Determine the Sign: Solving -4/-0.4 ÷ -1.7 Step by Step

Sign Determination with Mixed Operations

What will be the sign of the result?

40.4:1.7 \frac{-4}{-0.4}:-1.7

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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
00:09 Negative divided by negative always equals positive
00:16 Positive divided by negative always equals negative
00:20 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 sign of the result?

40.4:1.7 \frac{-4}{-0.4}:-1.7

2

Step-by-step solution

In this question, we only need to know whether the resulting number is negative or positive.

In that case, we can rewrite the division exercise as follows:

:= \frac{-}{-}:-=

If we solve the exercise from left to right, we will first divide the numerator of the negative fraction by the denominator of the negative fraction.

Therefore, the resulting fraction will be positive:

=+ \frac{-}{-}=+

Now the remaining exercise will look like this:

+:= +:-=-

Therefore, the sign of the result will be negative.

3

Final Answer

-

Key Points to Remember

Essential concepts to master this topic
  • Division Rule: Negative divided by negative always equals positive
  • Order Technique: Work left to right: 40.4=+10 \frac{-4}{-0.4} = +10 , then +10 ÷ (-1.7)
  • Check: Count negative signs: odd number means negative result ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations when determining signs
    Don't try to determine the final sign by counting all negative signs at once = wrong answer! This ignores that division creates intermediate results. Always work step-by-step from left to right, determining signs after each operation.

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 negative divided by negative positive?

+

Think of it as "opposite of opposite" - when you divide a negative by a negative, you're essentially removing the negative, making it positive. Just like 62=3 \frac{-6}{-2} = 3 !

Can I just count all the negative signs to find the answer?

+

No! You must follow order of operations. In this problem, you first do 40.4 \frac{-4}{-0.4} to get a positive result, then divide by -1.7.

What if I get confused about which operation to do first?

+

Remember PEMDAS! Division operations of equal priority work left to right. So 40.4÷(1.7) \frac{-4}{-0.4} ÷ (-1.7) means do the fraction first, then divide by -1.7.

Is there a shortcut for sign problems?

+

Yes! For multiplication and division, count negative signs in the final expression after following order of operations. Odd count = negative, even count = positive.

Why does the colon (:) mean division?

+

The colon (:) is another way to write division, just like ÷. So a:b a:b means the same as a÷b a ÷ b or ab \frac{a}{b} .

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