ExpertEasy1 markShort Answer
AQA GCSE · Question 07.2 · Algebra
Here is a different number machine. Complete the number machine.
Here is a different number machine. Complete the number machine.
How to approach this question
1. To find the missing operation, you need to work backwards from the output.
2. Start with the output, which is 9.
3. The last operation was "÷ 2". To reverse this, do the opposite: multiply by 2. So, 9 × 2 = 18.
4. This means the number in the middle, after the first operation, must be 18.
5. Now, find the operation that turns the input (7) into 18.
6. What do you do to 7 to get 18? 18 - 7 = 11. So the operation is "+ 11".
Full Answer
To find the missing operation, we can work backwards from the output to the input. This involves using inverse (opposite) operations.
1. **Output:** The final number is 9.
2. **Reverse the last operation:** The last operation is "÷ 2". The inverse operation is "× 2".
9 × 2 = 18.
This tells us that the number before the "÷ 2" operation must have been 18.
3. **Find the missing operation:** We now know that the input (7) goes through the missing operation to become 18.
We need to find what we do to 7 to get 18.
We can find the difference: 18 - 7 = 11.
So, the missing operation is "add 11" or "+ 11".
**Let's check by working forwards:**
Input = 7
First operation: 7 + 11 = 18
Second operation: 18 ÷ 2 = 9
Output = 9. This is correct.
Common mistakes
✗ Working forwards and guessing the operation.
✗ Using the wrong inverse operation (e.g., subtracting 2 instead of multiplying by 2).
✗ Making an arithmetic error.
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