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Chapter 10: Problem 35

Divide. $$ \frac{-11}{-13} $$

Short Answer

Expert verified
11/13

Step by step solution

01

Understand the problem

Devide the fraction \(\frac{-11}{-13}\).
02

Negative divided by negative

When dividing a negative number by another negative number, the result is a positive number since \(- \div - = +\).
03

Simplify the fraction

Since \-11\ divided by \-13\ will be positive, simplify the fraction to \(\frac{11}{13}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Negative Numbers in Fractions
Negative numbers can seem tricky, but they follow straightforward rules.
When you divide two negative numbers, you always end up with a positive result.
This is because the two negative signs cancel each other out.
In mathematical terms, \(- \div - = + \).
So, when you see something like \(\frac{-11}{-13}\), you know the result will be positive.
The challenge now is to just simplify it correctly.
Simplifying Fractions
Simplifying fractions is about making them as simple as possible without changing their value.
For instance, \(\frac{22}{26} \) can be simplified to \(\frac{11}{13}\), because both 22 and 26 can be divided by their greatest common divisor (GCD), which is 2.
In our example, \(\frac{-11}{-13}\), since we already established that a negative divided by a negative is positive, it simply becomes \(\frac{11}{13}\).
There's no further simplification in this particular problem because 11 and 13 are both prime numbers and don't have any common divisors other than 1.
Achieving a Positive Result
When doing arithmetic with fractions, especially when negative numbers are involved, it's important to understand how the signs work to achieve the correct results.
Start by addressing the negative signs first.
In \(\frac{-11}{-13}\), both negatives cancel each other out, leading to \(\frac{11}{13}\), which is positive.
In general:
  • A negative divided by a negative is always a positive
  • A positive divided by a positive is always a positive
  • A positive divided by a negative (or vice versa) is always a negative
Once you determine the sign, simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD).
This ensures your solution is in its simplest form, giving you the final and most clear answer.

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Most popular questions from this chapter

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