Solve the Multiplication Equation: 10 × ? = -100

Multiplication Equations with Negative Products

Fill in the missing number:

10?=100 10\cdot?=-100

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's find the unknown value, together.
00:11 Remember: Positive times negative always equals negative.
00:16 So, the unknown value must be negative.
00:19 Now, let's identify the unknown number.
00:27 Here's our unknown number. Don't forget, it's negative.
00:32 And that's the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing number:

10?=100 10\cdot?=-100

2

Step-by-step solution

Let's remember the law:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about which number we need to multiply by 10 to get 100:

10×10=100 10\times10=100

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

+10×(10)=100 +10\times(-10)=-100

3

Final Answer

10 -10

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Positive times negative always equals negative product
  • Technique: Find positive solution first: 10 × 10 = 100
  • Check: Substitute back: 10 × (-10) = -100 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the negative sign requirement
    Don't just solve 10 × ? = 100 and answer 10! This ignores that we need -100, not +100. The positive product gives the wrong sign. Always check if your answer matches the required sign in the equation.

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 10 is positive?

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Since we need a negative product (-100) and we're multiplying by a positive number (10), the missing number must be negative. Remember: positive × negative = negative!

How do I remember the sign rules for multiplication?

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Use this simple pattern: Same signs make positive, different signs make negative. So (+10) × (-10) = -100 because the signs are different.

What if I got +10 as my answer?

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Check your work! If you multiply 10 × 10, you get +100, not -100. The problem asks for 10×?=100 10 \times ? = -100 , so you need the negative version.

Can I check my answer a different way?

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Yes! Think about it as division: 100÷10=10 -100 \div 10 = -10 . This confirms that -10 is the correct missing number.

Why does the order of positive and negative matter?

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Actually, it doesn't for multiplication! Both (+10)×(10) (+10) \times (-10) and (10)×(+10) (-10) \times (+10) equal -100. Multiplication is commutative with signs too.

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