x + 3)) - (x + 3)/(4(x + 3)). Then, we subtract the numerators while keeping the common denominator: (4 - (x + 3))/(4(x + 3)) = (-x + 1)/(4(x + 3)).

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1 / (x - 5) + 1 / 6. The solution involves finding a common denominator, which is 6(x - 5), and then adding the fractions to get (x + 1) / (6(x - 5)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 6) / ((x - 5) * 6) + (1 * (x - 5)) / (6 * (x - 5)) = 6 / (6(x - 5)) + (x - 5) / (6(x - 5)). Then, we add the numerators while keeping the common denominator: (6 + x - 5) / (6(x - 5)) = (x + 1) / (6(x - 5)).

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1 / (x - 7) + 1 / 8. The solution involves finding a common denominator, which is 8(x - 7), and then adding the fractions to get (x + 1) / (8(x - 7)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 8) / ((x - 7) * 8) + (1 * (x - 7)) / (8 * (x - 7)) = 8 / (8(x - 7)) + (x - 7) / (8(x - 7)). Then, we add the numerators while keeping the common denominator: (8 + x - 7) / (8(x - 7)) = (x + 1) / (8(x - 7)).

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1 / (x - 9) - 1 / 10. The solution involves finding a common denominator, which is 10(x - 9), and then subtracting the fractions to get (-x + 19) / (10(x - 9)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 10) / ((x - 9) * 10) - (1 * (x - 9)) / (10 * (x - 9)) = 10 / (10(x - 9)) - (x - 9) / (10(x - 9)). Then, we subtract the numerators while keeping the common denominator: (10 - (x - 9)) / (10(x - 9)) = (19 - x) / (10(x - 9)) = (-x + 19) / (10(x - 9)).

Topic

Rational Expressions