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
00:00 Find the unknown
00:03 Positive times negative always equals negative
00:07 Therefore the unknown is negative
00:12 Now let's find the unknown
00:20 This is the unknown, now let's add its sign
00:23 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:

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

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 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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