Lesson title: Dividing terms
DO NOW: Copy then simplify
\(3 \times 4x\)
\(5y \times 2\)
\(2m \times 6m\)
\(2mn + 6nm\)
\(4a \times 3a\)
\(7 + 2p\)
\(3xy \times x\)
\(3xy^2 \times 4x\)
Today’s learning
By the end of this lesson, you will be able to:
- Divide terms correctly
- Understand the difference between multiplying and dividing terms
- Write your working clearly for division
- Check your working by using the opposite operation
Key vocabulary
Copy these definitions:
Quotient: The answer when we divide
- Example: in \(12 \div 3 = 4\), the quotient is 4.
Inverse operations: Operations that are opposites
- Multiplication and division are inverse operations
- We can check division by multiplying
Dividing a term by a number
Copy this example and answer questions:
Example:
\[\begin{align*}
15x \div 3 &= \substack{\color{red}{\div 3}\\ \color{red}{\div 3}} \frac{15x}{3} \\
&= \frac{5x}{1} \\
&= 5x
\end{align*}\]
Complete:
$$\[\begin{align*}
24p \div 8 &= \underline{\hspace{0.5cm}} \frac{24p}{8} \\
&= \underline{\hspace{1cm}}
\end{align*}\]$$
Your turn
Complete these with full working:
Check your working
Watch and listen:
To check \(21x \div 3 = 7x\), we multiply back:
\[7x \times 3 = 21x ✓\]
Now check these answers:
- Is \(16a \div 4 = 4a\) correct?
- Is \(30m \div 6 = 6m\) correct?
Dividing terms with same variables
Copy this new rule:
When dividing terms with the same variable:
\[\frac{x^2}{x} = x \text{ (because } x^2 \div x = x \times x \div x = x)\]
Example with coefficients:
\[\begin{align*}
\frac{12x^2}{3x} &= \frac{12}{3} \times \frac{x^2}{x} \\
&= 4 \times x \\
&= 4x
\end{align*}\]
Study solution:
Jack’s (correct) simplification of \(\frac{20a^2}{4a}\):
\[\begin{align*}
\frac{20a^2}{4a} &= \frac{5a}{1} \\
&= 5a
\end{align*}\]
Answer these questions:
- What happened to the coefficients 20 and 4?
- What happened to \(a^2 \div a\)?
- Now you try: \(\frac{15b^2}{3b}\)
Practice - Term ÷ Term
Complete these with full working:
Find and fix the error
Find the mistake and write the correct solution:
Sam’s working:
\[\begin{align*}
\frac{18x^2}{3x} &= \frac{18-3}{x^2-x} \\
&= \frac{15}{x} \\
&= 15x
\end{align*}\]
What went wrong? Write the correct solution.
Mixed practice
Complete these (check the operation!):
\(5x \times 3x\)
\(20a \div 4\)
\(\frac{12m^2}{3m}\)
\(8p + 2p\)
\(\frac{21y}{7}\)
\(6n \times 2n\)
Check these answers
Use inverse operations to check if these are correct:
Is \(24x \div 6 = 4x\) correct?
Is \(\frac{15a^2}{3a} = 12a\) correct?
Is \(\frac{28m}{4} = 7m\) correct?
Common mistakes
Which is correct? Thumbs up when I say the correct answer:
\(\frac{12x}{4} = ?\)
- \(3x\)
- \(8x\)
- \(3\)
\(\frac{20a^2}{5a} = ?\)
- \(4a\)
- \(4a^2\)
- \(15a\)
\(\frac{18m}{6} = ?\)
- \(12m\)
- \(3m\)
- \(3\)
Operation summary
Copy this comparison:
Addition: \(3x + 2x = 5x\) (add coefficients)
Multiplication: \(3x \times 2x = 6x^2\) (multiply everything)
Division: \(6x^2 \div 2x = 3x\) (divide coefficients, subtract powers)
Key: Each operation has different rules!
Exercises
Do Ex 3.06 Q1,2,3…