Solve Division Problem: Finding the Quotient of -9 ÷ -3

Q: Why is the answer positive when both numbers are negative?

When you divide two numbers with the same sign (both negative), the result is always positive. Think of it as: negative ÷ negative = positive, just like positive ÷ positive = positive.

Q: How can I remember the sign rules for division?

Use this simple rule: Same signs = positive result, Different signs = negative result. So (-9) ÷ (-3) has same signs, giving +3!

Q: What if I wrote this as a fraction instead?

Perfect! $ \frac{-9}{-3} $ is the same as (-9) ÷ (-3). The negative signs cancel out when dividing, leaving you with $ \frac{9}{3} = 3 $.

Q: How do I check if my division answer is correct?

Multiply your answer by the divisor! If $ 3 \times (-3) = -9 $, then your division is correct. This works because division and multiplication are opposite operations.

Q: Would the answer be different if it was -9 ÷ 3?

Yes! With different signs (negative ÷ positive), the answer would be $ -3 $. Different signs always give negative results in division.

Integer Division with Negative Numbers

Solve the following problem:

$-9:-3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Let's break down 9 into factors 3 and 3

00:11 Let's reduce what we can

00:17 Negative divided by negative is always positive

00:21 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$-9:-3=$

Step-by-step solution

Let's write the exercise in the form of a simple fraction:

$\frac{-9}{-3}=$

We'll factor the numerator of the fraction into a multiplication exercise:

$\frac{-3\times3}{-3}=$

We'll cancel out the 3 in the numerator and denominator of the fraction.

Remember that since we are dividing a negative number by a negative number, the result must be a positive number.

Therefore, the answer is:

$3$

Final Answer

$3$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing two negative numbers always gives a positive result
Technique: Factor numerator: $\frac{-3 \times 3}{-3}$ then cancel common factors
Check: Multiply answer by divisor: $3 \times (-3) = -9$ ✓

Common Mistakes

Avoid these frequent errors

Getting confused about signs and choosing -3
Don't think that dividing negative numbers gives negative results = wrong sign! This ignores the fundamental rule that negative ÷ negative = positive. Always remember: same signs divide to positive, different signs divide to negative.

Practice Quiz

Test your knowledge with interactive questions

Convert $\frac{7}{2}$ into its reciprocal form:

FAQ

Everything you need to know about this question

Why is the answer positive when both numbers are negative?

When you divide two numbers with the same sign (both negative), the result is always positive. Think of it as: negative ÷ negative = positive, just like positive ÷ positive = positive.

How can I remember the sign rules for division?

Use this simple rule: Same signs = positive result, Different signs = negative result. So (-9) ÷ (-3) has same signs, giving +3!

What if I wrote this as a fraction instead?

Perfect! $\frac{-9}{-3}$ is the same as (-9) ÷ (-3). The negative signs cancel out when dividing, leaving you with $\frac{9}{3} = 3$ .

How do I check if my division answer is correct?

Multiply your answer by the divisor! If $3 \times (-3) = -9$ , then your division is correct. This works because division and multiplication are opposite operations.

Would the answer be different if it was -9 ÷ 3?

Yes! With different signs (negative ÷ positive), the answer would be $-3$ . Different signs always give negative results in division.

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