Math worksheet for practicing missing number problems in addition and multiplication, aligned with 6AS/MD-2 standards.

Let's solve each part of the worksheet step by step, using arithmetic properties, inverse relationships, and place value understanding as required.

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a)

1. $ 436 + 287 = 440 + \boxed{?} $

We are changing 436 to 440 (adding 4), so we must subtract 4 from 287 to keep the sum the same.

- $ 287 - 4 = 283 $
- So: $ 436 + 287 = 440 + 283 $

✔ Answer: $ \boxed{283} $

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2. $ 35 \times 46 = 70 \times \boxed{?} $

Note: $ 70 = 2 \times 35 $, so we're doubling one factor.

To keep the product the same, we must halve the other factor:

- $ 46 \div 2 = 23 $
- So: $ 35 \times 46 = 70 \times 23 $

✔ Answer: $ \boxed{23} $

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b)

1. $ 572 + 266 = 560 + \boxed{?} $

Change 572 → 560 (subtract 12), so add 12 to 266 to balance:

- $ 266 + 12 = 278 $
- So: $ 572 + 266 = 560 + 278 $

✔ Answer: $ \boxed{278} $

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2. $ 52 \times 45 = 26 \times \boxed{?} $

Note: $ 26 = 52 \div 2 $, so halving one factor → double the other:

- $ 45 \times 2 = 90 $
- So: $ 52 \times 45 = 26 \times 90 $

✔ Answer: $ \boxed{90} $

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c)

1. $ 390 + \boxed{?} = 416 + 297 $

First compute right-hand side:
- $ 416 + 297 = 713 $

Now: $ 390 + x = 713 $
- $ x = 713 - 390 = 323 $

✔ Answer: $ \boxed{323} $

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2. $ 15 \times 68 = \boxed{?} \times 17 $

Note: $ 17 = 15 + 2 $? Not helpful. But notice:
- $ 68 \div 17 = 4 $, so maybe think in terms of scaling.

Try to make both sides equal:
- Left: $ 15 \times 68 $
- Right: $ ? \times 17 $

We can write:
- $ 15 \times 68 = ? \times 17 $
- So $ ? = \frac{15 \times 68}{17} $

Calculate:
- $ 68 \div 17 = 4 $
- So $ ? = 15 \times 4 = 60 $

✔ Answer: $ \boxed{60} $

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d)

1. $ 640 + \boxed{?} = 161 + 638 $

Right side: $ 161 + 638 = 799 $

So: $ 640 + x = 799 $
- $ x = 799 - 640 = 159 $

✔ Answer: $ \boxed{159} $

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2. $ 38 \times 49 = \boxed{?} \times 19 $

Note: $ 38 = 2 \times 19 $, so we’re dividing one factor by 2 → multiply the other by 2

- $ 49 \times 2 = 98 $
- So: $ 38 \times 49 = 98 \times 19 $

✔ Answer: $ \boxed{98} $

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e)

1. $ \boxed{?} + 440 = 158 + 338 $

Right side: $ 158 + 338 = 496 $

So: $ x + 440 = 496 $
- $ x = 496 - 440 = 56 $

✔ Answer: $ \boxed{56} $

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2. $ \boxed{?} \times 57 = 6 \times 114 $

Right side: $ 6 \times 114 = 684 $

So: $ x \times 57 = 684 $
- $ x = 684 \div 57 $

Divide:
- $ 57 \times 12 = 684 $
- So $ x = 12 $

✔ Answer: $ \boxed{12} $

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f)

1. $ \boxed{?} + 360 = 157 + 736 $

Right side: $ 157 + 736 = 893 $

So: $ x + 360 = 893 $
- $ x = 893 - 360 = 533 $

✔ Answer: $ \boxed{533} $

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2. $ \boxed{?} \times 32 = 96 \times 15 $

Right side: $ 96 \times 15 $

We can simplify:
- $ 96 = 3 \times 32 $, so:
- $ 96 \times 15 = (3 \times 32) \times 15 = 3 \times 15 \times 32 = 45 \times 32 $

So: $ ? \times 32 = 45 \times 32 $
→ $ ? = 45 $

✔ Answer: $ \boxed{45} $

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g)

1. $ 520 + \boxed{?} = 326 + 592 $

Right side: $ 326 + 592 = 918 $

So: $ 520 + x = 918 $
- $ x = 918 - 520 = 398 $

✔ Answer: $ \boxed{398} $

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2. $ 144 \times 25 = 75 \times \boxed{?} $

Note: $ 144 \div 75 = ? $ — not obvious.

But notice:
- $ 144 = 3 \times 48 $, $ 75 = 3 \times 25 $ — maybe not helpful.

Alternative: Use factoring.

Let’s write:
- $ 144 \times 25 = ? \times 75 $
- $ ? = \frac{144 \times 25}{75} $

Simplify:
- $ \frac{25}{75} = \frac{1}{3} $
- So $ ? = 144 \times \frac{1}{3} = 48 $

✔ Answer: $ \boxed{48} $

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✔ Final Answers:

| Part | Question | Answer |
|------|--------|--------|
| a) | $ 436 + 287 = 440 + \boxed{?} $ | 283 |
| | $ 35 \times 46 = 70 \times \boxed{?} $ | 23 |
| b) | $ 572 + 266 = 560 + \boxed{?} $ | 278 |
| | $ 52 \times 45 = 26 \times \boxed{?} $ | 90 |
| c) | $ 390 + \boxed{?} = 416 + 297 $ | 323 |
| | $ 15 \times 68 = \boxed{?} \times 17 $ | 60 |
| d) | $ 640 + \boxed{?} = 161 + 638 $ | 159 |
| | $ 38 \times 49 = \boxed{?} \times 19 $ | 98 |
| e) | $ \boxed{?} + 440 = 158 + 338 $ | 56 |
| | $ \boxed{?} \times 57 = 6 \times 114 $ | 12 |
| f) | $ \boxed{?} + 360 = 157 + 736 $ | 533 |
| | $ \boxed{?} \times 32 = 96 \times 15 $ | 45 |
| g) | $ 520 + \boxed{?} = 326 + 592 $ | 398 |
| | $ 144 \times 25 = 75 \times \boxed{?} $ | 48 |

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🔍 Summary of Strategies Used:

- Addition: Adjust one number → adjust the other to keep sum constant.
- Multiplication: If one factor is multiplied/divided, compensate with the other.
- Inverse operations: Use subtraction to find missing addends, division for missing factors.
- Factoring & simplifying: Break numbers into known multiples (e.g., 70 = 2×35).

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