91Ó°ÊÓ

Simplifying fractions is a core mathematical skill that helps make fractions easier to understand and work with. When you simplify a fraction, you reduce it to its simplest form by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). For example, if you have the fraction \( \frac{8}{12} \), both 8 and 12 can be divided by 4 (their GCD). So, \( \frac{8}{12} \) simplifies to \( \frac{2}{3} \).
In our exercise, the fractions are already in their simplest forms because both numerators and denominators do not have a common factor other than 1. The fraction \( -\frac{3}{13} \) cannot be simplified further as 3 and 13 have no common factors. Simplifying fractions helps in making calculations quicker and makes the results easier to interpret.

Adding fractions might seem tricky at first, but it becomes simple if you follow a few steps. When adding fractions, it's crucial to have a common denominator. This is because fractions represent parts of a whole divided into equal pieces. For example, adding \( \frac{1}{4} \) and \( \frac{1}{3} \) directly isn't straightforward because they represent different parts (quarters and thirds) of a whole. You would need to convert them to a common denominator.
Fortunately, in our exercise, the fractions \( -\frac{3}{13} \) and \( -\frac{4}{13} \) already have a common denominator (13). So, we can directly add the numerators while keeping the denominator the same:
\( \frac{-3 + (-4)}{13} = \frac{-7}{13} \).
With this approach, we've successfully added the fractions.

Negative numbers in fractions can appear in both the numerator or the denominator, or even in front of the entire fraction. Handling negative numbers requires understanding that these negate or invert the value indicated by the fraction.
In our exercise, both fractions are negative: \( -\frac{3}{13} \) and \( -\frac{4}{13} \). When adding these, we still work with the absolute values normally and then apply the negative sign to our result. It’s as if we are moving 'backwards on a number line from zero’.
Here, when combining negative fractions, you're essentially adding more negative parts together, which makes the overall value more negative:
\( -\frac{3}{13} + (-\frac{4}{13}) = \frac{-7}{13} \). Understanding how to work with negative numbers in fractions will help you tackle diverse mathematical problems with confidence.