Solve the Equation: Find the Missing Factor in 7 × ? = -21

Integer Multiplication with Negative Products

Fill in the missing number:

7?=21 7\cdot?=-21

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's figure out what the unknown is.
00:09 Remember, when you multiply a positive by a negative, you get a negative.
00:15 So, the unknown must be negative.
00:21 Now, we need to find this unknown value.
00:27 Here it is, let's make sure to add the negative sign.
00:31 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing number:

7?=21 7\cdot?=-21

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 7 in order to get 21:

7×3=21 7\times3=21

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

+7×(3)=21 +7\times(-3)=-21

3

Final Answer

3 -3

Key Points to Remember

Essential concepts to master this topic
  • Rule: Positive times negative always equals negative
  • Technique: Find positive factor first: 7 × 3 = 21, then apply sign
  • Check: Substitute back: 7 × (-3) = -21 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting the negative sign
    Don't just find 7 × ? = 21 and answer 3! This ignores the negative result and gives +21 instead of -21. Always check if your product needs to be positive or negative, then apply the correct sign rules.

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 7 is positive?

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Because we need a negative product (-21)! When one factor is positive and the other is negative, the result is always negative. Since 7 is positive, the missing factor must be negative.

How do I remember the sign rules?

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Think of it like this: same signs give positive (+ × + or - × -), and different signs give negative (+ × - or - × +). Since we need -21, we need different signs!

What if I got +3 as my answer?

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Check your work! If you multiply 7 × 3, you get +21, not -21. The question asks for -21, so you need the negative factor: 3 -3 .

Can I check my answer a different way?

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Yes! Try division: 21÷7=3 -21 ÷ 7 = -3 . Division and multiplication are inverse operations, so this confirms your answer.

Why can't the answer be -7?

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Let's test it: 7×(7)=49 7 × (-7) = -49 , not -21! Always substitute your answer back into the original equation to verify it works.

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