Solve: (-1/7) - (-7/7) Negative Fraction Subtraction

Q: Why does subtracting a negative become addition?

Think of it as removing a debt! If you owe someone $7 and that debt is cancelled, it's the same as gaining $7. So $ -(-7) = +7 $.

Q: How do I remember the double negative rule?

Use the phrase "minus a minus makes a plus". The two negative signs cancel each other out, just like (-1) × (-1) = +1.

Q: Why is 7/7 equal to 1?

Any fraction where the numerator equals the denominator equals 1, because you're dividing something by itself. $ \frac{7}{7} = \frac{5}{5} = \frac{100}{100} = 1 $

Q: How do I add fractions with the same denominator?

Keep the same denominator and add the numerators: $ -\frac{1}{7} + \frac{7}{7} = \frac{-1+7}{7} = \frac{6}{7} $

Q: Should my answer be positive or negative?

Since we're adding $ -\frac{1}{7} + 1 $, and 1 is larger than $ \frac{1}{7} $, the result $ \frac{6}{7} $ should be positive!

Fraction Subtraction with Double Negatives

Solve the following exercise:

$(-\frac{1}{7})-(-\frac{7}{7})=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$(-\frac{1}{7})-(-\frac{7}{7})=$

Step-by-step solution

Let's position minus $\frac{1}{7}$ on the number line and move one step to the right, since $\frac{7}{7}=\frac{1}{1}=1$

We should note that our result is a positive number:

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form and solve it:

$-\frac{1}{7}+1=\frac{6}{7}$

Final Answer

$\frac{6}{7}$

Key Points to Remember

Essential concepts to master this topic

Double Negative Rule: Subtracting a negative number means adding positive
Technique: Convert $-(-\frac{7}{7})$ to $+1$ since $\frac{7}{7} = 1$
Check: $-\frac{1}{7} + 1 = \frac{6}{7}$ gives positive result ✓

Common Mistakes

Avoid these frequent errors

Treating double negative as regular subtraction
Don't compute $-\frac{1}{7} - \frac{7}{7} = -\frac{8}{7}$ ! This ignores the double negative rule and gives the wrong sign. Always convert $-(-x)$ to $+x$ first.

Practice Quiz

Test your knowledge with interactive questions

Solve the following expression:

$(+8)+(+12)=\text{ ?}$

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

Think of it as removing a debt! If you owe someone $7 and that debt is cancelled, it's the same as gaining $7. So $-(-7) = +7$ .

How do I remember the double negative rule?

Use the phrase "minus a minus makes a plus". The two negative signs cancel each other out, just like (-1) × (-1) = +1.

Why is 7/7 equal to 1?

Any fraction where the numerator equals the denominator equals 1, because you're dividing something by itself. $\frac{7}{7} = \frac{5}{5} = \frac{100}{100} = 1$

How do I add fractions with the same denominator?

Keep the same denominator and add the numerators: $-\frac{1}{7} + \frac{7}{7} = \frac{-1+7}{7} = \frac{6}{7}$

Should my answer be positive or negative?

Since we're adding $-\frac{1}{7} + 1$ , and 1 is larger than $\frac{1}{7}$ , the result $\frac{6}{7}$ should be positive!

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