Solve (-7) × (-3): Multiplying Two Negative Numbers

Q: Why does negative times negative equal positive?

Think of it like opposite directions! If you walk 7 steps backward (-7) and then reverse that action 3 times (-3), you end up moving forward (+21). The rule is: negative × negative = positive.

Q: How do I remember all the sign rules?

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

Q: What if I had (-7) × (+3) instead?

Then you'd have different signs, so the answer would be negative: (-7) × (+3) = -21. Different signs always give a negative result!

Q: Do I need to write the positive sign in my answer?

You can write $ +21 $ or just $ 21 $ - both are correct! When a number is positive, the + sign is optional but showing it helps demonstrate you understand the sign rules.

Q: How can I double-check my multiplication?

First multiply the absolute values: |−7| × |−3| = 7 × 3 = 21. Then apply the sign rule: negative × negative = positive. So your final answer is $ +21 $!

Integer Multiplication with Negative Factors

Complete the following exercise:

$(-7)\cdot(-3)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:07 Negative times negative is always positive

00:16 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:

$(-7)\cdot(-3)=$

Step-by-step solution

Let's recall the rule:

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

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

$-7\times-3=+21$

Final Answer

$21$

Key Points to Remember

Essential concepts to master this topic

Rule: Two negative numbers multiplied together always give a positive result
Technique: Multiply absolute values first: 7 × 3 = 21, then apply sign rule
Check: Verify (-7) × (-3) = +21 because negative × negative = positive ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rule for negative multiplication
Don't assume (-7) × (-3) = -21 because you see negative signs! This ignores the fundamental rule that negative times negative equals positive. Always remember: two negatives make a positive, so (-7) × (-3) = +21.

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 does negative times negative equal positive?

Think of it like opposite directions! If you walk 7 steps backward (-7) and then reverse that action 3 times (-3), you end up moving forward (+21). The rule is: negative × negative = positive.

How do I remember all the sign rules?

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

What if I had (-7) × (+3) instead?

Then you'd have different signs, so the answer would be negative: (-7) × (+3) = -21. Different signs always give a negative result!

Do I need to write the positive sign in my answer?

You can write $+21$ or just $21$ - both are correct! When a number is positive, the + sign is optional but showing it helps demonstrate you understand the sign rules.

How can I double-check my multiplication?

First multiply the absolute values: |−7| × |−3| = 7 × 3 = 21. Then apply the sign rule: negative × negative = positive. So your final answer is $+21$ !

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