Question

Приведите дроби к наименьшему общему знаменателю (459-461) мне нужно 459 2)6/11 и 4/9 4). 7/18 и 1/66). 5/7 и 3/4 8)5/8 и 3/4 ​

Answer 1

Ответ:

54/99 и 44/99

7/18, 3/18

20/28, 21/28,

10/16, 12/16

Пошаговое объяснение:

Answer 2

Finding the Least Common Denominator (LCD)

To find the least common denominator (LCD) for fractions, we need to find 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 and perform the necessary operations.

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

1) 6/11 and 4/9: - The denominators are 11 and 9. - The prime factorization of 11 is 11, and the prime factorization of 9 is 3 * 3. - The LCD is the product of the highest powers of all prime factors involved, so the LCD is 11 * 3 * 3 = 99.

2) 7/18 and 1/66: - The denominators are 18 and 66. - The prime factorization of 18 is 2 * 3 * 3, and the prime factorization of 66 is 2 * 3 * 11. - The LCD is the product of the highest powers of all prime factors involved, so the LCD is 2 * 3 * 3 * 11 = 396.

3) 5/7 and 3/4: - The denominators are 7 and 4. - The prime factorization of 7 is 7, and the prime factorization of 4 is 2 * 2. - The LCD is the product of the highest powers of all prime factors involved, so the LCD is 7 * 2 * 2 = 28.

4) 5/8 and 3/4: - The denominators are 8 and 4. - The prime factorization of 8 is 2 * 2 * 2, and the prime factorization of 4 is 2 * 2. - The LCD is the product of the highest powers of all prime factors involved, so the LCD is 2 * 2 * 2 = 8.

Converting Fractions to the LCD

Now that we have the LCD for each set of fractions, we can convert the fractions to have the same denominator and perform the necessary operations.

1) 6/11 and 4/9: - To convert 6/11 to have a denominator of 99, we multiply the numerator and denominator by 9: (6 * 9) / (11 * 9) = 54/99. - To convert 4/9 to have a denominator of 99, we multiply the numerator and denominator by 11: (4 * 11) / (9 * 11) = 44/99. - Now that both fractions have the same denominator, we can add them: 54/99 + 44/99 = 98/99.

2) 7/18 and 1/66: - To convert 7/18 to have a denominator of 396, we multiply the numerator and denominator by 22: (7 * 22) / (18 * 22) = 154/396. - To convert 1/66 to have a denominator of 396, we multiply the numerator and denominator by 6: (1 * 6) / (66 * 6) = 6/396. - Now that both fractions have the same denominator, we can add them: 154/396 + 6/396 = 160/396.

3) 5/7 and 3/4: - To convert 5/7 to have a denominator of 28, we multiply the numerator and denominator by 4: (5 * 4) / (7 * 4) = 20/28. - To convert 3/4 to have a denominator of 28, we multiply the numerator and denominator by 7: (3 * 7) / (4 * 7) = 21/28. - Now that both fractions have the same denominator, we can add them: 20/28 + 21/28 = 41/28.

4) 5/8 and 3/4: - To convert 5/8 to have a denominator of 8, we multiply the numerator and denominator by 1: (5 * 1) / (8 * 1) = 5/8. - To convert 3/4 to have a denominator of 8, we multiply the numerator and denominator by 2: (3 * 2) / (4 * 2) = 6/8. - Now that both fractions have the same denominator, we can add them: 5/8 + 6/8 = 11/8.

Summary

To summarize, here are the fractions converted to the least common denominator (LCD) and the results of the addition:

1) 6/11 and 4/9: - Converted to LCD 99: 54/99 and 44/99. - Result: 98/99.

2) 7/18 and 1/66: - Converted to LCD 396: 154/396 and 6/396. - Result: 160/396.

3) 5/7 and 3/4: - Converted to LCD 28: 20/28 and 21/28. - Result: 41/28.

4) 5/8 and 3/4: - Converted to LCD 8: 5/8 and 6/8. - Result: 11/8.

Please let me know if there's anything else I can help you with!