Question

Привидите дроби к наим общему знам.найдите ещё несколько общих знаменателей для каждой пары 1/2 и 1/18 , 3/10 и 33/100 , 5/8 и 2/3 , 7/15 и 5/9

Answer 1

а)4/8 и 1/8. (8/16 и 2/16)
б)30/100 и 33/100. ( 60/200 и 66/200)
в)15/24 и 16/24. (30/48 и 32/48)
г)21/45 и 25/45. 42/90 и 50/90)

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. Once we have the LCD, we can convert the fractions to have the same denominator, making it easier to compare or perform operations on them.

Let's find the LCD for each pair of fractions you provided:

1. 1/2 and 1/18: - The denominators are 2 and 18. - The factors of 2 are 2 and 1. - The factors of 18 are 2, 3, 3, and 1. - The LCD is the product of the highest powers of all the prime factors involved, which in this case is 2 * 3 * 3 = 18. - Therefore, the LCD for 1/2 and 1/18 is 18.

2. 3/10 and 33/100: - The denominators are 10 and 100. - The factors of 10 are 2 and 5. - The factors of 100 are 2, 2, 5, 5, and 1. - The LCD is the product of the highest powers of all the prime factors involved, which in this case is 2 * 2 * 5 * 5 = 100. - Therefore, the LCD for 3/10 and 33/100 is 100.

3. 5/8 and 2/3: - The denominators are 8 and 3. - The factors of 8 are 2, 2, and 2. - The factors of 3 are 3 and 1. - The LCD is the product of the highest powers of all the prime factors involved, which in this case is 2 * 2 * 2 * 3 = 24. - Therefore, the LCD for 5/8 and 2/3 is 24.

4. 7/15 and 5/9: - The denominators are 15 and 9. - The factors of 15 are 3, 5, and 1. - The factors of 9 are 3 and 3. - The LCD is the product of the highest powers of all the prime factors involved, which in this case is 3 * 3 * 5 = 45. - Therefore, the LCD for 7/15 and 5/9 is 45.

Additional Common Denominators

In addition to the LCDs mentioned above, there can be multiple common denominators for a pair of fractions. Some other common denominators for the given pairs of fractions are:

1. For 1/2 and 1/18, another common denominator is 36. 2. For 3/10 and 33/100, another common denominator is 200. 3. For 5/8 and 2/3, another common denominator is 48. 4. For 7/15 and 5/9, another common denominator is 135.

These are just a few examples of common denominators. There can be infinitely many common denominators for any pair of fractions.

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