Multiplying and dividing (AQA GCSE Maths): Revision Notes
Multiplying and dividing
Multiplying and dividing are essential skills you need to master for your GCSE maths exam. You must be able to perform calculations both with and without a calculator, using different methods depending on the complexity of the numbers involved.
These fundamental arithmetic operations appear frequently in GCSE maths exams, so mastering both mental and written methods is crucial for success.
Mental methods for quick calculations
Mental methods allow you to calculate multiplication and division quickly in your head. These techniques are particularly useful for non-calculator exam questions and can save you valuable time.
Partitioning for multiplication
Partitioning means splitting a number into smaller, more manageable parts that are easier to work with. This method works especially well when one number can be broken down using numbers you know from your times tables.
Worked Example: Using Partitioning
To calculate 37 × 8:
- Split 37 into 30 + 7
- Calculate each part separately: 30 × 8 = 240 and 7 × 8 = 56
- Add the results together: 240 + 56 = 296
Using multiplication facts for division
Division becomes much simpler when you can identify multiplication facts that help you find the answer directly.
Worked Example: Using Multiplication Facts
To calculate 54 ÷ 6:
- Think: "What number multiplied by 6 gives 54?"
- Since 6 × 9 = 54, the answer is 9
Your times tables up to 10 × 10 are the foundation for both mental multiplication and division. The better you know them, the faster and more accurate your calculations will be.
Written multiplication method
For larger numbers or when mental methods aren't practical, you need to use the formal written method for multiplication. This involves setting up the calculation in columns and working systematically.
Step-by-step process
The written multiplication method requires you to multiply from right to left and handle any carrying over carefully.
Worked Example: Single-Digit Multiplication
49 × 3:
- Set up the numbers in columns with 49 on top and 3 below
- Start with the units: 9 × 3 = 27
- Write down 7 and carry over 2 (representing 2 tens)
- Multiply the tens: 4 × 3 = 12, then add the carried 2 = 14
- Write down 14, giving the final answer: 147
Multi-digit multiplication
For calculations like 36 × 24, you need to break this into separate multiplications:
Worked Example: Multi-Digit Multiplication
36 × 24:
- Calculate 36 × 4 = 144
- Calculate 36 × 20 = 720 (multiply by 2, then add a zero)
- Add the results: 144 + 720 = 864
Always show each step of your working clearly. In non-calculator questions, you must demonstrate your method to receive full marks.
Long division method
Long division is the formal written method for dividing larger numbers. It involves a systematic process of dividing, multiplying, and subtracting.
The long division process
Worked Example: Long Division
288 ÷ 9:
- Check if division is possible: Does 9 divide into 2? No. Does 9 divide into 28? Yes.
- Find how many times: 9 × 3 = 27, so 9 goes into 28 three times with remainder 1
- Bring down the next digit: Bring down the 8 to make 18
- Repeat the process: 9 goes into 18 exactly 2 times
- Final answer: 32
You can verify your answer by checking if 9 × 32 = 288. This confirms your solution is correct.
Exam strategies and tips
Understanding the calculation methods is only part of success - you also need to master exam technique and presentation.
Showing your working
In GCSE exams, showing your working is crucial, especially for multi-mark questions. Even if your final answer is incorrect, you can still earn marks for using the correct method.
Word problems requiring justification
Some exam questions ask you to determine whether something is possible and justify your answer. For these questions:
Approach for Justification Questions:
- Calculate the required amounts step by step
- Compare your results with what's needed
- State clearly whether the answer is "yes" or "no"
- Show all working to support your conclusion
For example, if asked whether someone has bought enough items:
- Calculate the total number needed
- Calculate the total number bought
- Compare the numbers
- Give a clear yes/no answer with justification
Key Points to Remember:
- Master your times tables up to 10 × 10 - they're essential for both mental and written methods
- Use partitioning to break down difficult mental calculations into easier parts
- Always multiply from right to left in written methods and handle carrying over carefully
- Show all your working in exam questions, even if you're confident in your answer
- Check your answers using inverse operations when possible (multiplication to check division, and vice versa)