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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 18: Subtraction in Equivalent Expressions

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Numerical Expressions--Order of Operations--Example 03 Math Example--Numerical Expressions--Order of Operations--Example 03 Math Example--Numerical Expressions--Order of Operations--Example 03

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.

Subtraction isn't commutative.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 04 Math Example--Numerical Expressions--Order of Operations--Example 04 Math Example--Numerical Expressions--Order of Operations--Example 04

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 05 Math Example--Numerical Expressions--Order of Operations--Example 05 Math Example--Numerical Expressions--Order of Operations--Example 05

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 06 Math Example--Numerical Expressions--Order of Operations--Example 06 Math Example--Numerical Expressions--Order of Operations--Example 06

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 07 Math Example--Numerical Expressions--Order of Operations--Example 07 Math Example--Numerical Expressions--Order of Operations--Example 07

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 08 Math Example--Numerical Expressions--Order of Operations--Example 08 Math Example--Numerical Expressions--Order of Operations--Example 08

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 09 Math Example--Numerical Expressions--Order of Operations--Example 09 Math Example--Numerical Expressions--Order of Operations--Example 09

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 10 Math Example--Numerical Expressions--Order of Operations--Example 10 Math Example--Numerical Expressions--Order of Operations--Example 10

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 11 Math Example--Numerical Expressions--Order of Operations--Example 11 Math Example--Numerical Expressions--Order of Operations--Example 11

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 12 Math Example--Numerical Expressions--Order of Operations--Example 12 Math Example--Numerical Expressions--Order of Operations--Example 12

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 13 Math Example--Numerical Expressions--Order of Operations--Example 13 Math Example--Numerical Expressions--Order of Operations--Example 13

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.

Numerical Expressions
Math Example--Numerical Expressions--Order of Operations--Example 14 Math Example--Numerical Expressions--Order of Operations--Example 14 Math Example--Numerical Expressions--Order of Operations--Example 14

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 06 Math Example--Numerical Expressions--Subtracting Two Integers: Example 06 Math Example--Numerical Expressions--Subtracting Two Integers: Example 06

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 07 Math Example--Numerical Expressions--Subtracting Two Integers: Example 07 Math Example--Numerical Expressions--Subtracting Two Integers: Example 07

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 08 Math Example--Numerical Expressions--Subtracting Two Integers: Example 08 Math Example--Numerical Expressions--Subtracting Two Integers: Example 08

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 09 Math Example--Numerical Expressions--Subtracting Two Integers: Example 09 Math Example--Numerical Expressions--Subtracting Two Integers: Example 09

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 10 Math Example--Numerical Expressions--Subtracting Two Integers: Example 10 Math Example--Numerical Expressions--Subtracting Two Integers: Example 10

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 11 Math Example--Numerical Expressions--Subtracting Two Integers: Example 11 Math Example--Numerical Expressions--Subtracting Two Integers: Example 11

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 12 Math Example--Numerical Expressions--Subtracting Two Integers: Example 12

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.

Numerical Expressions
Math Example--Numerical Expressions--Subtracting Two Integers: Example 13 Math Example--Numerical Expressions--Subtracting Two Integers: Example 13 Math Example--Numerical Expressions--Subtracting Two Integers: Example 13

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.

Numerical Expressions
Math Example--Rational Concepts--Rational Expressions: Example 1 Math Example--Rational Concepts--Rational Expressions: Example 1 Math Example--Rational Concepts--Rational Expressions: Example 1

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.

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 10 Math Example--Rational Concepts--Rational Expressions: Example 10 Math Example--Rational Concepts--Rational Expressions: Example 10

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 11 Math Example--Rational Concepts--Rational Expressions: Example 11 Math Example--Rational Concepts--Rational Expressions: Example 11

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 12 Math Example--Rational Concepts--Rational Expressions: Example 12 Math Example--Rational Concepts--Rational Expressions: Example 12

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 13 Math Example--Rational Concepts--Rational Expressions: Example 13 Math Example--Rational Concepts--Rational Expressions: Example 13

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)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 14 Math Example--Rational Concepts--Rational Expressions: Example 14 Math Example--Rational Concepts--Rational Expressions: Example 14

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)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 15 Math Example--Rational Concepts--Rational Expressions: Example 15 Math Example--Rational Concepts--Rational Expressions: Example 15

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)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 16 Math Example--Rational Concepts--Rational Expressions: Example 16 Math Example--Rational Concepts--Rational Expressions: Example 16

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)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 17 Math Example--Rational Concepts--Rational Expressions: Example 17 Math Example--Rational Concepts--Rational Expressions: Example 17

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)).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 18 Math Example--Rational Concepts--Rational Expressions: Example 18 Math Example--Rational Concepts--Rational Expressions: Example 18

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 19 Math Example--Rational Concepts--Rational Expressions: Example 19 Math Example--Rational Concepts--Rational Expressions: Example 19

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 2 Math Example--Rational Concepts--Rational Expressions: Example 2 Math Example--Rational Concepts--Rational Expressions: Example 2

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.

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 20 Math Example--Rational Concepts--Rational Expressions: Example 20 Math Example--Rational Concepts--Rational Expressions: Example 20

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 21 Math Example--Rational Concepts--Rational Expressions: Example 21 Math Example--Rational Concepts--Rational Expressions: Example 21

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 22 Math Example--Rational Concepts--Rational Expressions: Example 22 Math Example--Rational Concepts--Rational Expressions: Example 22

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 23 Math Example--Rational Concepts--Rational Expressions: Example 23 Math Example--Rational Concepts--Rational Expressions: Example 23

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 24 Math Example--Rational Concepts--Rational Expressions: Example 24 Math Example--Rational Concepts--Rational Expressions: Example 24

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 25 Math Example--Rational Concepts--Rational Expressions: Example 25 Math Example--Rational Concepts--Rational Expressions: Example 25

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 26 Math Example--Rational Concepts--Rational Expressions: Example 26 Math Example--Rational Concepts--Rational Expressions: Example 26

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 27 Math Example--Rational Concepts--Rational Expressions: Example 27 Math Example--Rational Concepts--Rational Expressions: Example 27

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 28 Math Example--Rational Concepts--Rational Expressions: Example 28 Math Example--Rational Concepts--Rational Expressions: Example 28

Topic

Rational Expressions

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 3 Math Example--Rational Concepts--Rational Expressions: Example 3 Math Example--Rational Concepts--Rational Expressions: Example 3

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 4 Math Example--Rational Concepts--Rational Expressions: Example 4 Math Example--Rational Concepts--Rational Expressions: Example 4

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 5 Math Example--Rational Concepts--Rational Expressions: Example 5 Math Example--Rational Concepts--Rational Expressions: Example 5

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 6 Math Example--Rational Concepts--Rational Expressions: Example 6 Math Example--Rational Concepts--Rational Expressions: Example 6

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 7 Math Example--Rational Concepts--Rational Expressions: Example 7 Math Example--Rational Concepts--Rational Expressions: Example 7

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 8 Math Example--Rational Concepts--Rational Expressions: Example 8 Math Example--Rational Concepts--Rational Expressions: Example 8

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).

Rational Expressions
Math Example--Rational Concepts--Rational Expressions: Example 9 Math Example--Rational Concepts--Rational Expressions: Example 9 Math Example--Rational Concepts--Rational Expressions: Example 9

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).

Rational Expressions
Math Example: Language of Math--Numerical Expressions--Addition--Example 1 Math Example: Language of Math--Numerical Expressions--Addition--Example 1 Math Example: Language of Math--Numerical Expressions--Addition--Example 1

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.

Numerical Expressions
Math Example: Language of Math--Numerical Expressions--Addition--Example 10 Math Example: Language of Math--Numerical Expressions--Addition--Example 10 Math Example: Language of Math--Numerical Expressions--Addition--Example 10

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.

Numerical Expressions