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

Solve the following exercise:

\( (+6)\cdot(+9)= \)

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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