https://file.aiquickdraw.com/mathbot/file/1725933842958fxyzbkc5.jpg

The expression provided in the image is:

\[
3 \times \frac{2}{5} - 2 \frac{1}{3} + 6
\]

Let's break it down step by step:

### 1. First, evaluate the multiplication \( 3 \times \frac{2}{5} \):
\[
3 \times \frac{2}{5} = \frac{6}{5}
\]

### 2. Next, convert the mixed number \( 2 \frac{1}{3} \) into an improper fraction:
\[
2 \frac{1}{3} = \frac{7}{3}
\]

### 3. Substitute these values back into the expression:
\[
\frac{6}{5} - \frac{7}{3} + 6
\]

### 4. Find a common denominator to subtract and add fractions. The least common denominator between 5 and 3 is 15. So we convert each fraction:
\[
\frac{6}{5} = \frac{18}{15}, \quad \frac{7}{3} = \frac{35}{15}
\]

The expression becomes:
\[
\frac{18}{15} - \frac{35}{15} + 6
\]

### 5. Now, subtract the fractions:
\[
\frac{18}{15} - \frac{35}{15} = \frac{-17}{15}
\]

### 6. Add the integer 6, converting it to a fraction with denominator 15:
\[
6 = \frac{90}{15}
\]

Thus, the expression is now:
\[
\frac{-17}{15} + \frac{90}{15} = \frac{73}{15}
\]

So, the final answer is:
\[
\boxed{\frac{73}{15}} \quad \text{or approximately} \quad 4.867
\]

Would you like further details or clarifications?

Here are 5 related questions for practice:
1. What is the value of \( 4 \times \frac{3}{7} - 1 \frac{2}{5} + 8 \)?
2. How do you convert a mixed number like \( 3 \frac{1}{4} \) into an improper fraction?
3. Can you simplify the fraction \( \frac{45}{60} \)?
4. What is the least common denominator of 6 and 8?
5. How do you add fractions with different denominators?

**Tip:** Always simplify mixed numbers into improper fractions before performing operations like addition or subtraction.

Learn how to solve the expression 3 × 2/5 - 2 1/3 + 6. This step-by-step solution covers multiplication of fractions, converting mixed numbers to improper fractions, and finding common denominators. Suitable for students in Grades 5-7.

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