Multiplying and dividing (Edexcel GCSE Maths): Revision Notes
Multiplying and dividing
You need to be able to multiply and divide numbers without a calculator. These skills are essential for non-calculator questions in your GCSE exam.
Mental methods
Mental methods allow you to work out multiplication and division quickly in your head using number facts and partitioning. These techniques are particularly useful when you need to calculate quickly during exams or when a calculator isn't available.
Mental methods rely heavily on your knowledge of times tables and number bonds. The better you know these basic facts, the faster and more accurate your mental calculations will become.
Mental multiplication
To multiply larger numbers mentally, you can split numbers into easier parts:
- Partitioning method: Break down one number into tens and units
- Multiply each part separately
- Add the results together
Worked Example: Partitioning Method
Calculate: 37 × 8
Step 1: Split 37 into 30 and 7 Step 2: Calculate each part
- 30 × 8 = 240
- 7 × 8 = 56
Step 3: Add the results together 240 + 56 = 296
Therefore: 37 × 8 = 296
Mental division
For division, use your multiplication facts to find the answer:
- Think "what number multiplied by the divisor gives the dividend?"
- Use known times tables to help
Worked Example: Using Times Tables for Division
Calculate: 54 ÷ 6
Step 1: Ask yourself "6 × ? = 54" Step 2: From your times tables: 6 × 9 = 54 Step 3: Therefore: 54 ÷ 6 = 9
Written multiplication methods
When numbers are too large for mental methods, use long multiplication. This systematic approach ensures accuracy when dealing with larger numbers.
Long multiplication process
- Always multiply from right to left
- Start with the units digit
- Work systematically through each digit
- Remember to add any carried numbers
Worked Example: Single-digit Long Multiplication
Calculate: 49 × 3
Step 1: Start with units: 9 × 3 = 27 (write 7, carry 2) Step 2: Tens place: 4 × 3 = 12, plus carried 2 = 14 Step 3: Write the final answer: 147
Worked Example: Two-digit Long Multiplication
Calculate: 36 × 24
Step 1: 36 × 4 = 144 Step 2: 36 × 20 = 720 Step 3: Add together: 144 + 720 = 864
Written division methods
Use long division for larger division calculations. This method breaks down complex divisions into manageable steps.
Long division process
- Set up the calculation with the divisor outside the bracket
- Work through digit by digit from left to right
- Ask "how many times does the divisor go into each part?"
- Write remainders and continue
Worked Example: Long Division
Calculate: 288 ÷ 9
Step 1: 9 goes into 28 three times (3 × 9 = 27) Step 2: Remainder: 28 - 27 = 1 Step 3: Bring down the 8 to make 18 Step 4: 9 goes into 18 exactly twice Step 5: Answer: 32
Checking division with multiplication
You can check if a number divides exactly by using multiplication facts:
- Does 9 divide into 27? Yes, because 9 × 3 = 27
- Does 9 divide into 28? Yes, 9 × 3 = 27 with remainder 1
Exam guidance
Critical Exam Tips:
- These are non-calculator questions - show all working
- Multiplying and dividing are much easier if you know your times tables up to 10 × 10
- Always show your method clearly for full marks
- Check your answers using inverse operations where possible
Common exam requirements:
- Work out calculations step by step
- Show all working for method marks
- Give final answers clearly
Key Points to Remember:
- Mental methods use partitioning and known number facts for quick calculations
- Long multiplication works from right to left, carrying numbers when needed
- Long division breaks numbers down systematically, working left to right
- Times tables knowledge makes all multiplication and division much faster
- Always show your working in non-calculator exam questions