Dividing Monomials: Key Concepts and Techniques

What is a monomial?

• A quotient of numbers and variables

• A difference of numbers and variables

• A sum of numbers and variables

• A number, a variable, or a product of numbers and variables

What does it mean to write a monomial in expanded form?

• To multiply the coefficients

• To add the exponents

• To subtract the exponents

• To write out the variables without exponents

In the first example, what is the result of dividing 10x^7 by 5x^2?

• 2x^5

• 5x^4

• 2x^4

• 5x^5

In the second example, what is the result of dividing 21x^4 by 7x^2?

• 3x^2

• 3x^3

• 7x^2

• 7x^3

When dividing monomials with two variables, what should you do after expanding the variables?

• Multiply the coefficients

• Add the coefficients

• Subtract the coefficients

• Divide the coefficients

In the example with two variables, what is the result of dividing 40x^3y^3 by 8xy?

• 5x^2y^2

• 5xy

• 5xy^2

• 5x^2y

In the final example, what is the reduced form of 14/6?

• 2/7

• 7/2

• 7/3

• 3/7

In the final example, where do the remaining x's end up after canceling?

• They remain unchanged

• They are completely canceled out

• In the denominator

• In the numerator

In the final example, how many y's are left in the denominator after canceling?

• Four

• Two

• One

• Three

What should you be careful about when writing your final answer?

• Ensuring the coefficients are correct

• Ensuring the variables are in the correct place

• Ensuring the exponents are added

• Ensuring the exponents are subtracted