Questions and Answers
What is a number increased by two?
x + 2
What is the product of nine and a number?
9y
What is the quotient of nine and a number?
9/y
What is the difference of twice a number and five?
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What is the sum of a number squared and ten?
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What is six more than a number?
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What is triple a number increased by twelve?
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What is a number decreased by sixteen?
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What is double a number increased by five?
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What is the sum of half a number and four?
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What is the quotient of 11 and 9?
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What is the difference of 11 and 9?
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What is the product of 11 and 9?
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What is the sum of 11 and 9?
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What is a number squared?
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What is a number cubed?
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What is the number next to the variable?
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What is a number on its own without a variable?
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What is a letter which stands in place of a number?
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What is the Distributive Property?
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What is fourteen less than a number?
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What is the difference of x and 3?
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What is the quotient of 9 and the difference of x and p?
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What is ten less than the product of 4 and r?
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What is four times the sum of x and y?
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What is four more than the product of 5 and y?
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What is the product of 3 and the difference of x and 9?
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Study Notes
Algebraic Expressions and Definitions
- A number increased by two: Represented as ( x + 2 )
- The product of nine and a number: Denoted as ( 9y )
- The quotient of nine and a number: Written as ( \frac{9}{y} )
- The difference of twice a number and five: Expressed as ( 2x - 5 )
- The sum of a number squared and ten: Denoted by ( x^2 + 10 )
- Six more than a number: Represented as ( x + 6 )
- Triple a number increased by twelve: Described as ( 3x + 12 )
- A number decreased by sixteen: Written as ( y - 16 )
- Double a number increased by five: Expressed as ( 2x + 5 )
- The sum of half a number and four: Represented as ( \frac{x}{2} + 4 )
Basic Operations and Terms
- The quotient of 11 and 9: Noted as ( \frac{11}{9} )
- The difference of 11 and 9: Calculated as ( 11 - 9 )
- The product of 11 and 9: Expressed as ( 11 \times 9 )
- The sum of 11 and 9: Denoted by ( 11 + 9 )
Powers and Variables
- A number squared: Represented as ( x^2 ) (e.g., ( 3 \times 3 ))
- A number cubed: Denoted as ( x^3 ) (e.g., ( 4 \times 4 \times 4 ))
- Coefficient: The number next to a variable
- Constant term: A number on its own without a variable
- Variable: A letter which stands in place of a number
Properties and Expressions
- Distributive Property: Illustrated as ( 3(a-4) = 3a - 12 )
- Fourteen less than a number: Represented as ( x - 14 )
- The difference of x and 3: Denoted by ( x - 3 )
- The quotient of 9 and the difference of x and p: Written as ( \frac{9}{(x - p)} )
- Ten less than the product of 4 and r: Expressed as ( 4r - 10 )
- Four times the sum of x and y: Represented as ( 4(x + y) )
- Four more than the product of 5 and y: Denoted by ( 5y + 4 )
- The product of 3 and the difference of x and 9: Written as ( 3(x - 9) )
These notes encapsulate key algebraic expressions and definitions to aid in understanding their meanings and applications.
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