Inverse Operations - Worksheet | Maths Year 5 - Free Printable

Let's go through each question on the Inverse Operations (Addition and Subtraction) Worksheet step by step and solve them with clear explanations.

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1) Complete the number fact family.

Given:
157 + 441 = 598

We need to write the related subtraction facts using the same numbers.

- Addition:
$ 157 + 441 = 598 $

- Subtraction facts (inverse operations):
$ 598 - 157 = 441 $
$ 598 - 441 = 157 $

✔ Answer:
```
157 + 441 = 598
598 - 157 = 441
598 - 441 = 157
```

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2) Use the inverse to check the calculation below.

Given:
2,853 + 309 = 3,162

To check, use the inverse operation: Subtract one addend from the sum.

So:
$$
3,162 - 309 = ?
$$

Let’s calculate:

```
3,162
- 309
-------
2,853
```

✔ Check: Yes, it gives back 2,853 → So the original addition is correct.

Fill in the grid:
```
3 1 6 2
- 3 0 9
--------
2 8 5 3
```

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3) Circle the addition calculation that is the inverse of this subtraction: 6,432 – 1,821 = 4,611

The inverse of a subtraction is adding the two parts to get the whole.

So:
- $ 6,432 - 1,821 = 4,611 $
- Inverse: $ 1,821 + 4,611 = 6,432 $

Now look at the options:

- ✔ 1,821 + 4,611 → This is correct.
- ✘ 1,821 + 6,432 → Too big, not matching.
- ✘ 6,432 + 4,611 → Also too big.

✔ Circle: 1,821 + 4,611

---

4) Use the inverse operation to find the missing number.

Given:
______ + 4,612 = 8,951

To find the missing number, subtract 4,612 from 8,951:

$$
8,951 - 4,612 = ?
$$

Let’s compute:

```
8,951
- 4,612
-------
4,339
```

✔ So the missing number is 4,339

Now fill in the subtraction grid:
```
8 9 5 1
- 4 6 1 2
--------
4 3 3 9
```

---

5) Complete the calculation below and use the inverse to check your answer.

Addition:
```
1 1 4 3 1
+ 5 4 2 1
-----------
```

Align the numbers properly:

```
11431
+ 5421
-------
```

Add:

```
11431
+ 5421
-------
16852
```

Now check using inverse: Subtract one addend from the sum.

Check:
$ 16,852 - 5,421 = ? $

```
16,852
- 5,421
--------
11,431
```

✔ Matches the other addend.

So fill in the grids:

Addition:
```
1 1 4 3 1
+ 5 4 2 1
-----------
1 6 8 5 2
```

Subtraction (check):
```
1 6 8 5 2
- 5 4 2 1
-----------
1 1 4 3 1
```

---

6) Use the inverse to find the missing number in the bar model.

Bar model shows:
- Total: 852
- One part: 391
- Missing part: ?

So:
$ ? = 852 - 391 $

Calculate:
```
852
- 391
-----
461
```

✔ Missing number is 461

Now check using inverse:
$ 461 + 391 = 852 $?
Yes, because $ 461 + 391 = 852 $

Now fill in the subtraction grid:
```
8 5 2
- 3 9 1
-------
4 6 1
```

---

7) Bella says: "I'm thinking of a number. When I subtract 687 from it, I get 4,665." What number is Bella thinking of?

Let the unknown number be $ x $.
Then:
$ x - 687 = 4,665 $

To find $ x $, add 687 to 4,665 (inverse of subtraction):

$$
x = 4,665 + 687
$$

Calculate:
```
4,665
+ 687
-------
5,352
```

✔ So Bella is thinking of 5,352

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8) Jamal and Kody are playing a game. Jamal has won 3,932 points. Together they have won 7,576 points. How many points has Kody won?

Total = Jamal + Kody
So:
$$
Kody = 7,576 - 3,932
$$

Calculate:
```
7,576
- 3,932
-------
3,644
```

✔ Kody has won 3,644 points.

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✔ Final Answers Summary:

1)
- 157 + 441 = 598
- 598 - 157 = 441
- 598 - 441 = 157

2)
- 3,162 - 309 = 2,853 → ✔️ Checks out.

3) Circle: 1,821 + 4,611

4) Missing number: 4,339
$ 8,951 - 4,612 = 4,339 $

5)
- Addition: $ 11,431 + 5,421 = 16,852 $
- Check: $ 16,852 - 5,421 = 11,431 $

6) Missing part: 461
$ 852 - 391 = 461 $

7) Bella’s number: 5,352

8) Kody’s points: 3,644

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