Add the fractions. Write your answer in simplest form.
$\frac{3}{7}+\frac{1}{4}$
The goal is to calculate the sum of the two fractions \(\frac{3}{7}\) and \(\frac{1}{4}\). To add fractions with different denominators, we first need to find a common denominator. This allows us to combine the fractions into a single fraction representing the sum. Once the fractions have a common denominator, we add the numerators while keeping the common denominator, and then simplify the resulting fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD), if any.
The denominators of the fractions are \(7\) and \(4\). Since these two numbers have no common factors other than \(1\), the least common denominator (LCD) is their product:
\[7 \times 4 = 28\]
Now, we rewrite each fraction with \(28\) as the denominator:
For \(\frac{3}{7}\): \(\frac{3 \times 4}{7 \times 4} = \frac{12}{28}\)
For \(\frac{1}{4}\): \(\frac{1 \times 7}{4 \times 7} = \frac{7}{28}\)
Adding these together gives:
\[\frac{12}{28} + \frac{7}{28} = \frac{12 + 7}{28} = \frac{19}{28}\]
We check for common factors between \(19\) and \(28\). Since \(19\) is a prime number and is not a factor of \(28\), the fraction is already in its simplest form.
Fractions are used daily in cooking, for example, if a recipe calls for 3/7 of a cup of water and you decide to add another 1/4 of a cup, you are performing fraction addition to determine the total amount. Mastering this skill helps in managing recipes, measuring materials in DIY projects, and understanding proportions in real-world scenarios. It is a fundamental skill for everyday math.