Solve -x/-(-y): Double Negative Fraction with Values 4 and 1/3

Double Negative Rules with Fraction Division

x(y) \frac{-x}{-(-y)}

Substitute the following into the equation above and calculate:

  1. y=13,x=4 y=-\frac{1}{3},x=4

  2. y=+13,x=4 y=+\frac{1}{3},x=-4

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Set up and calculate
00:05 Let's start by setting up the first option
00:10 Make sure to use parentheses
00:15 Negative times negative always equals positive
00:25 Negative divided by negative always equals positive
00:34 Instead of dividing, multiply by the reciprocal
00:40 This is the solution for option A, now let's calculate option B
00:43 Let's set up according to the data for option B
00:48 Make sure to use parentheses
00:54 Negative times negative always equals positive
01:04 Positive divided by positive always equals positive
01:15 Instead of dividing, multiply by the reciprocal
01:20 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

x(y) \frac{-x}{-(-y)}

Substitute the following into the equation above and calculate:

  1. y=13,x=4 y=-\frac{1}{3},x=4

  2. y=+13,x=4 y=+\frac{1}{3},x=-4

2

Step-by-step solution

Let's start with the first option.

Let's substitute the numbers in the given expression:

4((13)= \frac{-4}{-(-(-\frac{1}{3})}=

Let's remember the rule:

(x)=+x -(-x)=+x

Therefore:

4(+13)= \frac{-4}{-(+\frac{1}{3})}=

Let's remember the rule:

(+x)=x -(+x)=-x

Now the exercise we got is:

413= \frac{-4}{-\frac{1}{3}}=

Note that we are dividing between two negative numbers, so the result must be a positive number:

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

413= \frac{4}{\frac{1}{3}}=

Let's convert the division to multiplication and remember to switch between the numerator and denominator of the simple fraction:

4×31=121=12 4\times\frac{3}{1}=\frac{12}{1}=12

Let's move on to solve the second option.

Let's substitute the numbers in the given expression:

(4)((+13)= \frac{-(-4)}{-(-(+\frac{1}{3})}=

Let's remember the rules:

(x)=+x -(-x)=+x

(+x)=x -(+x)=-x

Now we get:

+4(13)=+4+13= \frac{+4}{-(-\frac{1}{3})}=\frac{+4}{+\frac{1}{3}}=

Note that we are dividing between two positive numbers, so the result must be a positive number:

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

Let's convert the division to multiplication and remember to switch between the numerator and denominator of the simple fraction:

4×31=121=12 4\times\frac{3}{1}=\frac{12}{1}=12

The final answer is:

1,2=+12 1,2=+12

3

Final Answer

1,2=+12 1,2=+12

Key Points to Remember

Essential concepts to master this topic
  • Double Negative Rule: Two negative signs cancel out to become positive
  • Technique: Simplify (y) -(-y) to +y +y first, then divide
  • Check: Both cases should give +12 when signs are handled correctly ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the double negative in the denominator
    Don't leave (y) -(-y) as is = wrong signs throughout! Students often miss that (y)=+y -(-y) = +y , leading to incorrect negative results. Always simplify double negatives first before substituting values.

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 -(-y) become +y?

+

The double negative rule states that two negative signs cancel each other out. Think of it as: "the negative of a negative is positive". So (13)=+13 -(-\frac{1}{3}) = +\frac{1}{3} .

How do I handle the negative in front of x?

+

The x -x in the numerator stays as is initially. Only after simplifying the denominator do you substitute the actual values. So x -x with x=4 x = 4 becomes 4 -4 .

Why do both answers come out to +12?

+

Both cases result in dividing two numbers with the same sign. Case 1: 413 \frac{-4}{-\frac{1}{3}} (negative ÷ negative = positive). Case 2: +4+13 \frac{+4}{+\frac{1}{3}} (positive ÷ positive = positive).

How do I divide by a fraction like 1/3?

+

To divide by a fraction, multiply by its reciprocal. So 4÷13=4×31=4×3=12 4 ÷ \frac{1}{3} = 4 × \frac{3}{1} = 4 × 3 = 12 . Remember: flip the fraction and multiply!

What if I get confused with all the negative signs?

+

Take it step by step! First simplify (y) -(-y) to +y +y , then substitute values, and finally apply the division rule for signs. Don't try to do everything at once.

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