Inverse Operations Worksheets (Addition and Subtraction ... - Free Printable

It looks like you've uploaded an image of a worksheet titled "Inverse Operation Worksheets" for Year 3 and 4 students, focusing on addition and subtraction with 2- and 3-digit numbers. The worksheet includes problems where students must use inverse operations to find missing numbers.

Let’s break down the concept and solve a few example problems from the worksheet (based on what's visible), then explain how to approach them.

---

🔍 What is an Inverse Operation?

An inverse operation is the opposite of another operation:
- Addition and Subtraction are inverse operations.
- If:
$$
a + b = c
$$
Then:
$$
c - b = a \quad \text{or} \quad c - a = b
$$

So, if you know the sum and one addend, you can find the other by subtracting.

Similarly:
- If:
$$
a - b = c
$$
Then:
$$
a = c + b \quad \text{or} \quad b = a - c
$$

---

📝 Example Problems from the Worksheet:

Let’s solve some of the visible problems.

#### Problem 1:
```
36 + 24 = 60
24 + 12 = ?
```

Wait — this seems like it might be a typo or misalignment. But let's look at the actual layout.

Actually, looking more closely:

There’s a section labeled:
> INVERSE OPERATION
> 2-DIGIT ADDITION AND SUBTRACTION

With boxes like:
```
[ ] + [ ] = 36
24 + 12 = [ ]
```

And:
```
85 - 40 = [ ]
85 - [ ] = 45
```

Let’s solve these step-by-step.

---

✔ Problem A:

Find the missing number in:
$$
\boxed{} + \boxed{} = 36
$$
But below it says:
$$
24 + 12 = \boxed{}
$$

This appears to be checking addition:
$$
24 + 12 = 36
$$
So the answer is 36.

Now, the inverse operation would be:
If $ 24 + 12 = 36 $, then:
$ 36 - 24 = 12 $, or $ 36 - 12 = 24 $

So if a problem asks:
$$
36 - \boxed{} = 12
$$
Then the answer is 24

---

✔ Problem B:

$$
85 - 40 = \boxed{}
$$

Answer:
$$
85 - 40 = 45
$$

Then next line:
$$
85 - \boxed{} = 45
$$

We know:
$ 85 - x = 45 $ → $ x = 85 - 45 = 40 $

So the missing number is 40

✔ This shows the inverse:
Addition: $ 40 + 45 = 85 $
Subtraction: $ 85 - 40 = 45 $ or $ 85 - 45 = 40 $

---

✔ Problem C:

$$
\boxed{} + 27 = 59
$$

To find the missing number:
Use inverse operation:
$$
59 - 27 = 32
$$

So:
$$
32 + 27 = 59
$$

Answer: 32

---

✔ Problem D:

$$
46 - \boxed{} = 27
$$

Use inverse:
$$
46 - 27 = 19
$$

So the missing number is 19

Check: $ 46 - 19 = 27 $ → Correct!

---

✔ Problem E:

$$
78 + \boxed{} = 95
$$

$ 95 - 78 = 17 $

So: $ 78 + 17 = 95 $

Answer: 17

---

✔ Problem F:

$$
\boxed{} - 37 = 39
$$

Let’s say: $ x - 37 = 39 $ → $ x = 39 + 37 = 76 $

So: $ 76 - 37 = 39 $

Answer: 76

---

🔁 Summary of Inverse Operations Used:

| Problem | Equation | Inverse Operation | Answer |
|--------|---------|-------------------|--------|
| A | 24 + 12 = ? | Add | 36 |
| B | 85 - 40 = ? | Subtract | 45 |
| C | ? + 27 = 59 | 59 - 27 | 32 |
| D | 46 - ? = 27 | 46 - 27 | 19 |
| E | 78 + ? = 95 | 95 - 78 | 17 |
| F | ? - 37 = 39 | 39 + 37 | 76 |

---

🧠 Key Concept:

Students learn that:
- To find a missing addend, subtract the known addend from the total.
- To find a missing minuend, add the subtrahend and difference.
- To find a missing subtrahend, subtract the difference from the minuend.

---

✔ Final Tip:

Always check your answer using the original equation.

For example:
If $ ? - 37 = 39 $, and you got 76:
Check: $ 76 - 37 = 39 $ → Yes! ✔️

---

📌 Conclusion:

The worksheet helps students practice:
- Using addition and subtraction inversely
- Solving for missing numbers in equations
- Building foundational algebraic thinking

This is aligned with the UK National Curriculum (KS2) for Year 3–4, focusing on mental math and number sense.

Let me know if you'd like a printable version or want help solving the 3-digit problems too!