Solve (+10):(-5): Integer Division with Sign Rules

Q: Why is the answer negative when I'm dividing two numbers?

The sign rule determines the result! When you divide numbers with opposite signs (one positive, one negative), the answer is always negative. Think of it as: different signs = negative result.

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

Use this memory trick: same signs = positive, different signs = negative. So (+)÷(+) = (+), (-)÷(-) = (+), but (+)÷(-) = (-) and (-)÷(+) = (-).

Integer Division with Opposite Signs

$(+10):(-5)=$

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Step-by-step video solution

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00:00 Solve

00:03 Positive divided by negative is always negative

00:07 Let's calculate the quotient

00:10 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

$(+10):(-5)=$

Step-by-step solution

Due to the fact that we are dividing a positive number by a negative number, the result must be a negative number:

$+:-=-$

Therefore:

$-(10:5)=-2$

Final Answer

$-2$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by negative always equals negative
Technique: Apply sign first: (+10)÷(-5) = -(10÷5) = -2
Check: Multiply answer by divisor: (-2)×(-5) = +10 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the sign rule when dividing
Don't just divide 10÷5 = 2 and ignore the signs! This gives a positive answer when it should be negative. Always apply the sign rule first: positive÷negative = negative result.

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 negative when I'm dividing two numbers?

The sign rule determines the result! When you divide numbers with opposite signs (one positive, one negative), the answer is always negative. Think of it as: different signs = negative result.

What's the difference between (+10):(-5) and (-10):(+5)?

Both give the same answer: -2! In both cases, you're dividing numbers with opposite signs, so the result is negative. The colon (:) just means division (÷).

How do I remember the sign rules for division?

Use this memory trick: same signs = positive, different signs = negative. So (+)÷(+) = (+), (-)÷(-) = (+), but (+)÷(-) = (-) and (-)÷(+) = (-).

Can I check my answer without using multiplication?

Yes! Think logically: if I have 10 positive things and divide them into 5 negative groups, each group must be negative 2. The negative sign makes sense!

What if the numbers were switched to (-10):(+5)?

You'd still get -2! The rule stays the same: negative÷positive = negative. The order doesn't change the sign rule for division.

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