find the greatest number that divides 7 / 2 and 35 / 4

2/7 7/4 4/7

To solve this problem, we need to find the greatest common divisor (GCD) of the fractions \(\frac{7}{2}\) and \(\frac{35}{4}\).

### Step 1: Express the fractions
\[
\text{Fraction 1: } \frac{7}{2} = \frac{7}{2}
\]
\[
\text{Fraction 2: } \frac{35}{4} = \frac{35}{4}
\]

### Step 2: Find the GCD of the numerators
- Numerator of Fraction 1: \(7\)
- Numerator of Fraction 2: \(35\)

The GCD of \(7\) and \(35\) is \(7\).

### Step 3: Find the LCM of the denominators
- Denominator of Fraction 1: \(2\)
- Denominator of Fraction 2: \(4\)

The least common multiple (LCM) of \(2\) and \(4\) is \(4\).

### Step 4: Construct the greatest common divisor of the fractions
The greatest number that divides both fractions is:
\[
\frac{\text{GCD of the numerators}}{\text{LCM of the denominators}} = \frac{7}{4}
\]

So, the greatest number that divides \(\frac{7}{2}\) and \(\frac{35}{4}\) is **\(\frac{7}{4}\)**.

Would you like further clarification or have any other questions?

Here are 5 related questions you might consider:
1. What is the greatest common divisor of \(\frac{8}{3}\) and \(\frac{16}{6}\)?
2. How do you find the least common multiple (LCM) of two fractions?
3. What is the smallest fraction that divides \(\frac{7}{2}\) and \(\frac{35}{4}\)?
4. What is the GCD of \(\frac{14}{5}\) and \(\frac{21}{10}\)?
5. How do you simplify the fraction \(\frac{35}{4}\)?

**Tip:** When comparing or finding common divisors of fractions, always work separately with the numerators and denominators.

Learn how to find the greatest number that divides the fractions 7/2 and 35/4 using the concept of Greatest Common Divisor (GCD) and Least Common Multiple (LCM). Understand step-by-step how to apply GCD and LCM to fractions. Suitable for students in Grades 6-8.

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