Algebraic Expressions and Operations

This video tutorial covers solving 10 algebraic expression problems from a review sheet. It explains how to translate verbal phrases into algebraic expressions, focusing on operations like sum, difference, product, and quotient. Each question is broken down step-by-step, highlighting key terms and their mathematical meanings. The tutorial emphasizes the flexibility of variable choice and the importance of order in expressions.

What is the algebraic expression for 'the sum of four and a number'?

• n/4

• 4n

• n - 4

• 4 + n

How would you express 'six less than a number' in algebraic terms?

• 6n

• 6 - n

• n + 6

• n - 6

What is the expression for 'the product of three and the square of a number'?

• 3n^2

• 3n

• 3 + n^2

• n^2 - 3

How do you write 'the quotient of seven and the difference of a number and two'?

• 7n - 2

• (n - 2)/7

• 7n/2

• 7/(n - 2)

What is the algebraic expression for 'the sum of twice a number and six'?

• 2n + 6

• n/2 + 6

• 6n + 2

• 2(n + 6)

How would you express 'four more than a number'?

• 4n

• n + 4

• n - 4

• 4/n

What is the expression for 'nine increased by a number cubed'?

• 9/n^3

• n^3 - 9

• 9n^3

• 9 + n^3

How do you write 'the product of the sum of a number and six, and the difference of a number and six'?

• (n + 6)(n - 6)

• n + 6 - n - 6

• n^2 + 6

• n^2 - 36

What is the algebraic expression for 'the quotient of nine increased by a number and the product of five and the number'?

• 9 + n - 5n

• 5n/(9 + n)

• 9n + 5

• (9 + n)/(5n)

How would you express 'the difference of three times a number and the quotient of the number and four'?

• 3n + n/4

• 3n - n/4

• n/4 - 3n

• 3n/4