To solve the expression \( 4 \frac{2}{7} + 2 \frac{4}{21} - \frac{1}{3} \), follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
For \( 4 \frac{2}{7} \):
\[
4 \frac{2}{7} = \frac{(4 \times 7) + 2}{7} = \frac{28 + 2}{7} = \frac{30}{7}
\]

For \( 2 \frac{4}{21} \):
\[
2 \frac{4}{21} = \frac{(2 \times 21) + 4}{21} = \frac{42 + 4}{21} = \frac{46}{21}
\]

Now the expression becomes:
\[
\frac{30}{7} + \frac{46}{21} - \frac{1}{3}
\]

### Step 2: Find a common denominator
The denominators are 7, 21, and 3. The least common denominator (LCD) of 7, 21, and 3 is 21.

### Step 3: Convert the fractions to have the same denominator
Convert \( \frac{30}{7} \) to have a denominator of 21:
\[
\frac{30}{7} = \frac{30 \times 3}{7 \times 3} = \frac{90}{21}
\]

Convert \( \frac{1}{3} \) to have a denominator of 21:
\[
\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}
\]

Now the expression is:
\[
\frac{90}{21} + \frac{46}{21} - \frac{7}{21}
\]

### Step 4: Add and subtract the fractions
Since all the fractions now have the same denominator, we can combine the numerators:
\[
\frac{90 + 46 - 7}{21} = \frac{129}{21}
\]

### Step 5: Simplify the fraction
To simplify \( \frac{129}{21} \), find the greatest common divisor (GCD) of 129 and 21, which is 3. So:
\[
\frac{129}{21} = \frac{129 \div 3}{21 \div 3} = \frac{43}{7}
\]

Thus, the simplified answer is \( \frac{43}{7} \), or as a mixed number:
\[
6 \frac{1}{7}
\]

### Final Answer:
\[
4 \frac{2}{7} + 2 \frac{4}{21} - \frac{1}{3} = 6 \frac{1}{7}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you convert improper fractions back to mixed numbers?
2. What are the steps to find the least common denominator for fractions?
3. How do you simplify a fraction using the greatest common divisor?
4. How do you add or subtract mixed numbers without converting them to improper fractions?
5. How do you solve an equation with fractions and mixed numbers?

**Tip:** Always simplify fractions at the end to avoid working with unnecessarily large numbers during calculations.

Discover how to solve the expression 4 2/7 + 2 4/21 - 1/3 using mixed numbers and fractions. Learn to convert mixed numbers to improper fractions, find the least common denominator, and simplify the result. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation