Illustrative Math Alignment: Grade 7 Unit 7

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Watch the following video on Order of Operations. (The transcript is included.)

Video Transcript

A numerical expression includes numbers and operation symbols, addition, subtraction, multiplication, and division.

Because addition is commutative, adding from left to right, or right to left, gives you the same result.

The expressions 2 + 3 and 3 + 2 give the same result. But this isn't the case with all operations.

Topic

Integers

Description

This example demonstrates the operation: Subtract: 14 - 5. The solution states to subtract them like whole numbers. 14 - 5 = 9.

Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively.

Topic

Integers

Description

This example demonstrates the operation: Subtract: 8 - 10. The solution 8 = 10 = -2.

Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively.

Topic

Integers

Description

This example demonstrates the operation: Subtract: 16 - 16. The solution shows that 16 - 16 = 0.

Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively.

Topic

Integers

Description

This example demonstrates the operation: Subtract: 8 - (-3). The solution shows that it is rewritten as addition: 8 + 3 = 11.

Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively.

Topic

Integers

Description

This example demonstrates the operation: Subtract: -3 - 5. Solution: Subtracting a positive integer from a negative integer results in a negative difference. -3 - 5 = -8.

Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively.

Topic

Integers

Description

This example demonstrates the operation: Subtract: -8 - (-3). Solution involves rewriting the subtraction as an addition statement. -8 + 3 = -5.

Integer operations are fundamental in mathematics as they provide essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such a variety helps learners grasp the concepts effectively.

Two Integers: Example 12

Topic

Integers

Description

This example demonstrates the operation of subtracting two negative integers: -4 - (-6). The solution shows that when subtracting a negative integer, it can be rewritten as an addition statement: -4 + 6 = 2.

Integer operations are crucial in mathematics as they provide foundational skills for more advanced topics. This collection explores various examples of integer subtraction, highlighting how rules apply across different scenarios. Such variety helps learners grasp concepts effectively.

Topic

Integers

Description

This example demonstrates subtracting a negative integer from another negative integer: -7 - (-7). The solution involves rewriting the subtraction as an addition statement, resulting in -7 + 7 = 0.

Integer operations are fundamental in mathematics, providing essential skills for tackling more advanced topics. This collection explores various examples of integer subtraction, showcasing how the rules apply across diverse scenarios. Such variety helps learners grasp concepts effectively.

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

Topic

Rational Expressions

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/4 - 1/5. The solution involves finding a common denominator, which is 20, and then subtracting the fractions to get 1/20. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 5/5) - (1 * 4/4) = 5/20 - 4/20. Then, we subtract the numerators while keeping the common denominator: (5 - 4)/20 = 1/20.

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Topic

Rational Expressions

Description

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

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/x - 1/2. The solution involves finding a common denominator, which is 2x, and then subtracting the fractions to get (x - 2)/2x. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 2/2) - (1 * x/x) = 2/(2x) - x/(2x). Then, we subtract the numerators while keeping the common denominator: (2 - x)/(2x) = (x - 2)/(2x).

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(2x) + 1/5. The solution involves finding a common denominator, which is 10x, and then adding the fractions to get (2x + 5)/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2x)/(5 * 2x) = 5/(10x) + 2x/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2x)/(10x).

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(4x) - 1/7. The solution involves finding a common denominator, which is 28x, and then subtracting the fractions to get (7 - 4x)/(28x), which simplifies to (4x - 7)/(28x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 7)/(4x * 7) - (1 * 4x)/(7 * 4x) = 7/(28x) - 4x/(28x). Then, we subtract the numerators while keeping the common denominator: (7 - 4x)/(28x).

Topic

Rational Expressions

Description

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

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/(9x) - 1/3. The solution involves finding a common denominator, which is 9x, and then subtracting the fractions to get (1 - 3x)/(9x), which simplifies to (3x - 1)/(9x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * x)/(9x * x) - (3 * x)/(3 * x) = 1/(9x) - 3x/(9x). Then, we subtract the numerators while keeping the common denominator: (1 - 3x)/(9x).

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(2x) + 1/(5x). The solution involves finding a common denominator, which is 10x, and then adding the fractions to get 7/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2)/(5x * 2) = 5/(10x) + 2/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2)/(10x) = 7/(10x).

Topic

Numerical Expressions

Description

This example demonstrates how to convert a verbal addition statement into a numerical expression. The phrase "One plus fourteen" is highlighted and translated into the expression 1 + 14. This conversion helps students understand how to represent spoken mathematical language in written form.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the phrase "Seven more than eighteen" into a numerical expression. The image shows how this verbal statement translates to the expression 18 + 7, emphasizing that "more than" indicates addition with a specific order of numbers.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Eleven plus negative twenty" into a numerical expression. The image demonstrates how this verbal statement translates directly to the expression 11 + (-20), introducing the concept of adding negative numbers.

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the phrase "Nineteen increased by negative four" into a numerical expression. The image shows how this verbal statement translates to the expression 19 + (-4), further exploring the concept of adding negative numbers.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Negative five added to thirteen" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 13 + (-5), emphasizing the order of numbers when using the phrase "added to."

Topic

Numerical Expressions

Description

This example demonstrates the conversion of the phrase "Negative three in addition to four" into a numerical expression. The image shows how this verbal statement translates to the expression 4 + (-3), highlighting the importance of word order in determining the structure of the expression.

Topic

Numerical Expressions

Description

This example illustrates the conversion of the phrase "Negative twenty more than nine" into a numerical expression. The image demonstrates how this verbal statement translates to the expression 9 + (-20), emphasizing the interpretation of "more than" when dealing with negative numbers.