Determine the Sign: Solving (-14)÷(+8) in Integer Division

Integer Division with Sign Rules

Determine the resulting sign from the following exercise:

(14):(+8) (-14):(+8)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 First, let's determine the sign of the result.
00:11 We'll check the sign of each number involved.
00:15 Remember, a negative divided by a positive is always negative.
00:20 And that's how we solve this problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine the resulting sign from the following exercise:

(14):(+8) (-14):(+8)

2

Step-by-step solution

We will only look at whether the number is negative or positive.

In other words, the division exercise looks like this:

:+= -:+=

Since we are dividing a negative number by a positive number, the result must be a negative number.

3

Final Answer

-

Key Points to Remember

Essential concepts to master this topic
  • Rule: Negative divided by positive always equals negative
  • Technique: Focus only on signs: ()÷(+)=() (-) ÷ (+) = (-)
  • Check: Calculate full division: (14)÷(+8)=1.75 (-14) ÷ (+8) = -1.75 (negative) ✓

Common Mistakes

Avoid these frequent errors
  • Confusing division sign rules with multiplication rules
    Don't think that dividing two different signs gives positive = wrong sign! This confuses division with addition rules. Always remember: different signs in division give negative results.

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 does negative divided by positive equal negative?

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Think of division as repeated subtraction. When you divide -14 by +8, you're asking "how many times can I subtract 8 from -14?" Since you start with a negative number, the result must be negative!

Are the sign rules the same for multiplication and division?

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Yes! Both follow the same pattern:

  • Same signs: positive result
  • Different signs: negative result

Do I need to calculate the exact decimal answer?

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Not when the question only asks for the sign! Focus on whether the result is positive or negative. However, calculating the full answer (1.75 -1.75 ) can help verify your sign is correct.

What if I have more complex expressions like (-6) ÷ (-3) ÷ (+2)?

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Work left to right: First (6)÷(3)=(+2) (-6) ÷ (-3) = (+2) , then (+2)÷(+2)=(+1) (+2) ÷ (+2) = (+1) . The final result is positive!

How can I remember the sign rules easily?

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Use this simple rule: "Different signs = Negative result" and "Same signs = Positive result". This works for both multiplication and division!

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