Let's simplify the given expression step by step:

The expression is:

\[
\frac{2}{3} \div 5 + \frac{1}{4} \div 5
\]

### Step 1: Simplify each division
To divide a fraction by a number, we multiply the fraction by the reciprocal of that number.

For the first term \(\frac{2}{3} \div 5\):
\[
\frac{2}{3} \div 5 = \frac{2}{3} \times \frac{1}{5} = \frac{2}{15}
\]

For the second term \(\frac{1}{4} \div 5\):
\[
\frac{1}{4} \div 5 = \frac{1}{4} \times \frac{1}{5} = \frac{1}{20}
\]

### Step 2: Add the two fractions
Now, we need to add \(\frac{2}{15} + \frac{1}{20}\). To do this, we need a common denominator.

The least common denominator (LCD) of 15 and 20 is 60. Let's rewrite each fraction with 60 as the denominator.

\[
\frac{2}{15} = \frac{2 \times 4}{15 \times 4} = \frac{8}{60}
\]
\[
\frac{1}{20} = \frac{1 \times 3}{20 \times 3} = \frac{3}{60}
\]

Now, add the fractions:
\[
\frac{8}{60} + \frac{3}{60} = \frac{11}{60}
\]

### Final Answer:
\[
\frac{2}{3} \div 5 + \frac{1}{4} \div 5 = \frac{11}{60}
\]

---

Would you like further explanation on any step? Here are some related questions:

1. How do you find the least common denominator of two fractions?
2. What is the reciprocal of a number and why do we use it in division?
3. How do you convert a mixed number to an improper fraction?
4. Can you add or subtract fractions with different denominators without finding a common denominator?
5. How do you multiply fractions and simplify the result?

**Tip:** When adding fractions with different denominators, always first find the least common denominator (LCD) to simplify the addition process!

Learn how to solve the expression 2/3 ÷ 5 + 1/4 ÷ 5 by simplifying each fraction division and adding them with a common denominator. This problem involves fraction division, addition, and the use of least common denominators, suitable for Grades 6-8.

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