To find the HCF and LCM of fractions, all fractions must first be expressed in their simplest form. The HCF of a set of fractions equals the HCF of the numerators divided by the LCM of the denominators. Similarly, the LCM of fractions equals the LCM of the numerators divided by the HCF of the denominators.

To find the HCF and LCM of fractions, all fractions must first be expressed in their simplest form. The HCF of a set of fractions equals the HCF of the numerators divided by the LCM of the denominators. Similarly, the LCM of fractions equals the LCM of the numerators divided by the HCF of the denominators.

The HCF of the numerators 2 and 8 is the product of common prime factors with the smallest exponent, which gives 2^1 = 2. The LCM of the denominators 3 and 9 is the product of the highest powers of each prime factor, which gives 3² = 9. Thus, the HCF is (2)/(9).

The HCF of the numerators 2 and 8 is the product of common prime factors with the smallest exponent, which gives 2^1 = 2. The LCM of the denominators 3 and 9 is the product of the highest powers of each prime factor, which gives 3² = 9. Thus, the HCF is (2)/(9).

The LCM of the numerators 2 and 8 is 2³ = 8. The HCF of the denominators 3 and 9 is 3^1 = 3. Dividing the LCM of the numerators by the HCF of the denominators yields (8)/(3).

Fraction prime factor LCM HCF etc.

Answer: $\text{HCF of fractions} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}}, \quad \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}$

Step-by-step solution

Step 1: State formulas for HCF and LCM of fractions

To find the $\text{HCF}$ and $\text{LCM}$ of fractions, all fractions must first be expressed in their simplest form. The $\text{HCF}$ of a set of fractions equals the $\text{HCF}$ of the numerators divided by the $\text{LCM}$ of the denominators. Similarly, the $\text{LCM}$ of fractions equals the $\text{LCM}$ of the numerators divided by the $\text{HCF}$ of the denominators.

Step 2: Set up an example and express terms in prime factor form

Let us consider an example with two fractions, $\frac{2}{3}$ and $\frac{8}{9}$ . We find the prime factorization of each numerator: $2 = 2^1$ and $8 = 2^3$ . For the denominators, we have $3 = 3^1$ and $9 = 3^2$ .

Step 3: Calculate the HCF of the fractions

The $\text{HCF}$ of the numerators $2$ and $8$ is the product of common prime factors with the smallest exponent, which gives $2^1 = 2$ . The $\text{LCM}$ of the denominators $3$ and $9$ is the product of the highest powers of each prime factor, which gives $3^2 = 9$ . Thus, the $\text{HCF}$ is $\frac{2}{9}$ .

Step 4: Calculate the LCM of the fractions

The $\text{LCM}$ of the numerators $2$ and $8$ is $2^3 = 8$ . The $\text{HCF}$ of the denominators $3$ and $9$ is $3^1 = 3$ . Dividing the $\text{LCM}$ of the numerators by the $\text{HCF}$ of the denominators yields $\frac{8}{3}$ .

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