Questions and Answers
What does coefficient mean?
The amount that a letter has been multiplied by.
What does difference mean?
The answer to the subtraction of two numbers.
What is a factor?
A number which divides exactly into another number.
What is a factor pair?
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What is the highest common factor?
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What is an integer?
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What is the perimeter?
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What are powers?
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What's a prime number?
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What's a product?
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What is the quadratic equation?
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What is a sum?
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What is a term?
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What are expressions in algebra?
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How is the perimeter of a rectangle defined?
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What does simplifying expressions involve?
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Study Notes
Coefficient
- A coefficient indicates the amount multiplied by a variable, e.g., in 3a, the coefficient of a is 3.
Difference
- The difference is the result of subtracting one number from another; for example, the difference between 8 and 2 is 6.
Factor
- A factor is a number that divides another number exactly, with 1 being a factor of all numbers; factors of 10 include 1, 2, 5, and 10.
Factor Pair
- Factor pairs consist of two factors that, when multiplied together, yield a particular product.
Highest Common Factor (HCF)
- The HCF of two numbers is the largest number that divides both; for instance, the HCF of 24 and 36 is 12.
Integer
- Integers are whole numbers, which can be positive, negative, or zero.
Perimeter
- The perimeter is the total distance around a shape, determined by adding the lengths of all its sides.
Powers
- Powers represent a number multiplied by itself a specified number of times.
Prime Number
- A prime number has exactly two factors: 1 and itself.
Product
- The product refers to the outcome of multiplying two numbers; for example, the product of 5 and 8 is 40.
Quadratic Equation
- A quadratic equation is one where the highest power of a variable is 2, e.g., 2x².
Sum
- A sum is the result of adding numbers together; for instance, the sum of 8 and 4 is 12.
Term
- Terms are the individual components of expressions or equations, like 7a or 4 in the expression 7a + 4.
Expressions and Equations
- In algebra, letters represent values that can change (variables) or unknown values. An expression combines terms using operations (+, -, ×, ÷), while an equation states that two expressions are equal.
Identical and Identity
- An identity is a true statement for all variable values; for example, 4a × a² = 4a³ is always true.
Rectangle Perimeter Example
- The perimeter of a rectangle can be calculated by adding the lengths of all sides: for width (x) and height (x - 3), it results in (4x - 6).
Simplifying Expressions
- Simplifying involves collecting like terms in an expression, such as combining 5a and 3a, or 2b and -6b for clarity and efficiency.
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Test your understanding of algebraic expressions with these flashcards. Each card features a key term like coefficient, difference, or factor, along with its definition and an illustrative example. Perfect for quick reviews and reinforcing your algebra skills.