135r. Review Multiplying and Dividing Terms

Learning Intentions

• To understand the meaning of and
• multiply terms and Simplify the result
• divide terms and simplify the result

Pre-requisite Summary

• Know that a pronumeral can represent a number
• Understand that multiplication can be written without the sign, for example
• Know that repeated multiplication can be written Use powers
• Recall that coefficients are the numerical parts of terms
• Be able to simplify basic numerical multiplication and division
• Know that a fraction bar can represent division

Worked Examples

Worked Example 1

State the meaning of each expression:

a)

b)

c)

Worked Example 2

Multiply the terms and simplify:

a)

b)

c)

Worked Example 3

Multiply the terms and simplify:

a)

b)

c)

Worked Example 4

Divide the terms and simplify:

a)

b)

c)

Worked Example 5

Divide the terms and simplify:

a)

b)

c)

Worked Example 6

Simplify each expression:

a)

b)

c)

Problems

Problem 1

State the meaning of each expression:

a)

b)

c)

Problem 2

Multiply the terms and simplify:

a)

b)

c)

Problem 3

Multiply the terms and simplify:

a)

b)

c)

Problem 4

Divide the terms and simplify:

a)

b)

c)

Problem 5

Divide the terms and simplify:

a)

b)

c)

Problem 6

Simplify each expression:

a)

b)

c)

Exercises

Understanding and Fluency

Exercise 1.

State the meaning of each expression:

a)

b)

c)

d)

Exercise 2.

Write each repeated multiplication using powers:

a)

b)

c)

d)

Exercise 3.

Multiply the terms and simplify:

a)

b)

c)

d)

Exercise 4.

Multiply the terms and simplify:

a)

b)

c)

d)

Exercise 5.

Divide the terms and simplify:

a)

b)

c)

d)

Exercise 6.

Divide the terms and simplify:

a)

b)

c)

d)

Exercise 7.

Simplify each expression:

a)

b)

c)

d)

Exercise 8.

Simplify each expression:

a)

b)

c)

d)

Reasoning

Exercise 9.

Explain why means and not .

Exercise 10.

A student says that means . Explain the mistake.

Exercise 11.

Noah says that . Is he correct? Explain.

Exercise 12.

Explain why .

Exercise 13.

A student simplifies to . Describe the error.

Problem-solving

Exercise 14.

A square has side length cm. Write an expression for its area.

Exercise 15.

A cube has side length cm. Write an expression for its volume.

Exercise 16.

A rectangle has side lengths cm and cm. Write a simplified expression for its area.

Exercise 17.

A packet contains marbles and this amount is shared equally among students. Write a simplified expression for the number of marbles each student gets.

Exercise 18.

A strip has length cm and is cut into pieces of length cm. Write a simplified expression for the number of pieces.

Exercise 19.

A garden has length m and width m. Write a simplified expression for its area.

Potential Misunderstandings

• Students may think means instead of
• Students may think means instead of
• Students may forget to multiply coefficients when multiplying terms
• Students may not Recognise that
• Students may confuse multiplying terms with adding like terms
• Students may divide coefficients correctly but not simplify the pronumeral part
• Students may think
• Students may cancel pronumerals incorrectly in division
• Students may lose pronumerals or coefficients when simplifying

Next: 136e. Intro to Algebraic Fractions and Common Denominators