Question

Звести до найменшого спільного знаменника дроби 5/24, 3/16 і 7/96

Answer 1

Ответ:

20/96, 18/96, 7/96 відповідно

Пошаговое объяснение:

24*4 = 96 -> 5/24 = (5*4)/96 = 20/96

16*6 = 96 -> 3/16 = (3*6)/96 = 18/96

7/96 так і залишаємо

Answer 2

Finding the Least Common Denominator for Fractions

To find the least common denominator (LCD) for the fractions 5/24, 3/16, and 7/96, we need to determine the smallest multiple that all the denominators can divide evenly into.

First, let's find the prime factorization of each denominator to identify the common factors.

The prime factorization of 24 is 2^3 * 3, the prime factorization of 16 is 2^4, and the prime factorization of 96 is 2^5 * 3.

Identifying the Least Common Denominator

To find the LCD, we need to consider the highest power of each prime factor that appears in any of the denominators. In this case, the highest power of 2 is 5 (from 96), and the highest power of 3 is 1 (from 24). Therefore, the LCD is 2^5 * 3, which equals 96.

Converting Fractions to the Common Denominator

Now that we have the LCD, we can convert each fraction to have a denominator of 96.

For 5/24: 5/24 * (4/4) = 20/96

For 3/16: 3/16 * (6/6) = 18/96

For 7/96: Already in terms of the LCD.

Conclusion

So, the fractions 5/24, 3/16, and 7/96 can be brought to the common denominator of 96, resulting in 20/96, 18/96, and 7/96 respectively.