Solve: -1/25 + (-1/5) - (-19/25) | Negative Fraction Operations

Q: Why do I need to find a common denominator when adding fractions?

You can only add or subtract fractions when they have the same denominator. Think of it like adding apples - you can't add 1/5 of an apple to 1/25 of an apple without making them the same size pieces first!

Q: What does the double negative -(-19/25) really mean?

The double negative -(-19/25) means 'subtract negative 19/25'. Since subtracting a negative is the same as adding a positive, this becomes +19/25. Remember: two negatives make a positive!

Q: How do I convert -1/5 to twenty-fifths?

Since $ \frac{1}{5} = \frac{5}{25} $ (multiply top and bottom by 5), we have $ -\frac{1}{5} = -\frac{5}{25} $. The negative sign stays with the fraction.

Q: Can I add the numerators directly once I have the same denominator?

Yes! Once all fractions have denominator 25, you can add the numerators: $ -1 + (-5) + 19 = 13 $, giving you $ \frac{13}{25} $.

Fraction Operations with Mixed Signs

$-\frac{1}{25}+(-\frac{1}{5})-(-\frac{19}{25})=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:08 Positive times negative always equals negative

00:13 Open parentheses

00:17 Negative times negative always equals positive

00:23 Open parentheses

00:31 Multiply by 5 to get a common denominator

00:45 Add all fractions under one denominator

00:58 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-\frac{1}{25}+(-\frac{1}{5})-(-\frac{19}{25})=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert all fractions to a common denominator of $25$ .
Step 2: Simplify the expression using equivalent fractions and arithmetic operations.
Step 3: Combine the results following the arithmetic rules.

Now, let's work through each step:
Step 1: Convert $-\frac{1}{5}$ to an equivalent fraction with denominator $25$ . Since $\frac{1}{5} = \frac{5}{25}$ , we have: $-\frac{1}{5} = -\frac{5}{25}$ .
Step 2: The expression becomes $-\frac{1}{25} + (-\frac{5}{25}) + \frac{19}{25}$ . The $-(-\frac{19}{25})$ simplifies to $+\frac{19}{25}$ .
Step 3: Perform the arithmetic on the numerators: $-1 + (-5) + 19 = -1 -5 + 19 = 13$ .
Therefore, the solution simplifies to $\frac{13}{25}$ .

Therefore, the solution to the problem is $\frac{13}{25}$ .

Final Answer

$\frac{13}{25}$

Key Points to Remember

Essential concepts to master this topic

Common Denominator: Convert all fractions to denominator 25 before combining
Sign Rules: Double negative -(-19/25) becomes positive +19/25
Check: Verify -1 - 5 + 19 = 13, so answer is 13/25 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly handling double negatives
Don't change -(-19/25) to -19/25 = wrong sign throughout! The double negative means subtract a negative, which equals addition. Always remember that -(-x) = +x.

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 do I need to find a common denominator when adding fractions?

You can only add or subtract fractions when they have the same denominator. Think of it like adding apples - you can't add 1/5 of an apple to 1/25 of an apple without making them the same size pieces first!

What does the double negative -(-19/25) really mean?

The double negative -(-19/25) means 'subtract negative 19/25'. Since subtracting a negative is the same as adding a positive, this becomes +19/25. Remember: two negatives make a positive!

How do I convert -1/5 to twenty-fifths?

Since $\frac{1}{5} = \frac{5}{25}$ (multiply top and bottom by 5), we have $-\frac{1}{5} = -\frac{5}{25}$ . The negative sign stays with the fraction.

Can I add the numerators directly once I have the same denominator?

Yes! Once all fractions have denominator 25, you can add the numerators: $-1 + (-5) + 19 = 13$ , giving you $\frac{13}{25}$ .

How do I know if 13/25 can be simplified further?

Check if 13 and 25 share any common factors. Since 13 is prime and doesn't divide 25, the fraction $\frac{13}{25}$ is already in lowest terms!

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