Algebra Simplification Techniques

Questions and Answers

What is the result of combining like terms in the expression 2x + 3x?

x^2

4x^2

2x^2

5x (correct)

What is the first step in removing parentheses in the expression 2(3x + 2)?

Distribute the number outside the parentheses to each term inside (correct)

Divide by the coefficient of x

Combine like terms

Subtract the terms inside the parentheses

What is the result of simplifying the expression -2x + 3 = 5?

x = 2

x = 1

x = 3

x = -1 (correct)

What is the result of cancelling out common factors in the fraction 12/16?

3/4 Signup and view all the answers

What is the result of simplifying the mixed number 2 1/3?

7/3 Signup and view all the answers

What is the result of combining like indices in the expression 2^3 × 2^4?

2^7 Signup and view all the answers

What is the result of simplifying the surd √(16)?

4 Signup and view all the answers

What is the purpose of rationalizing denominators?

To remove surds from the denominator Signup and view all the answers

What is the main characteristic of a simple sentence in the present tense?

It has a subject and a verb in its base form. Signup and view all the answers

What is the function of a conjunction in a compound sentence?

To join two or more independent clauses. Signup and view all the answers

What is the difference between an independent clause and a dependent clause?

An independent clause can stand alone, while a dependent clause cannot. Signup and view all the answers

What is an example of a sentence fragment in the present tense?

Writing. Signup and view all the answers

How do you correct a sentence fragment?

By adding the missing element(s) to form a complete sentence. Signup and view all the answers

What is the purpose of a subordinating conjunction in a complex sentence?

To introduce a dependent clause. Signup and view all the answers

What is the main difference between a compound sentence and a complex sentence?

A compound sentence joins two independent clauses, while a complex sentence has an independent clause and a dependent clause. Signup and view all the answers

Which of the following is an example of a complex sentence?

I write because I want to express myself. Signup and view all the answers

What is the function of the verb in a simple sentence in the present tense?

To agree with the subject in number. Signup and view all the answers

Study Notes

Simplification of Algebraic Expressions

Combining like terms is possible when terms have the same variable(s) and coefficient, e.g., 2x + 3x = 5x
To remove parentheses, distribute the number outside the parentheses to each term inside, e.g., 2(3x + 2) = 6x + 4
Numerical terms can be combined, e.g., 2 + 3 = 5
To simplify expressions with negative terms, subtract the term from both sides of the equation, e.g., -2x + 3 = 5 -> -2x = 2 -> x = -1

Simplification of Fractions

To simplify fractions, cancel out common factors by dividing both the numerator and denominator by the greatest common divisor (GCD), e.g., 12/16 = 3/4
Fractions with negative terms can be simplified by simplifying the numerator and denominator separately, e.g., -3/-4 = 3/4
Mixed numbers can be simplified by converting them to improper fractions and then simplifying the fraction, e.g., 2 1/3 = 7/3 -> 7/3 = 7/3 (already simplified)

Simplification of Indices and Surds

Indices can be simplified by combining like indices, e.g., 2^3 × 2^4 = 2^(3+4) = 2^7
Surds can be simplified by expressing them in their simplest form, e.g., √(16) = √(4^2) = 4
Rationalizing denominators involves multiplying the numerator and denominator by the conjugate of the denominator, e.g., 1/√2 = 1/√2 × √2/√2 = √2/2

Sentence Structure in the Present Tense

Simple Sentences

A simple sentence consists of a subject and a verb in its base form (except for third person singular, which adds -s/-es).
The verb agrees with the subject in number (singular or plural).
Examples of simple sentences in the present tense:
- I write.
- You write.
- He/She/It writes.
- We write.
- They write.

Compound Sentences

A compound sentence joins two or more independent clauses using a conjunction.
Each independent clause has a subject and a verb in the present tense.
Examples of compound sentences in the present tense:
- I write, and she types.
- They are working, but he is not.

Complex Sentences

A complex sentence has an independent clause and one or more dependent clauses.
The dependent clause is introduced by a subordinating conjunction and has a subject and a verb in the present tense.
Examples of complex sentences in the present tense:
- I write because I want to express myself.
- Since I am tired, I will go to bed.

Sentence Fragments

Sentence fragments are incomplete sentences that lack a subject, verb, or both.
Fragments can be corrected by adding the missing element(s) to form a complete sentence.
Examples of sentence fragments and their corrections:
- Writing → I am writing.
- In the morning → I exercise in the morning.

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Description

Learn how to simplify algebraic expressions by combining like terms, removing parentheses, combining constants, and handling negative terms. Master these techniques to become proficient in algebra.