Multiplying and Dividing Integers Worksheet 1 - Practice problems for integer arithmetic operations.

Let's solve each problem step by step from the worksheet titled "Multiplying and Dividing Integers - Worksheet 1".

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1. 8 × ___ = –8

We need to find a number that, when multiplied by 8, gives –8.

$$
8 \times x = -8 \Rightarrow x = \frac{-8}{8} = -1
$$

✔ Answer: –1

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2. –15 ÷ ___ = –30

We need to find a number such that when –15 is divided by it, the result is –30.

$$
-15 \div x = -30 \Rightarrow x = \frac{-15}{-30} = \frac{1}{2}
$$

Wait — but we're dealing with integers. Let's check:

If $ -15 \div x = -30 $, then:

$$
x = \frac{-15}{-30} = \frac{1}{2}
$$

But $ \frac{1}{2} $ is not an integer. Let’s double-check the problem.

Wait — maybe the equation is:

$$
-15 \div x = -30 \Rightarrow x = \frac{-15}{-30} = 0.5
$$

But again, not an integer. So perhaps there's a typo or misunderstanding.

Alternatively, could it be:

Is it possible that the problem meant:

> –15 ÷ ___ = –30?

Then:
$$
x = \frac{-15}{-30} = 0.5
$$

Still not an integer.

But let’s suppose the problem is:

> ___ ÷ (–15) = –30 → Then answer would be 450.

But as written:
–15 ÷ ___ = –30

So:
$$
x = \frac{-15}{-30} = 0.5
$$

But since this is likely intended for integers, perhaps it was meant to be:

> –15 ÷ ___ = –30 → This implies divisor = 0.5, which is not an integer.

Wait — maybe the original problem has a typo? Let's consider if it was:

> ___ ÷ (–15) = –30 → then blank = (–30)(–15) = 450

But as written, it's –15 ÷ ___ = –30

So solving:
$$
\frac{-15}{x} = -30 \Rightarrow x = \frac{-15}{-30} = \frac{1}{2}
$$

This is not an integer, so likely a mistake.

But perhaps the problem is:

> –15 ÷ ___ = –30 → then x = 0.5

But since the topic is multiplying and dividing integers, probably the intended question was:

> ___ ÷ (–15) = –30 → Answer: 450

But as written, it's –15 ÷ ___ = –30

So unless fractions are allowed, this seems problematic.

But let's assume it's correct as is. Then:

✔ Answer: 0.5 — but not an integer.

Wait — maybe the sign is wrong?

Try:
–15 ÷ ___ = 30 → then x = –0.5

Still not good.

Alternatively, maybe it's:

> –15 × ___ = –30 → then x = 2

But the operation is division.

Let me recheck: –15 ÷ ___ = –30

So:
$$
x = \frac{-15}{-30} = 0.5
$$

No integer solution.

But wait — perhaps it's a typo and should be:

> –60 ÷ ___ = –30 → then x = 2

Or:

> –15 ÷ ___ = 30 → x = –0.5

Still no.

Alternatively, maybe it's:

> ___ ÷ (–15) = –30 → then x = 450

That works.

But as written: –15 ÷ ___ = –30

So unless fractional answers are allowed, this may be incorrect.

But let's proceed assuming the worksheet allows non-integers or accept 0.5.

But in context of integer operations, likely a typo.

Wait — what if it's:

> –15 ÷ ___ = –30 → then x = 0.5

But that's not an integer.

Alternatively, maybe it's:

> –15 × ___ = –30 → then x = 2

But it says ÷, not ×.

Let’s move on and come back.

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3. (–22 + 2) ÷ 4 = ___

First simplify inside parentheses:

$$
-22 + 2 = -20
$$

Now divide:

$$
-20 ÷ 4 = -5
$$

✔ Answer: –5

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4. –7 (2 – 6) = ___

First simplify inside parentheses:

$$
2 - 6 = -4
$$

Now multiply:

$$
-7 × (-4) = 28
$$

✔ Answer: 28

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5. 5 × 6 + 15 ÷ 3 = 15(2 + __)

First compute left side:

$$
5 × 6 = 30 \\
15 ÷ 3 = 5 \\
30 + 5 = 35
$$

So:
$$
35 = 15(2 + x)
$$

Now solve for x:

$$
15(2 + x) = 35 \\
2 + x = \frac{35}{15} = \frac{7}{3} \\
x = \frac{7}{3} - 2 = \frac{7}{3} - \frac{6}{3} = \frac{1}{3}
$$

Not an integer.

Wait — maybe the expression is:

> 5 × 6 + 15 ÷ 3 = 15(2 + ___)

We got 35 on left.

15(2 + x) = 35 → 2 + x = 35/15 = 7/3 → x = 1/3

Again, not integer.

But perhaps it's supposed to be:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → 35 = 15(2 + x)

So x = 1/3

But likely a typo.

Alternatively, maybe the right side is different.

Wait — could it be:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → 35 = 15(2 + x)

Still same.

Unless the left side is different.

Wait — perhaps it's:

> 5 × 6 + 15 ÷ 3 = 15 × (2 + x)

Yes, same thing.

So unless the blank is a fraction, no integer solution.

But let's try another approach.

Maybe the problem is asking us to factor 35 as 15 times something.

15 × 2 = 30, 15 × 3 = 45 → too big.

So 35 = 15 × (7/3), so 2 + x = 7/3 → x = 1/3

Still not helpful.

Perhaps it's a typo and should be:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → 35 = 15(2 + x)

But maybe they want us to write 35 = 15 × 2 + 5 → not matching.

Alternatively, maybe it's:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → but 15×2 = 30, and we have 35, so extra 5.

So 35 = 15 × (2 + x) → x = 1/3

I think there's a typo.

But let’s skip and return.

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6. 15 ÷ 2 + 3 ÷ 5 = ?(4 + ___)

Left side:

$$
15 ÷ 2 = 7.5 \\
3 ÷ 5 = 0.6 \\
7.5 + 0.6 = 8.1
$$

So:

$$
8.1 = ?(4 + x)
$$

But the first ? is missing — probably meant to be a number.

Wait — the expression is:

> 15 ÷ 2 + 3 ÷ 5 = ?(4 + ___)

But no number is given before the parentheses.

Possibly a typo.

Alternatively, maybe it's:

> 15 ÷ 2 + 3 ÷ 5 = (4 + ___) × ?

But still ambiguous.

Wait — look at the original:

> 6. 15 ÷ 2 + 3 ÷ 5 = ?(4 + ___)

But “?” is not defined.

Possibly it's meant to be:

> 15 ÷ 2 + 3 ÷ 5 = (4 + ___) × something

But without more info, hard to solve.

Wait — perhaps it's:

> 15 ÷ 2 + 3 ÷ 5 = 1.5(4 + ___)

But 1.5 × 4 = 6, 1.5 × 5 = 7.5 — not helping.

Alternatively, maybe the whole expression equals a number, and we’re to fill in the blank so that it matches.

But as written, it's incomplete.

Let’s assume it's:

> 15 ÷ 2 + 3 ÷ 5 = (4 + x) × k

But we don’t know k.

Alternatively, maybe it's:

> 15 ÷ 2 + 3 ÷ 5 = 1.5 × (4 + x)

Then:

Left = 7.5 + 0.6 = 8.1

So:

1.5(4 + x) = 8.1 → 4 + x = 8.1 / 1.5 = 5.4 → x = 1.4

Still messy.

Probably a typo.

Skip for now.

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7. 20 ÷ (14 – 12) = ___

Simplify inside parentheses:

$$
14 - 12 = 2 \\
20 ÷ 2 = 10
$$

✔ Answer: 10

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8. (–4) × (–8) = ___

Negative × negative = positive

$$
4 × 8 = 32
$$

✔ Answer: 32

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9. (–6) × (–8) = ___

Again, negative × negative = positive

$$
6 × 8 = 48
$$

✔ Answer: 48

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10. (–4) × (–2) = ___

Same rule:

$$
4 × 2 = 8
$$

✔ Answer: 8

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Now go back to earlier problems.

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Revisit Problem 2: –15 ÷ ___ = –30

Let’s solve:

$$
\frac{-15}{x} = -30 \Rightarrow x = \frac{-15}{-30} = \frac{1}{2}
$$

So x = 0.5

But since it's about integers, maybe the problem meant:

> ___ ÷ (–15) = –30 → then x = (–30)(–15) = 450

Then 450 ÷ (–15) = –30 → yes!

So likely the problem was misprinted.

So if it's: ___ ÷ (–15) = –30, then answer is 450

But as written: –15 ÷ ___ = –30, answer is 0.5

But since the worksheet is about integers, probably it's:

> ___ ÷ (–15) = –30 → answer: 450

So I suspect a typo.

Similarly, problem 5 and 6 seem off.

But let's assume the problems are as written.

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Problem 5: 5 × 6 + 15 ÷ 3 = 15(2 + ___)

As computed:

Left = 30 + 5 = 35

Right = 15(2 + x)

So:

$$
15(2 + x) = 35 \Rightarrow 2 + x = \frac{35}{15} = \frac{7}{3} \Rightarrow x = \frac{7}{3} - 2 = \frac{1}{3}
$$

So x = 1/3

But again, not integer.

But maybe the expression is:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → 35 = 15(2 + x)

No integer solution.

Alternatively, maybe it's:

> 5 × 6 + 15 ÷ 3 = 15 × (2 + x) → same

Or perhaps it's:

> 5 × 6 + 15 ÷ 3 = 15 × 2 + 5 → but that's just rewriting.

Wait — maybe the blank is meant to be the value of the expression, not part of the equation.

But it says: "Fill in the blanks"

And the blank is inside the parentheses.

So likely: 15(2 + ___) = 35 → so 2 + ___ = 35/15 = 7/3 → ___ = 1/3

So answer: 1/3

But again, not integer.

Perhaps the problem is:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → and we are to solve for x

So x = 1/3

But maybe the original was:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → and they expect decimal or fraction.

But in context, maybe it's okay.

Alternatively, maybe it's:

> 5 × 6 + 15 ÷ 3 = 15 × (2 + x) → and x = 1/3

So answer: 1/3

But let’s move to problem 6.

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Problem 6: 15 ÷ 2 + 3 ÷ 5 = ?(4 + ___)

This is unclear because of the "?". Perhaps it's a typo and meant to be:

> 15 ÷ 2 + 3 ÷ 5 = 1.5(4 + ___)

But 1.5 × 4 = 6, 1.5 × 5 = 7.5 — not matching.

Wait — 15 ÷ 2 = 7.5, 3 ÷ 5 = 0.6, sum = 8.1

Now, suppose it's:

> 15 ÷ 2 + 3 ÷ 5 = 1.5 × (4 + x)

Then:

1.5(4 + x) = 8.1 → 4 + x = 8.1 / 1.5 = 5.4 → x = 1.4

Still not nice.

Alternatively, maybe it's:

> 15 ÷ 2 + 3 ÷ 5 = (4 + x) × 1.5 → same

Or perhaps it's:

> 15 ÷ 2 + 3 ÷ 5 = (4 + x) × something

But without knowing the multiplier, can't solve.

Wait — maybe the "?" is a placeholder for a number.

But it's written as "?", so likely a typo.

Perhaps it's meant to be:

> 15 ÷ 2 + 3 ÷ 5 = 1.5 × (4 + x)

Then x = 1.4

But not ideal.

Alternatively, maybe it's:

> 15 ÷ 2 + 3 ÷ 5 = 15 ÷ (2 + x) → but that doesn't make sense.

Too many issues.

But let's focus on the ones we can solve clearly.

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Final Answers (Best Effort):

1. –1
2. 0.5 (but likely typo; if it were ___ ÷ (–15) = –30, then 450)
3. –5
4. 28
5. 1/3 (or 0.333...)
6. Unclear due to "?"; possibly typo
7. 10
8. 32
9. 48
10. 8

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Most Likely Corrected Version (Assuming Typos):

Let’s assume:

- Problem 2: ___ ÷ (–15) = –30 → answer: 450
- Problem 5: Maybe it's 5 × 6 + 15 ÷ 3 = 15 × (2 + x) → but still 35 = 15(2 + x) → x = 1/3 → maybe not
- Alternatively, maybe it's: 5 × 6 + 15 ÷ 3 = 15 × 2 + 5 → so the blank is 5? But not matching format.

Wait — maybe it's:

> 5 × 6 + 15 ÷ 3 = 15(2 + x) → and they want x = 1/3

But perhaps the problem is:

> 5 × 6 + 15 ÷ 3 = 15 × (2 + x) → and x = 1/3

So we'll go with that.

For problem 6, perhaps it's:

> 15 ÷ 2 + 3 ÷ 5 = 1.5 × (4 + x) → x = 1.4

But not clean.

Alternatively, maybe it's:

> 15 ÷ 2 + 3 ÷ 5 = (4 + x) × 1.5 → same

So unless there's a better interpretation, let's skip.

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Final Answer Key (Based on Given Problems):

1. –1
2. 0.5 (but likely intended as 450 if problem is reversed)
3. –5
4. 28
5. 1/3
6. Insufficient information / typo
7. 10
8. 32
9. 48
10. 8

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But since the user said "solve the problem", and based on standard integer operations, here are the most plausible answers:

✔ Corrected Answers (Assuming Typo in #2 and #5):

1. –1
2. 450 *(if it's ___ ÷ (–15) = –30)*
3. –5
4. 28
5. 1/3 *(no integer solution)*
6. Unclear
7. 10
8. 32
9. 48
10. 8

But since the worksheet is about multiplying and dividing integers, and only #1, #3, #4, #7, #8, #9, #10 are clear, we can say:

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✔ Final Clean Answers:

1. –1
2. 0.5 *(fractional, not integer)*
3. –5
4. 28
5. 1/3 *(fractional)*
6. Unknown
7. 10
8. 32
9. 48
10. 8

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Conclusion:

The only problems with clear integer answers are:

- 1: –1
- 3: –5
- 4: 28
- 7: 10
- 8: 32
- 9: 48
- 10: 8

Problems 2, 5, and 6 appear to have typos or require non-integer solutions.

If you can confirm the exact wording of problems 2, 5, and 6, I can refine the answers.