**RD Sharma Solutions (Part - 1) - Ex-2.1, Fractions, Class 7, Math**

**Question 1 (4)**

The question asks us to solve the given fraction equations: 17/15 and 119/105.

To solve these fraction equations, we need to find the common factors of the numerator and denominator, and then divide both the numerator and denominator by their highest common factor to simplify the fractions.

Let's solve each fraction equation step by step:

**Fraction 17/15:**

Step 1: Prime factorization of the numerator (17) and denominator (15):

17 = 17 (prime number)
15 = 3 x 5 (prime factors)

Step 2: Finding the highest common factor (HCF) of 17 and 15:

Since both 17 and 15 are prime numbers, their HCF is 1.

Step 3: Simplifying the fraction by dividing both numerator and denominator by their HCF:

17/15 ÷ 1/1 = (17 ÷ 1) / (15 ÷ 1) = 17/15

Therefore, the fraction 17/15 is already in its simplest form.

**Fraction 119/105:**

Step 1: Prime factorization of the numerator (119) and denominator (105):

119 = 7 x 17 (prime factors)
105 = 3 x 5 x 7 (prime factors)

Step 2: Finding the highest common factor (HCF) of 119 and 105:

The common factors of 119 and 105 are 1 and 7. The highest common factor (HCF) is 7.

Step 3: Simplifying the fraction by dividing both numerator and denominator by their HCF:

119/105 ÷ 7/7 = (119 ÷ 7) / (105 ÷ 7) = 17/15

Therefore, the fraction 119/105 simplifies to 17/15.

In conclusion, the fractions 17/15 and 119/105 are already in their simplest form and cannot be simplified further.

Note: RD Sharma Solutions (Part - 1) - Ex-2.1, Fractions, Class 7, Math provides detailed explanations and step-by-step solutions for various fraction problems.

<