Questions and Answers
An algebraic expression always contains a variable.
True
Only ___________ terms can be added or subtracted in an algebraic expression.
like
A number multiplied with a variable is called a ____________.
co-efficient
6x and 6y are like terms.
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5y + 3 is a numerical expression.
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-10 - 2 = _________
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4 + (2 + 1) = _________
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29y and -3y are like terms.
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What are the two conditions for algebraic terms to be like terms?
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In PEMDAS, E stands for explanation.
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Define constant in an algebraic expression.
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Using the multiplication table, give the perfect square of 7.
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Using the multiplication table, give the square root of 256.
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Can you add 3y and 13x? Why not?
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What is the distributive property of multiplication?
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Define algebraic expression.
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Define numerical expression.
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Identify the operation in 5/2.
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Identify the terms in 3x + 5 - 3y.
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Identify the coefficient in z + 12.
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Study Notes
Algebraic Expressions
- An algebraic expression must contain at least one variable.
- Terms can only be added or subtracted if they are like terms, meaning they share the same variable and exponent.
Terms and Coefficients
- A term multiplied by a variable is referred to as a coefficient.
- Unlike terms cannot be combined; for example, 6x and 6y are unlike due to different variables.
Numerical vs. Algebraic Expressions
- An expression like 5y + 3 is algebraic, not numerical, because it contains a variable.
- A numerical expression consists solely of numbers, such as 5/2, which is identified as a division operation.
Operations and Properties
- Parentheses indicate that operations within them should be solved first, e.g., 4 + (2 + 1) equals 7.
- The distributive property allows the multiplication of a single term with all terms inside parentheses.
Constants and Perfect Squares
- A constant is a standalone integer, fraction, or decimal without a variable.
- The perfect square of 7, derived from multiplication, is 49, while the square root of 256 is 16.
Identifying Terms and Coefficients
- In the expression 3x + 5 - 3y, there are three terms: 3x, 5, and -3y.
- Coefficients can be identified even when not explicitly stated; for instance, in z + 12, the coefficient of z is 1.
PEMDAS and Operations
- In PEMDAS, "E" refers to exponents, not explanation, maintaining the order of operations in calculations.
Combining Like Terms
- Terms must be like terms to be combined; for instance, 3y and 13x cannot be added together as they do not share the same variable.
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Test your knowledge of Algebra-I concepts with these flashcards. Each card provides a definition or statement related to algebraic expressions and terms. It's a great way to reinforce your understanding of algebraic fundamentals.