Calculate the Product: 2 Times (-7) Integer Multiplication

Q: Why is positive times negative always negative?

Think of it as repeated subtraction! When you have $ 2 \times (-7) $, you're adding -7 twice: -7 + (-7) = -14. Adding negative numbers always gives a negative result.

Q: How do I remember all the sign rules?

Use this simple pattern: Same signs = positive, Different signs = negative. Since 2 is positive and -7 is negative (different signs), the answer must be negative!

Q: What if I have trouble with negative numbers?

Try using a number line! Start at 0, then take 2 jumps of 7 units to the left (negative direction). You'll land on -14.

Q: Is there a faster way to do this?

Yes! First multiply the absolute values: $ 2 \times 7 = 14 $. Then apply the sign rule: positive × negative = negative, so the answer is -14.

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

Use the commutative property: $ 2 \times (-7) $ should equal $ (-7) \times 2 $. Both give -14, confirming your answer is correct!

Integer Multiplication with Opposite Signs

Complete the following exercise:

$2\cdot(-7)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Positive times negative 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:

$2\cdot(-7)=$

Step-by-step solution

Let's recall the rule:

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

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

$+2\times-7=-14$

Final Answer

$-14$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive times negative always equals negative
Technique: Calculate $2 \times 7 = 14$ , then apply negative sign
Check: Verify $2 \times (-7) = -14$ using number line ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't just multiply 2 × 7 = 14 and forget the sign! This ignores the negative factor and gives a positive result instead of negative. Always apply the sign rule: positive × negative = negative.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$(+6)\cdot(+9)=$

FAQ

Everything you need to know about this question

Why is positive times negative always negative?

Think of it as repeated subtraction! When you have $2 \times (-7)$ , you're adding -7 twice: -7 + (-7) = -14. Adding negative numbers always gives a negative result.

How do I remember all the sign rules?

Use this simple pattern: Same signs = positive, Different signs = negative. Since 2 is positive and -7 is negative (different signs), the answer must be negative!

What if I have trouble with negative numbers?

Try using a number line! Start at 0, then take 2 jumps of 7 units to the left (negative direction). You'll land on -14.

Is there a faster way to do this?

Yes! First multiply the absolute values: $2 \times 7 = 14$ . Then apply the sign rule: positive × negative = negative, so the answer is -14.

How can I check if my answer is right?

Use the commutative property: $2 \times (-7)$ should equal $(-7) \times 2$ . Both give -14, confirming your answer is correct!

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