Algebraic Fractions : Introduction and Expansion of Algebraic Expression

Subject : Mathematics

Class : JSS 2

Term : Second Term

Week : Week

Topic :

Algebraic Fractions : Introduction and Expansion of Algebraic Expression

Previous Lesson :

LINEAR INEQUALITIES IN ONE VARIABLE, GRAPHICAL PRESENTATIONS OF SOLUTION OF LINEAR INEQUALITIES.

 

Objective: Students will be able to understand and solve algebraic fractions and expand algebraic expressions using the distributive property of multiplication.

Materials:

• Whiteboard and markers
• Workbook with algebraic fraction problems and expansion problems
• Calculator (optional)

Online Reference 

• Khan Academy – Algebra Basics: This website offers free online lessons and practice exercises for algebraic expressions, equations, and functions. https://www.khanacademy.org/math/algebra-basics
• Math Is Fun – Algebra: This website provides interactive tutorials, games, and worksheets on algebraic expressions, equations, and inequalities. https://www.mathsisfun.com/algebra/
• Mathway – Algebra Solver: This website offers step-by-step solutions to algebraic problems, including algebraic fractions and expanding algebraic expressions. https://www.mathway.com/Algebra
• IXL – Algebra: This website offers interactive quizzes and practice exercises on algebraic expressions, equations, and inequalities for students in grades K-12. https://www.ixl.com/math/algebra-1
• Mathplanet – Algebra: This website offers free online courses on algebraic expressions, equations, and functions, including algebraic fractions and expanding algebraic expressions. https://www.mathplanet.com/education/algebra-1

 

 

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Content ;

Algebraic Fractions : Introduction and Expansion of Algebraic Expression

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Hello! Let’s talk about algebraic fractions, which are a type of math problem where we combine variables (letters) and numbers using fractions.

First, let’s look at a simple algebraic expression: 2x + 3. This expression has both a number (3) and a variable (x). We can think of this expression as a “recipe” for finding the value of 2x + 3 when we know the value of x.

Now let’s add some fractions to the mix. An algebraic fraction is simply a fraction where the numerator and/or denominator contains one or more variables. For example, (2x + 3) / 5 is an algebraic fraction because the numerator (2x + 3) contains the variable x.

We can also combine algebraic fractions using addition, subtraction, multiplication, and division. For example:

(2x + 3) / 5 + (x + 1) / 2 = (4x + 13) / 10

Here, we added two algebraic fractions by finding a common denominator (10) and then adding the numerators. We can simplify the resulting fraction by dividing both the numerator and denominator by their greatest common factor (which is 2 in this case) to get the final answer of (2x + 13/5).

We can also expand algebraic expressions by multiplying them out. For example:

(x + 3)(x – 2) = x^2 + x – 6

Here, we used the distributive property (remember that from multiplication?) to multiply each term in the first set of parentheses by each term in the second set of parentheses. We can simplify the resulting expression by combining like terms (in this case, x and -2x cancel each other out) to get the final answer of x^2 + x – 6.

So algebraic fractions and expanding algebraic expressions are just different ways of working with variables and fractions. With practice, you’ll get the hang of it!

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Expansion of Algebraic Expression

Expanding algebraic expressions involves multiplying out the terms of an expression that is written using parentheses or brackets. The distributive property of multiplication is used to do this.

Let’s consider an example:

(x + 2)(x – 3)

To expand this expression, we need to multiply the first term (x) in the first set of parentheses by each term (x and -3) in the second set of parentheses, and then multiply the second term (2) in the first set of parentheses by each term (x and -3) in the second set of parentheses.

Using the distributive property, we get:

x(x) + x(-3) + 2(x) + 2(-3)

Simplifying this expression by multiplying and adding the terms, we get:

x^2 – x + 2x – 6

Combining like terms, we get:

x^2 + x – 6

So, (x + 2)(x – 3) expands to x^2 + x – 6.

Let’s try another example:

(2x + 3)(x – 4)

Using the distributive property, we get:

2x(x) + 2x(-4) + 3(x) + 3(-4)

Simplifying this expression, we get:

2x^2 – 8x + 3x – 12

Combining like terms, we get:

2x^2 – 5x – 12

So, (2x + 3)(x – 4) expands to 2x^2 – 5x – 12.

 

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Evaluation

1. What is an algebraic fraction? a) A fraction with a variable in the numerator or denominator b) A fraction with a number in the numerator or denominator c) A fraction with a variable and a number in the numerator or denominator d) A fraction with a letter in the numerator or denominator
2. Which of the following expressions is an algebraic fraction? a) 2x + 3 b) 3/4 c) x + 1/2 d) (2x + 3) / 5
3. What is the first step in expanding an algebraic expression? a) Divide the expression by the common denominator b) Add the numerators of the fractions c) Multiply the terms inside the parentheses d) Subtract the numerators of the fractions
4. What is the expansion of (x + 4)(x – 3)? a) x^2 + x + 12 b) x^2 – 7x – 12 c) x^2 – x – 12 d) x^2 + x – 12
5. What is the expansion of (2x – 1)(3x + 2)? a) 6x^2 + 5x – 2 b) 6x^2 – x – 2 c) 6x^2 + x – 2 d) 6x^2 + 5x + 2
6. What is the sum of (2x + 3)/5 and (x + 1)/2? a) (3x + 13)/5 b) (3x + 13)/10 c) (3x + 8)/5 d) (3x + 8)/10
7. What is the product of (x + 2)(x – 2)? a) x^2 – 4 b) x^2 + 4 c) x^2 – 2 d) x^2 + 2
8. What is the product of (3x – 1)(2x + 5)? a) 6x^2 + 13x – 5 b) 6x^2 + 7x – 5 c) 6x^2 + 13x + 5 d) 6x^2 + 7x + 5
9. What is the difference of (3x + 2)/(x – 1) and (5x + 1)/(x + 1)? a) (8x + 1)/(x^2 – 1) b) (2x + 1)/(x^2 – 1) c) (8x – 1)/(x^2 – 1) d) (2x – 1)/(x^2 – 1)
10. What is the simplified form of (4x^2 + 8x)/(2x)? a) 2x + 4 b) 2x^2 + 4x c) 2x + 8 d) 2x^2 + 8x [the_ad id=”40092″]
11. Which expression is equal to (x + 2)(x – 3)? a) x^2 – x – 6 b) x^2 – x + 6 c) x^2 + x – 6 d) x^2 + x + 6
12. What is the expansion of (2x + 3)(x – 4)? a) 2x^2 – 5x – 12 b) 2x^2 + x – 12 c) 2x^2 – 7x – 12 d) 2x^2 – 7x + 12
13. What is the expansion of (3x – 2)(4x + 1)? a) 12x^2 + 5x – 2 b) 12x^2 – 5x – 2 c) 12x^2 + 5x + 2 d) 12x^2 – 5x + 2
14. What is the expansion of (x + 1)(x + 1)? a) x^2 – 1 b) x^2 + 2x + 1 c) x^2 – 2x + 1 d) x^2 + 1
15. What is the expansion of (2x – 1)(2x + 1)? a) 4x^2 – 1 b) 4x^2 + 1 c) 4x^2 – 2x – 1 d) 4x^2 + 2x – 1
16. What is the expansion of (3x + 2)(2x – 1)? a) 6x^2 + x – 2 b) 6x^2 – x – 2 c) 6x^2 + x + 2 d) 6x^2 – x + 2
17. What is the expansion of (x – 3)(x – 3)? a) x^2 – 9 b) x^2 – 6x + 9 c) x^2 + 6x + 9 d) x^2 + 9
18. What is the expansion of (4x – 1)(4x + 1)? a) 16x^2 – 1 b) 16x^2 + 1 c) 16x^2 – 2x – 1 d) 16x^2 + 2x – 1
19. What is the expansion of (2x + 3)(3x – 4)? a) 6x^2 – 5x – 12 b) 6x^2 + 5x – 12 c) 6x^2 – 5x + 12 d) 6x^2 + 5x + 12
20. What is the expansion of (x – 2)(x + 2)? a) x^2 – 4 b) x^2 + 4 c) x^2 – 2x – 4 d) x^2 + 2x – 4

Lesson Presentation

Revision of previous lesson

• LINEAR INEQUALITIES IN ONE VARIABLE, GRAPHICAL PRESENTATIONS OF SOLUTION OF LINEAR INEQUALITIES.

Introduction (5 minutes):

• Begin by asking students if they know what algebraic expressions are.
• Review the basic concept of algebraic expressions by showing examples such as 2x + 3, x – 4, etc.
• Introduce the topic of algebraic fractions by asking students if they know what a fraction is and showing examples such as 1/2, 3/4, etc.
• Define an algebraic fraction as a fraction where the numerator and/or denominator contains one or more variables.

Instruction (25 minutes):

• Demonstrate how to add and subtract algebraic fractions by finding a common denominator.
• Show examples of algebraic fractions such as (2x + 3)/5 + (x + 1)/2 and (3x + 2)/(x – 1) – (5x + 1)/(x + 1) and walk through the steps of finding the common denominator and simplifying the fractions.
• Explain how to expand algebraic expressions by multiplying out the terms of an expression that is written using parentheses or brackets.
• Show examples of expanding algebraic expressions such as (x + 2)(x – 3) and (2x + 3)(x – 4) and demonstrate the steps of using the distributive property to expand the expressions.
• Provide Workbook with practice problems for students to work on independently or in pairs.

Evaluation

1. What is an algebraic expression?
2. What is an algebraic fraction?
3. What is the numerator of an algebraic fraction?
4. What is the denominator of an algebraic fraction?
5. How do you add and subtract algebraic fractions?
6. What is a common denominator?
7. What is the first step in expanding an algebraic expression?
8. What is the distributive property of multiplication?
9. What is the expansion of (x + 2)(x – 3)?
10. What is the expansion of (2x + 3)(x – 4)?
11. What is the expansion of (3x – 2)(4x + 1)?
12. What is the expansion of (x + 1)(x + 1)?
13. What is the expansion of (2x – 1)(2x + 1)?
14. What is the expansion of (3x + 2)(2x – 1)?
15. What is the expansion of (x – 3)(x – 3)?
16. What is the expansion of (4x – 1)(4x + 1)?
17. How do you simplify algebraic fractions?
18. What is the sum of (2x + 3)/5 and (x + 1)/2?
19. What is the difference of (3x + 2)/(x – 1) and (5x + 1)/(x + 1)?
20. What is the simplified form of (4x^2 + 8x)/(2x)?

Assessment (10 minutes):

• Ask students to share their answers to the practice problems and work through them as a class, checking for understanding.
• Provide feedback and corrections as needed.

Conclusion (5 minutes):

• Summarize the key concepts covered in the lesson.
• Emphasize the importance of understanding algebraic fractions and expanding algebraic expressions in solving more complex math problems.
• Encourage students to continue practicing and exploring the topic on their own.

Extensions:

• Provide more challenging algebraic fraction and expansion problems for advanced students.
• Discuss real-world applications of algebraic fractions and algebraic expressions, such as in engineering, finance, or science.

Weekly Assessment /Test

1. An _______________ is a mathematical expression that contains one or more variables.
2. An _______________ fraction is a fraction where the numerator and/or denominator contains one or more variables.
3. To add or subtract algebraic fractions, you must first find a _______________ denominator.
4. The distributive property of multiplication states that a(b + c) = _______________.
5. To expand an algebraic expression, you must multiply out the terms using the _______________ property of multiplication.
6. The expansion of (x + 1)(x – 1) is _______________.
7. The expansion of (2x + 3)(x – 4) is _______________.
8. The expansion of (3x – 2)(4x + 1) is _______________.
9. The expansion of (x + 1)(x + 1) is _______________.
10. The expansion of (2x – 1)(2x + 1) is _______________.
11. The expansion of (3x + 2)(2x – 1) is _______________.
12. The expansion of (x – 3)(x – 3) is _______________.
13. The expansion of (4x – 1)(4x + 1) is _______________.
14. To simplify an algebraic fraction, you must find a common _______________ of the numerator and denominator.
15. The sum of (2x + 3)/5 and (x + 1)/2 is _______________.
16. The difference of (3x + 2)/(x – 1) and (5x + 1)/(x + 1) is _______________.
17. The simplified form of (4x^2 + 8x)/(2x) is _______________.
18. The first step in expanding an algebraic expression is to use the _______________ property of multiplication.
19. The expansion of (x + 2)(x – 3) is _______________.
20. The expansion of (2x + 3)(x – 4) is _______________. [the_ad id=”40092″]