Question

Find each sum or difference. $$\frac{13}{32}+\frac{13}{32}+\frac{6}{32}$$

Short answer

1

Step-by-step solution

Identify the common denominator

For the problem \(\frac{13}{32}+\frac{13}{32}+\frac{6}{32}\), all fractions have the same denominator which is 32.

Add the numerators

Since the denominators are the same, you can simply add the numerators: \(13 + 13 + 6 = 32\).

Write the result over the common denominator

Place the sum of the numerators over the common denominator: \(\frac{32}{32}\).

Simplify the fraction

Simplify the fraction \(\frac{32}{32} = 1\).

Key concepts

Common Denominator

When adding fractions, finding a common denominator is key. The denominator is the bottom part of a fraction that represents the total number of equal parts. In the exercise \(\frac{13}{32}+\frac{13}{32}+\frac{6}{32}\), all fractions already have the same denominator, which is 32. This makes it much easier to add them together.
If the denominators were different, you would need to find the least common multiple (LCM) of the denominators to convert each fraction to an equivalent one with this common denominator. Once all fractions share the same denominator, you can then proceed to the next step of adding the numerators.

Numerators

The numerator is the top part of a fraction and it represents how many parts we have. In the problem \(\frac{13}{32}+\frac{13}{32}+\frac{6}{32}\), the numerators are 13, 13, and 6.
When fractions have a common denominator, adding them becomes straightforward because you only need to add the numerators. So, in this case, you add:

• 13 + 13 + 6 = 32

This means we have 32 parts out of 32, simplifying our work. Always remember: if the denominators are the same, focus on adding the numerators directly.

Simplifying Fractions

Once you have added the numerators and placed them over the common denominator, the next important step is to simplify the fraction. Simplifying means reducing the fraction to its simplest form.
In our exercise, after adding the numerators, the result was \(\frac{32}{32}\). A fraction where the numerator and denominator are the same equals 1. Therefore, \(\frac{32}{32} = 1\).
To simplify, you need to look for the greatest common divisor (GCD) of the numerator and denominator. Divide both by this number to make the fraction as simple as possible. Simplifying fractions makes them easier to understand and use in further calculations.