Solve (-1/6) - (-4 2/6): Mixed Number Subtraction with Negatives

Q: Why does subtracting a negative number become addition?

Think of it like removing debt! If you remove a debt of $5, you actually gain $5. So $ -(-5) = +5 $.

Q: How do I remember the double negative rule?

Use the phrase "minus a minus makes a plus" or remember that two negatives cancel out just like in English grammar!

Q: What if I have more than two negative signs?

Work from right to left in pairs. For example: $ -(-(-3)) = -(+3) = -3 $. Odd number of negatives = negative, even number = positive.

Q: How do I check my work with mixed numbers?

Substitute back: $ (-\frac{1}{6}) - (-4\frac{2}{6}) $ should equal $ 4\frac{1}{6} $. Convert everything to sixths: $ -\frac{1}{6} + \frac{26}{6} = \frac{25}{6} = 4\frac{1}{6} $ ✓

Mixed Number Subtraction with Double Negatives

$(-\frac{1}{6})-(-4\frac{2}{6})=$

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Step-by-step video solution

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00:00 Solve

00:03 Negative times negative is always positive

00:09 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$(-\frac{1}{6})-(-4\frac{2}{6})=$

Step-by-step solution

Let's remember the rule:

$-(-x)=+x$

Now let's write the exercise in the appropriate form:

$-\frac{1}{6}+4\frac{2}{6}=$

We'll use the substitution law and solve:

$4\frac{2}{6}-\frac{1}{6}=4\frac{1}{6}$

Final Answer

$4\frac{1}{6}$

Key Points to Remember

Essential concepts to master this topic

Double Negative Rule: Subtracting a negative equals adding a positive
Technique: Convert $-(-4\frac{2}{6})$ to $+4\frac{2}{6}$
Check: Final answer $4\frac{1}{6}$ is positive when subtracting negative from negative ✓

Common Mistakes

Avoid these frequent errors

Ignoring the double negative sign
Don't treat $-(-4\frac{2}{6})$ as just $-4\frac{2}{6}$ = wrong negative answer! The double negative creates addition, not more subtraction. Always change $-(-x)$ to $+x$ first.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why does subtracting a negative number become addition?

Think of it like removing debt! If you remove a debt of $5, you actually <em>gain</em>$ 5. So $-(-5) = +5$ .

How do I remember the double negative rule?

Use the phrase "minus a minus makes a plus" or remember that two negatives cancel out just like in English grammar!

What if I have more than two negative signs?

Work from right to left in pairs. For example: $-(-(-3)) = -(+3) = -3$ . Odd number of negatives = negative, even number = positive.

Should I convert mixed numbers to improper fractions first?

Not necessary here! Since we're adding/subtracting whole parts and fractional parts separately, keep them as mixed numbers for easier calculation.

How do I check my work with mixed numbers?

Substitute back: $(-\frac{1}{6}) - (-4\frac{2}{6})$ should equal $4\frac{1}{6}$ . Convert everything to sixths: $-\frac{1}{6} + \frac{26}{6} = \frac{25}{6} = 4\frac{1}{6}$ ✓

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