Solve for Missing Divisor in -9×-7÷?=-3: Step-by-Step Solution

Division with Negative Products

97:?=3 -9\cdot-7:?=-3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 First, let's find the unknown value.
00:10 Next, write the division as a fraction. This makes it easier to work with.
00:22 Remember, a negative number times another negative always equals a positive.
00:36 Now, let's isolate the unknown variable by getting it alone on one side.
00:59 We can factor nine into three times three to help us simplify.
01:05 Let's reduce or simplify any terms we can.
01:11 Remember, positive divided by negative always equals negative.
01:20 And there you have it! This is the solution to our problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

97:?=3 -9\cdot-7:?=-3

2

Step-by-step solution

Let's write the exercise in the following way:

9×7?=3 \frac{-9\times-7}{?}=-3

Note that in the numerator we are multiplying between two negative numbers, therefore the result must be a positive number:

9×7?=3 \frac{9\times7}{?}=-3

Let's multiply by the question mark and get:

9×7=3×? 9\times7=-3\times\text{?}

Let's divide by negative 3 and get:

9×73=? \frac{9\times7}{-3}=\text{?}

Let's factor the 9 into a multiplication exercise:

3×3×73=? \frac{3\times3\times7}{-3}=\text{?}

Let's reduce between the 3 in the numerator and denominator, noting that we are dividing a positive number by a negative number, therefore the result must be a negative number:

3×7=? -3\times7=\text{?}

21=? -21=\text{?}

3

Final Answer

21 -21

Key Points to Remember

Essential concepts to master this topic
  • Product Rule: Multiplying two negative numbers gives a positive result
  • Technique: Rewrite 9×7÷?=3 -9 \times -7 \div ? = -3 as 63?=3 \frac{63}{?} = -3
  • Check: Substitute back: 9×7÷(21)=63÷(21)=3 -9 \times -7 \div (-21) = 63 \div (-21) = -3

Common Mistakes

Avoid these frequent errors
  • Treating multiplication and division as separate problems
    Don't solve 9×7 -9 \times -7 first and forget about the division = wrong setup! This ignores the order of operations and structure. Always rewrite the expression as a single fraction to see the relationship clearly.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( (+6)\cdot(+9)= \)

FAQ

Everything you need to know about this question

Why does negative times negative equal positive?

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Think of it as "opposite of opposite" - when you reverse a negative direction twice, you end up going positive! So 9×7=+63 -9 \times -7 = +63 .

How do I know what sign the answer should have?

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Look at the final result you need: -3 is negative. Since 63÷?=3 63 \div ? = -3 , you need to divide a positive by a negative to get negative, so ? must be negative.

Can I solve this without rewriting as a fraction?

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You could work left to right, but rewriting as a fraction makes the relationship clearer: 63?=3 \frac{63}{?} = -3 shows you need 63 ÷ ? = -3 directly.

What if I got positive 21 instead?

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Check your signs! If you got +21, you probably forgot that dividing positive by positive gives positive, but we need -3. The divisor must be negative to make the quotient negative.

How can I verify my answer is correct?

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Substitute back step by step: 9×7=63 -9 \times -7 = 63 , then 63÷(21)=3 63 \div (-21) = -3 ✓. Both steps should give you the expected result!

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