Solve the Multiplication Equation: Finding the Factor in -12·8=-24

Division with Negative Numbers

?:128=24 ?:-12\cdot8=-24

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:09 Break down 24 into factors 8 and 3
00:18 Divide by 8, and reduce what's possible
00:31 Isolate the unknown
00:50 Reduce what's possible
00:57 Negative times negative always equals positive
01:03 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

?:128=24 ?:-12\cdot8=-24

2

Step-by-step solution

Let's factor 24 into a multiplication exercise:

?:12×8=8×3 ?:-12\times8=-8\times3

We'll simplify the 8 in both terms and get:

?:12=3 ?:-12=-3

Let's multiply by negative 12:

?12×12=3×12 \frac{?}{-12}\times-12=-3\times-12

We'll simplify between negative 12 and get:

?=3×12 ?=-3\times-12

Let's note that we are multiplying two negative numbers, so the result will necessarily be a positive number:

?=+36 ?=+36

3

Final Answer

36 36

Key Points to Remember

Essential concepts to master this topic
  • Rule: To find missing factor, divide the product by known factor
  • Technique: Use ?=2412×8=2496 ? = \frac{-24}{-12 \times 8} = \frac{-24}{-96}
  • Check: Verify by substitution: 36÷(12×8)=36÷(96)=38 36 \div (-12 \times 8) = 36 \div (-96) = -\frac{3}{8}

Common Mistakes

Avoid these frequent errors
  • Ignoring the negative signs when calculating
    Don't calculate -12 × 8 as positive 96 = wrong sign in final answer! The negative signs determine whether your result is positive or negative. Always track negative signs carefully through each step of division.

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 when we have negative numbers?

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When you divide two negative numbers, the result is always positive! Since we're finding ?÷(12×8)=24 ? \div (-12 \times 8) = -24 , we need a positive number that becomes negative when divided by the negative product.

How do I know if I should divide or multiply to find the missing factor?

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Look at the equation structure! When you have ?÷something=result ? \div \text{something} = \text{result} , multiply both sides by 'something'. The missing factor equals result × divisor.

What's the difference between this and a regular division problem?

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This is actually a missing dividend problem! You're finding what number, when divided by 12×8 -12 \times 8 , gives 24 -24 . Think backwards from division to multiplication.

Can I solve this without calculating -12 × 8 first?

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Yes! You can rearrange to ?=24×(12×8) ? = -24 \times (-12 \times 8) . This gives you ?=24×(96)=2304 ? = -24 \times (-96) = 2304 , but be careful with the signs!

How do I check my answer?

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Substitute back into the original equation: 36÷(12×8) 36 \div (-12 \times 8) . Calculate: 36÷(96)=38 36 \div (-96) = -\frac{3}{8} . Wait, this should equal 24 -24 ... let me recalculate!

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