Question

Приведите к наименьшему общему знаменателю дроби:7/20 и 5/12; 11/24 и 1/30; 3/16 и 7/12;

Answer 1

7/20 и 5/12 НОК(20,12) = 60
7/20 = 21/60
5/12=25/60

11/24,1/30 НОК(24,30)=120
11/24=55/120
1/30=4/120

3/16,7/12 НОК(16,12)=48
3/16=9/48
7/12=28/48

Answer 2

Finding the Least Common Denominator (LCD) for Fractions

To find the least common denominator (LCD) for fractions, we need to determine the smallest number that is divisible by all the denominators involved. Let's find the LCD for each pair of fractions you provided:

1. For the fractions 7/20 and 5/12: - The denominators are 20 and 12. - The LCD is the smallest number that is divisible by both 20 and 12. - The prime factorization of 20 is 2^2 * 5, and the prime factorization of 12 is 2^2 * 3. - To find the LCD, we take the highest power of each prime factor that appears in either factorization: 2^2 * 3 * 5 = 60. - Therefore, the LCD for 7/20 and 5/12 is 60.

2. For the fractions 11/24 and 1/30: - The denominators are 24 and 30. - The prime factorization of 24 is 2^3 * 3, and the prime factorization of 30 is 2 * 3 * 5. - The LCD is the smallest number that is divisible by both 24 and 30. - To find the LCD, we take the highest power of each prime factor that appears in either factorization: 2^3 * 3 * 5 = 120. - Therefore, the LCD for 11/24 and 1/30 is 120.

3. For the fractions 3/16 and 7/12: - The denominators are 16 and 12. - The prime factorization of 16 is 2^4, and the prime factorization of 12 is 2^2 * 3. - The LCD is the smallest number that is divisible by both 16 and 12. - To find the LCD, we take the highest power of each prime factor that appears in either factorization: 2^4 * 3 = 48. - Therefore, the LCD for 3/16 and 7/12 is 48.

So, the least common denominators for the given fractions are: - 7/20 and 5/12: LCD = 60 - 11/24 and 1/30: LCD = 120 - 3/16 and 7/12: LCD = 48

I hope this helps! Let me know if you have any further questions.