Questions and Answers
What is the result of combining like terms in the expression 2x + 3x?
What is the first step in removing parentheses in the expression 2(3x + 2)?
What is the result of simplifying the expression -2x + 3 = 5?
What is the result of cancelling out common factors in the fraction 12/16?
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What is the result of simplifying the mixed number 2 1/3?
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What is the result of combining like indices in the expression 2^3 × 2^4?
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What is the result of simplifying the surd √(16)?
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What is the purpose of rationalizing denominators?
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What is the main characteristic of a simple sentence in the present tense?
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What is the function of a conjunction in a compound sentence?
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What is the difference between an independent clause and a dependent clause?
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What is an example of a sentence fragment in the present tense?
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How do you correct a sentence fragment?
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What is the purpose of a subordinating conjunction in a complex sentence?
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What is the main difference between a compound sentence and a complex sentence?
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Which of the following is an example of a complex sentence?
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What is the function of the verb in a simple sentence in the present tense?
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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.