Solve: Finding the Sign of -4/(-0.4) ÷ -1.7 in Mathematics

Sign Determination with Mixed Operations

Will the exercise result in a negative or a positive sign:

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 what sign each number has
00:20 Positive divided by negative is always negative
00:27 Negative multiplied by negative is always positive
00:33 Positive divided by negative is always negative
00:36 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

Will the exercise result in a negative or a positive sign:

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

2

Step-by-step solution

We are only concentrating on whether the number is negative or positive.

In other words, the exercise should look like this:

×+:= -\times\frac{+}{-}:-=

If we solve the exercise from left to right, we must first multiply the fraction:

×+= -\times\frac{+}{-}=

Since the numerator of the fraction is positive and divides by the negative denominator, the resulting fraction will be negative.

Therefore the remaining exercise is as follows:

×:= -\times-:-=

If we then multiply minus by minus, we should obtain a positive number:

×=+ -\times-=+

The resulting exercise is:

+:= +:-=-

Therefore, the resulting sign of the exercise will be negative.

3

Final Answer

-

Key Points to Remember

Essential concepts to master this topic
  • Sign Rules: Negative divided by negative equals positive
  • Order: First evaluate 40.4=+10 -\frac{4}{-0.4} = +10 , then divide by -1.7
  • Check: Count negatives: one negative in final division gives negative result ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations with signs
    Don't treat all operations equally and work left to right without considering fractions first = wrong sign! The fraction must be evaluated completely before dividing by -1.7. Always handle fractions as single units first, then continue with remaining operations.

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 do I need to solve the fraction first before dividing by -1.7?

+

The fraction 40.4 -\frac{4}{-0.4} is one complete unit that must be calculated first. Think of it like solving what's in parentheses - you get +10, then divide +10 by -1.7.

How do I keep track of all these negative signs?

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Break it down step by step: negative divided by negative = positive, then positive divided by negative = negative. Count the negatives at each step!

What if I just multiply the negatives without doing the actual division?

+

That works perfectly for determining the sign only! You can ignore the numbers 4, 0.4, and 1.7, and just focus on: ()÷()÷()=() (-) ÷ (-) ÷ (-) = (-)

Why does negative divided by negative equal positive?

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Think of division as "how many times does the divisor go into the dividend?" When both numbers point in opposite directions from zero, the result points in the positive direction.

Can I use a calculator to check my sign work?

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Absolutely! Calculate 4÷(0.4)÷(1.7) -4 ÷ (-0.4) ÷ (-1.7) and see if your answer is negative or positive. This confirms your sign reasoning.

What's the difference between : and ÷ symbols?

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Both : and ÷ mean division - they're just different notation styles. In this problem, 40.4:1.7 -\frac{4}{-0.4}:-1.7 means the same as 40.4÷(1.7) -\frac{4}{-0.4} ÷ (-1.7)

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