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

Convert \( \frac{7}{2} \)into its reciprocal form:

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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