Solve the Equation: Finding the Missing Factor in (-3)⬜ = -15

Division Properties with Negative Numbers

Fill in the missing number:

(3)=15 (-3)\cdot⬜=-15

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's start by finding the unknown number.
00:15 Remember, a negative times a positive always gives us a negative.
00:19 So, the unknown number must be positive.
00:23 Let's work together to discover what this unknown number is.
00:34 And there you have it! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing number:

(3)=15 (-3)\cdot⬜=-15

2

Step-by-step solution

Let's remember the rule:

(x)×(+x)=x (-x)\times(+x)=-x

Let's think about what number we need to multiply by 3 to get 15:

3×5=15 3\times5=15

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

3×(+5)=15 -3\times(+5)=-15

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Rule: To find missing factor, divide the product by known factor
  • Technique: Calculate 15÷(3)=5 -15 ÷ (-3) = 5 using division
  • Check: Verify by multiplying: (3)×5=15 (-3) × 5 = -15

Common Mistakes

Avoid these frequent errors
  • Forgetting sign rules when working with negative numbers
    Don't just focus on the numbers 3 and 15 without considering signs = wrong answer like -5! This ignores that negative times positive equals negative. Always apply sign rules: (-3) × (+5) = -15.

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 positive 5 and not negative 5?

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Remember the sign rules! Since (3)×=15 (-3) × ⬜ = -15 , we need a positive number. Negative times positive gives negative: (3)×(+5)=15 (-3) × (+5) = -15 .

How do I know which operation to use?

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Since we have multiplication with a missing factor, use division! Divide the product by the known factor: 15÷(3)=5 -15 ÷ (-3) = 5 .

What if I get confused about the signs?

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Think step by step: What times 3 gives 15? That's 5. Now apply signs: negative times positive gives negative, so (3)×(+5)=15 (-3) × (+5) = -15 .

Can I check my answer a different way?

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Yes! Use the opposite operation. Since (3)×5=15 (-3) × 5 = -15 , then 15÷(3)=5 -15 ÷ (-3) = 5 and 15÷5=3 -15 ÷ 5 = -3 .

Why does negative divided by negative equal positive?

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Think of it as opposite directions! When you divide two negatives, you're going in the 'opposite of opposite' direction, which brings you back to positive. (15)÷(3)=+5 (-15) ÷ (-3) = +5 .

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