Calculate 3 × (-4): Multiplying a Positive and Negative Integer

Q: Why is the answer negative when I'm multiplying by 4?

You're actually multiplying by negative 4, not positive 4! The parentheses around -4 show it's a negative number. When you multiply a positive by a negative, the result is always negative.

Q: What's the difference between 3 × -4 and 3 - 4?

Multiplication vs. subtraction! $ 3 \times (-4) = -12 $ means 'three groups of negative four.' But $ 3 - 4 = -1 $ means 'three minus four.'

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

Use this pattern: Same signs = positive, Different signs = negative. So (+) × (+) = (+), (-) × (-) = (+), but (+) × (-) = (-) and (-) × (+) = (-).

Q: Can I think of this as repeated addition?

Yes! $ 3 \times (-4) $ means adding -4 three times: -4 + (-4) + (-4) = -12. This helps you see why the answer is negative.

Q: What if the numbers were switched to (-3) × 4?

You'd still get -12! The order doesn't matter in multiplication. Whether it's (+3) × (-4) or (-3) × (+4), different signs always give a negative result.

Integer Multiplication with Opposite Signs

Complete the following exercise:

$3\cdot(-4)=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's learn how to solve this problem.

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

00:18 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:

$3\cdot(-4)=$

Step-by-step solution

Let's remember the rule:

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

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

$+3\times-4=-12$

Final Answer

$-12$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive times negative always equals negative result
Technique: Multiply absolute values first: 3 × 4 = 12, then apply negative sign
Check: Verify sign pattern: (+) × (-) = (-), so 3 × (-4) = -12 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply the negative sign rule
Don't just multiply 3 × 4 = 12 and ignore the negative sign! This gives a positive result when the answer should be negative. Always remember: positive times negative equals negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why is the answer negative when I'm multiplying by 4?

You're actually multiplying by negative 4, not positive 4! The parentheses around -4 show it's a negative number. When you multiply a positive by a negative, the result is always negative.

What's the difference between 3 × -4 and 3 - 4?

Multiplication vs. subtraction! $3 \times (-4) = -12$ means 'three groups of negative four.' But $3 - 4 = -1$ means 'three minus four.'

How do I remember the sign rules for multiplication?

Use this pattern: Same signs = positive, Different signs = negative. So (+) × (+) = (+), (-) × (-) = (+), but (+) × (-) = (-) and (-) × (+) = (-).

Can I think of this as repeated addition?

Yes! $3 \times (-4)$ means adding -4 three times: -4 + (-4) + (-4) = -12. This helps you see why the answer is negative.

What if the numbers were switched to (-3) × 4?

You'd still get -12! The order doesn't matter in multiplication. Whether it's (+3) × (-4) or (-3) × (+4), different signs always give a negative result.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime