Question

20,688 Learners found this answer helpful

1. \\(\frac{5}{12}\\) and \\(\frac{3}{5}\\)
2. \\(\frac{5}{6}\\) and \\(\frac{8}{21}\\)

Explanation:

Assuming the problem is to find a common denominator or compare the fractions (since it's about two fractions, likely finding a common denominator or comparing them, here we'll do finding a common denominator as a common operation for such fraction pairs). Let's solve both sub - questions (5 and 9) one by one.

Sub - question 5: For $\frac{5}{12}$ and $\frac{3}{5}$

Step 1: Find the least common denominator (LCD)

To find the LCD of 12 and 5, we note that 12 and 5 are coprime (their greatest common divisor is 1). So, the LCD is the product of the two denominators.
$LCD = 12\times5=60$

Step 2: Rewrite the fractions with the LCD

For $\frac{5}{12}$, we multiply the numerator and denominator by 5: $\frac{5\times5}{12\times5}=\frac{25}{60}$
For $\frac{3}{5}$, we multiply the numerator and denominator by 12: $\frac{3\times12}{5\times12}=\frac{36}{60}$

Sub - question 9: For $\frac{5}{6}$ and $\frac{8}{21}$

Step 1: Find the least common denominator (LCD)

First, factorize the denominators:

• The prime factorization of 6 is $2\times3$
• The prime factorization of 21 is $3\times7$

To find the LCD, we take the highest power of each prime factor that appears. So, we have 2, 3, and 7.
$LCD = 2\times3\times7 = 42$

Step 2: Rewrite the fractions with the LCD

For $\frac{5}{6}$, we multiply the numerator and denominator by 7: $\frac{5\times7}{6\times7}=\frac{35}{42}$
For $\frac{8}{21}$, we multiply the numerator and denominator by 2: $\frac{8\times2}{21\times2}=\frac{16}{42}$

Final Answers

For sub - question 5: The fractions with a common denominator are $\frac{25}{60}$ and $\frac{36}{60}$
For sub - question 9: The fractions with a common denominator are $\frac{35}{42}$ and $\frac{16}{42}$

Answer:

Step 1: Find the least common denominator (LCD)

First, factorize the denominators:

• The prime factorization of 6 is $2\times3$
• The prime factorization of 21 is $3\times7$

To find the LCD, we take the highest power of each prime factor that appears. So, we have 2, 3, and 7.
$LCD = 2\times3\times7 = 42$

Step 2: Rewrite the fractions with the LCD

For $\frac{5}{6}$, we multiply the numerator and denominator by 7: $\frac{5\times7}{6\times7}=\frac{35}{42}$
For $\frac{8}{21}$, we multiply the numerator and denominator by 2: $\frac{8\times2}{21\times2}=\frac{16}{42}$

Final Answers

For sub - question 5: The fractions with a common denominator are $\frac{25}{60}$ and $\frac{36}{60}$
For sub - question 9: The fractions with a common denominator are $\frac{35}{42}$ and $\frac{16}{42}$