Solve the Multiplication Equation: (-3) × ? = -9

Division from Multiplication with Negative Integers

Fill in the missing number:

(3)?=9 (-3)\cdot?=-9

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:04 Negative times positive always equals negative
00:08 Therefore the unknown is positive
00:14 Now let's find the unknown
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing number:

(3)?=9 (-3)\cdot?=-9

2

Step-by-step solution

Remember the following law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 3 to get 9:

3×3=9 3\times3=9

Now let's put the numbers together with the appropriate sign as written in the law above as follows:

3×(+3)=9 -3\times(+3)=-9

3

Final Answer

3 3

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Negative times positive equals negative product
  • Division Method: Solve -3 × ? = -9 by calculating -9 ÷ (-3)
  • Check: Substitute back: (-3) × 3 = -9 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting negative sign rules in division
    Don't assume the answer is negative just because you see negative numbers = wrong sign! When dividing two negatives, the result is positive. Always remember: negative ÷ negative = positive.

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 positive 3 instead of negative 3?

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Great question! Remember that (-3) × (+3) = -9. The negative and positive multiply to give a negative result. If we used -3 instead, we'd get (3)×(3)=+9 (-3) \times (-3) = +9 , which is wrong!

How do I remember the sign rules for multiplication?

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Use this simple pattern: same signs = positive, different signs = negative. So (+) × (+) = (+), (-) × (-) = (+), but (+) × (-) = (-) and (-) × (+) = (-).

Can I just ignore the signs and add them later?

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Never ignore the signs! They're part of the number and change the entire answer. Always work with the complete numbers, including their signs, from the very beginning.

What's the fastest way to solve this type of problem?

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Think of it as division! If (-3) × ? = -9, then ? = (-9) ÷ (-3). Dividing -9 by -3 gives you +3 because you're dividing two negatives.

How can I check if my answer is correct?

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Always substitute back! Take your answer and multiply: (3)×3=9 (-3) \times 3 = -9 . If you get the original right side (-9), you're correct! ✓

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