Solve the Integer Problem: (-1) × 4 Step by Step

Q: Why is (-1) × 4 negative instead of positive?

When you multiply a negative number by a positive number, the result is always negative. Think of it as taking 4 groups of -1, which gives you -1 + (-1) + (-1) + (-1) = -4.

Q: How do I remember the sign rules for multiplication?

Use this simple pattern:Same signs (+ × + or - × -) = positiveDifferent signs (+ × - or - × +) = negativeSince (-1) and 4 have different signs, the answer is negative!

Q: Can I use repeated addition to check my answer?

Yes! $ (-1) \times 4 $ means "add -1 four times": -1 + (-1) + (-1) + (-1) = -4. This confirms our answer and helps you visualize why the result is negative.

Q: What if the problem was (-1) × (-4) instead?

Then the answer would be positive 4! When both numbers are negative, the result is positive. Remember: negative × negative = positive.

Integer Multiplication with Negative Numbers

Complete the following exercise:

$(-1)\cdot4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem together.

00:13 Remember, negative times positive always gives a negative result.

00:20 And that's how we find the solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$(-1)\cdot4=$

Step-by-step solution

Let's remember the rule:

$(+x)\times(-x)=-x$

Therefore, the sign of the exercise result will be negative:

$-1\times+4=-4$

Final Answer

$-4$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative times positive always gives a negative result
Technique: Apply sign rule first: (-1) × (+4) = -4
Check: Verify using number line or repeated addition: -1 + (-1) + (-1) + (-1) = -4 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't ignore the negative sign and write +4 instead of -4! This happens when students focus only on multiplying the numbers (1 × 4 = 4) but forget the sign rule. Always apply the sign rule first: negative × positive = negative.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why is (-1) × 4 negative instead of positive?

When you multiply a negative number by a positive number, the result is always negative. Think of it as taking 4 groups of -1, which gives you -1 + (-1) + (-1) + (-1) = -4.

What's the difference between (-1) × 4 and 1 × (-4)?

Both equal -4! The order doesn't matter in multiplication. Whether it's $(-1) \times 4$ or $1 \times (-4)$ , you're multiplying one negative and one positive number, so the answer is negative.

How do I remember the sign rules for multiplication?

Use this simple pattern:

Same signs (+ × + or - × -) = positive
Different signs (+ × - or - × +) = negative

Since (-1) and 4 have different signs, the answer is negative!

Can I use repeated addition to check my answer?

Yes! $(-1) \times 4$ means "add -1 four times": -1 + (-1) + (-1) + (-1) = -4. This confirms our answer and helps you visualize why the result is negative.

What if the problem was (-1) × (-4) instead?

Then the answer would be positive 4! When both numbers are negative, the result is positive. Remember: negative × negative = positive.

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