https://file.aiquickdraw.com/mathbot/file/17292688349005gvxlfj2.jpg

The expression shown in the image is:

\[
\frac{6}{17} \times \frac{34}{15} - \frac{6}{35} \text{ of } 2 \frac{1}{3}
\]

Let's break this down step by step:

### Step 1: Multiply the first two fractions
\[
\frac{6}{17} \times \frac{34}{15}
\]
Multiply the numerators: \( 6 \times 34 = 204 \)

Multiply the denominators: \( 17 \times 15 = 255 \)

So,
\[
\frac{6}{17} \times \frac{34}{15} = \frac{204}{255}
\]
Now, simplify the fraction:
\[
\gcd(204, 255) = 51 \quad \Rightarrow \quad \frac{204 \div 51}{255 \div 51} = \frac{4}{5}
\]

### Step 2: Convert the mixed number \( 2 \frac{1}{3} \) into an improper fraction
\[
2 \frac{1}{3} = \frac{7}{3}
\]

### Step 3: Multiply the second fraction by the mixed number
"Of" in math typically means multiplication, so we have:
\[
\frac{6}{35} \times \frac{7}{3}
\]
Multiply the numerators: \( 6 \times 7 = 42 \)

Multiply the denominators: \( 35 \times 3 = 105 \)

So,
\[
\frac{6}{35} \times \frac{7}{3} = \frac{42}{105}
\]
Simplify the fraction:
\[
\gcd(42, 105) = 21 \quad \Rightarrow \quad \frac{42 \div 21}{105 \div 21} = \frac{2}{5}
\]

### Step 4: Subtract the two results
Now, subtract:
\[
\frac{4}{5} - \frac{2}{5}
\]
Since the denominators are the same, subtract the numerators:
\[
\frac{4 - 2}{5} = \frac{2}{5}
\]

### Final Answer:
The value of the expression is \( \frac{2}{5} \).

Would you like any further clarification or more details on any of the steps?

Here are 5 related questions:
1. How do you simplify fractions?
2. What is the process for converting mixed numbers to improper fractions?
3. How do you add and subtract fractions with different denominators?
4. How do you find the greatest common divisor (GCD) of two numbers?
5. What is the significance of multiplying fractions by whole numbers?

**Tip**: Always simplify fractions at the end of a calculation to ensure the result is in its simplest form.

Learn how to solve the fraction expression 6/17 × 34/15 - 6/35 of 2 1/3. This step-by-step guide covers key concepts like multiplication and subtraction of fractions, as well as converting mixed numbers to improper fractions. Suitable for students in Grades 5-7.

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