Solve: -6·6÷-3÷? = 24 | Sequential Division Challenge

Sequential Division with Missing Divisors

66:3:?=24 -6\cdot6:-3:?=24

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:05 Write division as a fraction
00:12 Factor 6 into factors 3 and 2
00:25 Reduce what is possible
00:33 Isolate the unknown
00:57 Factor 24 into factors 12 and 2
01:02 Reduce what is possible
01:06 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

66:3:?=24 -6\cdot6:-3:?=24

2

Step-by-step solution

Let's write the exercise in the following form:

6×63:?=24 \frac{-6\times6}{-3}:?=24

We'll factor the 6 in the numerator into a multiplication exercise:

3×2×63:?=24 \frac{-3\times2\times6}{-3}:?=24

We'll cancel out the minus 3 found in the numerator and denominator of the fraction and get:

12:?=24 12:?=24

We'll multiply the question mark:

12=24×? 12=24\times?

We'll divide by 24:

1224=? \frac{12}{24}=?

We'll factor 24 into a multiplication exercise:

1212×2=? \frac{12}{12\times2}=\text{?}

We'll cancel out the 12 in the numerator and denominator of the fraction:

12=? \frac{1}{2}=\text{?}

3

Final Answer

12 \frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Order: Perform operations left to right after handling multiplication first
  • Technique: Convert -6×6÷(-3)÷? to 12÷? = 24 by simplifying
  • Check: Verify 12÷(1/2) = 12×2 = 24 ✓

Common Mistakes

Avoid these frequent errors
  • Solving for ? without simplifying the left side first
    Don't jump straight to finding ? = 12÷24 = 1/2 without calculating -6×6÷(-3) first! This skips crucial steps and can lead to sign errors. Always simplify the left side completely: -36÷(-3) = 12, then solve 12÷? = 24.

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 do I need to calculate -6×6÷(-3) before finding the missing divisor?

+

You must follow the order of operations and simplify the known parts first! Calculate 6×6÷(3)=12 -6 \times 6 ÷ (-3) = 12 , then solve the simpler equation 12÷?=24 12 ÷ ? = 24 .

How do I handle the negative signs in this problem?

+

Negative times positive = negative: 6×6=36 -6 \times 6 = -36
Negative divided by negative = positive: 36÷(3)=12 -36 ÷ (-3) = 12
Keep track of signs at each step!

Why is the answer 1/2 and not 2?

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When 12÷?=24 12 ÷ ? = 24 , we need a number that makes 12 larger when divided by it. Since 12÷12=12×2=24 12 ÷ \frac{1}{2} = 12 \times 2 = 24 , the answer is 12 \frac{1}{2} .

What's the difference between ÷ and the fraction bar?

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The colon (:) and division symbol (÷) mean the same thing - divide! The expression 6×6÷(3) -6 \times 6 ÷ (-3) can also be written as 6×63 \frac{-6 \times 6}{-3} .

How can I check my answer is correct?

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Substitute 12 \frac{1}{2} back into the original equation:
6×6÷(3)÷12=12÷12=12×2=24 -6 \times 6 ÷ (-3) ÷ \frac{1}{2} = 12 ÷ \frac{1}{2} = 12 \times 2 = 24

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