Solve the Multiplication Equation: Finding the Factor in 2 × ? = -8

Multiplication Equations with Negative Products

Fill in the missing number:

2?=8 2\cdot?=-8

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:05 Positive times negative always equals negative
00:09 Therefore the unknown is negative
00:12 Now let's find the unknown
00:18 This is the unknown, now let's add its sign
00:22 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:

2?=8 2\cdot?=-8

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 2 to get 8:

2×4=8 2\times4=8

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

+2×(4)=8 +2\times(-4)=-8

3

Final Answer

4 -4

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Positive times negative equals negative product
  • Technique: Find positive factor first: 2 × 4 = 8, then apply signs
  • Check: Substitute back: 2 × (-4) = -8 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to apply negative sign to the factor
    Don't just solve 2 × ? = 8 and answer 4 = wrong sign! This ignores the negative product requirement. Always check if your factor gives the correct sign when multiplied.

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 2 is positive?

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When you multiply a positive number by a negative number, the result is always negative. Since 2 is positive and we need -8, the missing factor must be negative.

How do I remember the sign rules for multiplication?

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Use this pattern: Same signs = positive, Different signs = negative. Since (+2) × (?) = (-8), the signs are different, so ? must be negative.

What if I got +4 as my answer?

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Check your work! 2×4=8 2 \times 4 = 8 , not -8. You found the right number but forgot the negative sign.

Can I solve this by dividing both sides?

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Yes! Divide both sides by 2: 82=4 \frac{-8}{2} = -4 . This is actually the fastest method for simple multiplication equations.

How do I check if -4 is really correct?

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Substitute back into the original equation: 2×(4)=8 2 \times (-4) = -8 . Since both sides equal -8, your answer is correct!

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