The problem is to add two fractions, $\frac{4}{10}$ and $\frac{5}{6}$, and express the sum as a single fraction in simplest form. The process involves finding a common denominator, adding the fractions, and then simplifying the resulting fraction.

1. Problem Description

The problem is to add two fractions, $\frac{4}{10}$ and $\frac{5}{6}$, and express the sum as a single fraction in simplest form. The process involves finding a common denominator, adding the fractions, and then simplifying the resulting fraction.

2. Solution Steps

First, we need to find a common denominator for the fractions $\frac{4}{10}$ and $\frac{5}{6}$. The least common multiple (LCM) of 10 and 6 is

3

0. Next, convert each fraction to have the common denominator of

3

0. $\frac{4}{10} = \frac{4 \times 3}{10 \times 3} = \frac{12}{30}$

$\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}$

So the addition problem becomes:

$\frac{4}{10} + \frac{5}{6} = \frac{12}{30} + \frac{25}{30}$

Now we add the numerators:

$\frac{12}{30} + \frac{25}{30} = \frac{12 + 25}{30} = \frac{37}{30}$

Now check if we can simplify the fraction. Since 37 is a prime number, the fraction $\frac{37}{30}$ is already in its simplest form.

3. Final Answer

$\frac{12}{30} + \frac{25}{30} = \frac{37}{30}$