Understanding Mathematical Expressions and Operations

The video tutorial explains how to convert verbal phrases into mathematical expressions, equations, or inequalities using the variable 'n' for unknown numbers. It covers five phrases, demonstrating the use of operations like addition, subtraction, multiplication, and comparison to form the correct mathematical statements. Each phrase is broken down step-by-step to illustrate the process of translating words into mathematical language.

What operation is indicated by the word 'difference' in the phrase 'two times the difference between a number and nine'?

• Division

• Multiplication

• Subtraction

• Addition

How would you express 'two times the difference between a number and nine' using a variable n?

• 2 - (n + 9)

• 2 + (n - 9)

• 2 * (n - 9)

• n - 9

In the phrase '3 less than x is 5 more than y', what does 'is' signify?

• Subtraction

• Greater than

• Equals

• Addition

How would you write the equation for '3 less than x is 5 more than y'?

• x - 3 > y + 5

• x - 3 = y + 5

• x + 3 = y - 5

• x + 3 < y - 5

What does 'more than' indicate in the phrase '2 more than x is more than 3 more than y'?

• Equals

• Less than

• Subtraction

• Greater than

How would you express '2 more than x is more than 3 more than y' as an inequality?

• x + 2 < y + 3

• x + 2 > y + 3

• x - 2 > y - 3

• x - 2 < y - 3

In the phrase 'nine fewer than the product of a number and three more than the number', what does 'product' imply?

• Addition

• Division

• Subtraction

• Multiplication

How would you write the expression for 'nine fewer than the product of a number and three more than the number'?

• n - (n * 3) + 9

• n * (n - 3) + 9

• n + (n * 3) - 9

• n * (n + 3) - 9

In the phrase '6 more than Z is 7 less than x', what does 'is' indicate?

• Greater than

• Equals

• Subtraction

• Addition

How would you express '6 more than Z is 7 less than x' as an equation?

• Z + 6 = x - 7

• Z + 6 > x - 7

• Z - 6 = x + 7

• Z - 6 < x + 7