Solve 30 × (-2): Multiplying with Negative Numbers

Q: Why is 30 × (−2) negative instead of positive?

Because of the multiplication sign rule: when you multiply a positive number by a negative number, the result is always negative. Think of it as 30 groups of −2, which gives you −60 total.

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

Use this simple pattern: Same signs = positive (+ × + or − × −), Different signs = negative (+ × − or − × +). Since 30 is positive and −2 is negative, they're different, so the answer is negative.

Q: What if I accidentally got +60 as my answer?

You forgot to apply the negative sign! Remember that $ 30 \times (-2) $ means you're multiplying by negative two, not just two. Always check your sign first.

Q: Is there a difference between −30 × 2 and 30 × (−2)?

No difference at all! Both equal −60 because you're still multiplying one positive and one negative number. The parentheses just help clarify which number is negative.

Q: How can I check if my answer is correct?

Use the sign rule: positive × negative = negative. Since 30 is positive and −2 is negative, your answer must be negative. Then multiply the absolute values: $ 30 \times 2 = 60 $, so the final answer is −60.

Integer Multiplication with Negative Factors

Complete the following exercise:

$30\cdot(-2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem together. Ready?

00:13 Remember, when a positive number is multiplied by a negative number, the result is always negative.

00:22 And that's how we find the answer! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the following exercise:

$30\cdot(-2)=$

Step-by-step solution

Let's recall the law:

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

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

$+30\times-2=-60$

Final Answer

$-60$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive times negative always equals negative
Calculation: Multiply absolute values: 30 × 2 = 60, then apply negative sign
Check: Verify sign pattern: (+)(−) = (−), so 30 × (−2) = −60 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to apply the negative sign
Don't just multiply 30 × 2 = 60 and ignore the negative! This gives the wrong sign and incorrect answer. Always remember: positive × negative = negative, so 30 × (−2) must equal −60.

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 30 × (−2) negative instead of positive?

Because of the multiplication sign rule: when you multiply a positive number by a negative number, the result is always negative. Think of it as 30 groups of −2, which gives you −60 total.

How do I remember the sign rules for multiplication?

Use this simple pattern: Same signs = positive (+ × + or − × −), Different signs = negative (+ × − or − × +). Since 30 is positive and −2 is negative, they're different, so the answer is negative.

What if I accidentally got +60 as my answer?

You forgot to apply the negative sign! Remember that $30 \times (-2)$ means you're multiplying by negative two, not just two. Always check your sign first.

Is there a difference between −30 × 2 and 30 × (−2)?

No difference at all! Both equal −60 because you're still multiplying one positive and one negative number. The parentheses just help clarify which number is negative.

How can I check if my answer is correct?

Use the sign rule: positive × negative = negative. Since 30 is positive and −2 is negative, your answer must be negative. Then multiply the absolute values: $30 \times 2 = 60$ , so the final answer is −60.

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