https://file.aiquickdraw.com/mathbot/file/17268613452967suh6ujh.jpg

Let's solve the given fraction addition problem:

\[
\frac{2}{21} + \frac{3}{14}
\]

### Step 1: Find the least common denominator (LCD)
The denominators are 21 and 14. The least common denominator of 21 and 14 is their least common multiple (LCM).

- Prime factorization of 21: \( 21 = 3 \times 7 \)
- Prime factorization of 14: \( 14 = 2 \times 7 \)

The LCM is \( 42 \).

### Step 2: Convert each fraction to have the LCD
Now, we will express both fractions with a denominator of 42.

\[
\frac{2}{21} = \frac{2 \times 2}{21 \times 2} = \frac{4}{42}
\]
\[
\frac{3}{14} = \frac{3 \times 3}{14 \times 3} = \frac{9}{42}
\]

### Step 3: Add the fractions
Now that the fractions have the same denominator, we can add them:

\[
\frac{4}{42} + \frac{9}{42} = \frac{4 + 9}{42} = \frac{13}{42}
\]

### Step 4: Simplify the result
Since 13 is a prime number and does not divide 42, the fraction is already in its simplest form.

Thus, the answer is:

\[
\frac{13}{42}
\]

Would you like more details or have any questions? Here are five related problems for practice:

1. Add \(\frac{5}{6} + \frac{3}{4}\) and simplify.
2. Subtract \(\frac{7}{15} - \frac{2}{5}\) and simplify.
3. Add \(\frac{1}{9} + \frac{2}{3}\) and simplify.
4. Subtract \(\frac{4}{7} - \frac{1}{14}\) and simplify.
5. Add \(\frac{5}{12} + \frac{7}{18}\) and simplify.

### Tip: When adding fractions, always find the least common denominator (LCD) before performing the addition!

Add 2/21 + 3/14 and simplify the fraction.

Learn how to add the fractions 2/21 and 3/14. This problem covers finding the least common denominator (LCD), adding the fractions, and simplifying the result. Suitable for Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation