Solve the Integer Problem: 2 × (-4) Multiplication

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

The answer is negative because you're multiplying by negative 4, not positive 4! The parentheses around (-4) show it's a negative number. Remember: positive × negative = negative.

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

Use this simple pattern:Same signs (+ × + or - × -) = positive resultDifferent signs (+ × - or - × +) = negative resultSince 2 is positive and (-4) is negative, they have different signs, so the answer is negative!

Q: What's the difference between -4 and (-4)?

They mean the same thing! Both represent negative four. The parentheses in (-4) just make it extra clear that the entire number is negative, especially when it follows an operation sign.

Q: Can I do this problem in my head?

Absolutely! Think: 2 times 4 is 8, and positive times negative gives negative, so the answer is -8. With practice, integer multiplication becomes quick mental math!

Q: What if the order was switched to (-4) × 2?

The answer would still be $ -8 $! Multiplication is commutative, meaning the order doesn't matter. Whether it's $ 2 \times (-4) $ or $ (-4) \times 2 $, you get the same result.

Integer Multiplication with Opposite Signs

Complete the following exercise:

$2\cdot(-4)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Negative times positive is always negative

00:14 And this is 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:

$2\cdot(-4)=$

Step-by-step solution

Let's recall the rule:

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

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

$+2\times-4=-8$

Final Answer

$-8$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive times negative always equals negative
Method: Multiply numbers first: 2 × 4 = 8, then apply negative sign
Check: $2 \times (-4) = -8$ because positive × negative = negative ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rules when multiplying integers
Don't just multiply 2 × 4 = 8 and forget about the negative sign! This gives you +8 instead of -8. The negative sign in (-4) changes the final answer. Always remember: positive × negative = 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?

The answer is negative because you're multiplying by negative 4, not positive 4! The parentheses around (-4) show it's a negative number. Remember: positive × negative = negative.

How do I remember the sign rules for multiplication?

Use this simple pattern:

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

Since 2 is positive and (-4) is negative, they have different signs, so the answer is negative!

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

They mean the same thing! Both represent negative four. The parentheses in (-4) just make it extra clear that the entire number is negative, especially when it follows an operation sign.

Can I do this problem in my head?

Absolutely! Think: 2 times 4 is 8, and positive times negative gives negative, so the answer is -8. With practice, integer multiplication becomes quick mental math!

What if the order was switched to (-4) × 2?

The answer would still be $-8$ ! Multiplication is commutative, meaning the order doesn't matter. Whether it's $2 \times (-4)$ or $(-4) \times 2$ , you get the same result.

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