Division Problem: Determining the Sign of (-7) ÷ (-3/5)

Division Signs with Negative Fractions

What will be the resulting sign from the following exercise?

(7):(35) (-7):(-\frac{3}{5})

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the result sign
00:03 Let's find the sign of each number
00:07 Negative divided by negative always equals positive
00:10 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

What will be the resulting sign from the following exercise?

(7):(35) (-7):(-\frac{3}{5})

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 negative number, the result must be a positive number.

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Negative divided by negative always equals positive
  • Technique: Look at signs only: ()÷()=(+) (-) \div (-) = (+)
  • Check: Calculate full answer: (7)÷(35)=+353 (-7) \div (-\frac{3}{5}) = +\frac{35}{3}

Common Mistakes

Avoid these frequent errors
  • Mixing up sign rules with different operations
    Don't think negative ÷ negative = negative like subtraction! This gives the wrong sign every time. Division and multiplication follow the same sign rules: two negatives always make a positive.

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 negative equal positive?

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Think of division as "how many groups". If you remove 3 negative objects at a time from 7 negative objects, you're doing a positive action! The two negatives cancel each other out.

Is this the same rule as multiplication?

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Yes! Division and multiplication use identical sign rules: same signs = positive, different signs = negative. Remember: ()×()=(+) (-) \times (-) = (+) and ()÷()=(+) (-) \div (-) = (+)

Do I need to calculate the actual number?

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Not always! When the question only asks for the sign, just focus on whether it's positive or negative. But calculating the full answer is great practice!

What if one number is positive and one is negative?

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Then the result is negative! Different signs always give a negative result: (+)÷()=() (+) \div (-) = (-) and ()÷(+)=() (-) \div (+) = (-)

How can I remember the sign rules?

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  • Same signs: "Friends agree" = positive result
  • Different signs: "Enemies disagree" = negative result

This works for both multiplication and division!

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