Question

приведите к наименьшему общему знаменателю дроби: 5/28 и 9/14; 13/16 и 11/12; 7/8 и 5/6; 3/7 и4/9; 3/8;5/6 и 1/4; 3/8 и 11/16; 11/15 и 3/8; 3/14; 4/21 и 5/6​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Finding the Least Common Denominator (LCD)

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 and then perform the necessary operations.

Let's find the LCD for each pair of fractions and then convert them accordingly.

Pair 1: 5/28 and 9/14

The denominators are 28 and 14. The LCD is the smallest number that is divisible by both 28 and 14, which is 28. Therefore, we need to convert both fractions to have a denominator of 28.

Converting 5/28: To convert 5/28 to have a denominator of 28, we multiply both the numerator and denominator by 1: 5/28 * (28/28) = 5/28

Converting 9/14: To convert 9/14 to have a denominator of 28, we multiply both the numerator and denominator by 2: 9/14 * (2/2) = 18/28

Now, we have the fractions 5/28 and 18/28 with the same denominator. We can perform the necessary operations.

Pair 2: 13/16 and 11/12

The denominators are 16 and 12. The LCD is the smallest number that is divisible by both 16 and 12, which is 48. Therefore, we need to convert both fractions to have a denominator of 48.

Converting 13/16: To convert 13/16 to have a denominator of 48, we multiply both the numerator and denominator by 3: 13/16 * (3/3) = 39/48

Converting 11/12: To convert 11/12 to have a denominator of 48, we multiply both the numerator and denominator by 4: 11/12 * (4/4) = 44/48

Now, we have the fractions 39/48 and 44/48 with the same denominator. We can perform the necessary operations.

Pair 3: 7/8 and 5/6

The denominators are 8 and 6. The LCD is the smallest number that is divisible by both 8 and 6, which is 24. Therefore, we need to convert both fractions to have a denominator of 24.

Converting 7/8: To convert 7/8 to have a denominator of 24, we multiply both the numerator and denominator by 3: 7/8 * (3/3) = 21/24

Converting 5/6: To convert 5/6 to have a denominator of 24, we multiply both the numerator and denominator by 4: 5/6 * (4/4) = 20/24

Now, we have the fractions 21/24 and 20/24 with the same denominator. We can perform the necessary operations.

Pair 4: 3/7 and 4/9

The denominators are 7 and 9. The LCD is the smallest number that is divisible by both 7 and 9, which is 63. Therefore, we need to convert both fractions to have a denominator of 63.

Converting 3/7: To convert 3/7 to have a denominator of 63, we multiply both the numerator and denominator by 9: 3/7 * (9/9) = 27/63

Converting 4/9: To convert 4/9 to have a denominator of 63, we multiply both the numerator and denominator by 7: 4/9 * (7/7) = 28/63

Now, we have the fractions 27/63 and 28/63 with the same denominator. We can perform the necessary operations.

Pair 5: 3/8 and 5/6

The denominators are 8 and 6. The LCD is the smallest number that is divisible by both 8 and 6, which is 24. Therefore, we need to convert both fractions to have a denominator of 24.

Converting 3/8: To convert 3/8 to have a denominator of 24, we multiply both the numerator and denominator by 3: 3/8 * (3/3) = 9/24

Converting 5/6: To convert 5/6 to have a denominator of 24, we multiply both the numerator and denominator by 4: 5/6 * (4/4) = 20/24

Now, we have the fractions 9/24 and 20/24 with the same denominator. We can perform the necessary operations.

Pair 6: 3/8 and 11/16

The denominators are 8 and 16. The LCD is the smallest number that is divisible by both 8 and 16, which is 16. Therefore, we need to convert both fractions to have a denominator of 16.

Converting 3/8: To convert 3/8 to have a denominator of 16, we multiply both the numerator and denominator by 2: 3/8 * (2/2) = 6/16

Converting 11/16: To convert 11/16 to have a denominator of 16, we multiply both the numerator and denominator by 1: 11/16 * (1/1) = 11/16

Now, we have the fractions 6/16 and 11/16 with the same denominator. We can perform the necessary operations.

Pair 7: 11/15 and 3/8

The denominators are 15 and 8. The LCD is the smallest number that is divisible by both 15 and 8, which is 120. Therefore, we need to convert both fractions to have a denominator of 120.

Converting 11/15: To convert 11/15 to have a denominator of 120, we multiply both the numerator and denominator by 8: 11/15 * (8/8) = 88/120

Converting 3/8: To convert 3/8 to have a denominator of 120, we multiply both the numerator and denominator by 15: 3/8 * (15/15) = 45/120

Now, we have the fractions 88/120 and 45/120 with the same denominator. We can perform the necessary operations.

Pair 8: 3/14 and 4/21

The denominators are 14 and 21. The LCD is the smallest number that is divisible by both 14 and 21, which is 42. Therefore, we need to convert both fractions to have a denominator of 42.

Converting 3/14: To convert 3/14 to have a denominator of 42, we multiply both the numerator and denominator by 3: 3/14 * (3/3) = 9/42

Converting 4/21: To convert 4/21 to have a denominator of 42, we multiply both the numerator and denominator by 2: 4/21 * (2/2) = 8/42

Now, we have the fractions 9/42 and 8/42 with the same denominator. We can perform the necessary operations.

Pair 9: 4/21 and 5/6

The denominators are 21 and 6. The LCD is the smallest number that is divisible by both 21 and 6, which is 42. Therefore, we need to convert both fractions to have a denominator of 42.

Converting 4/21: To convert 4/21 to have a denominator of 42, we multiply both the numerator and denominator by 2: 4/21 * (2/2) = 8/42

Converting 5/6: To convert 5/6 to have a denominator of 42, we multiply both the numerator and denominator by 7: 5/6 * (7/7) = 35/42

Now, we have the fractions 8/42 and 35/42 with the same denominator. We can perform the necessary operations.

Summary:

To find the least common denominator (LCD) for each pair of fractions, we determined the smallest number that is divisible by all the denominators involved. We then converted the fractions to have the same denominator and performed the necessary operations.

Here are the pairs of fractions and their least common denominators:

1. 5/28 and 9/14 (LCD: 28) 2. 13/16 and 11/12 (LCD: 48) 3. 7/8 and 5/6 (LCD: 24) 4. 3/7 and 4/9 (LCD: 63) 5. 3/8 and 5/6 (LCD: 24) 6. 3/8 and 11/16 (LCD: 16) 7. 11/15 and 3/8 (LCD: 120) 8. 3/14 and 4/21 (LCD: 42) 9. 4/21 and 5/6 (LCD: 42)

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