Question

Помогите с математикой: Приведите к наименьшому общему знаменателю дроби. а) 7/9 и 4/3; б)23/100 и 8/25; в) 5/16 и 5/8; г) 5/6 и 2/3; д) 5/2 и 19/10 е) 5/18 и 5/6. P.S. Заранее спасибо!

Answer 1

А) 7/9 и 16/9
б) 23/100 и 32/100
в) 5/16 и 10/16
г) 5/6 и 4/6
д) 25/10 и 19/10
е) 5/18 и 15/18

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 multiple that both denominators share. Once we find the LCD, we can convert the fractions to have the same denominator and perform operations on them.

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

a) 7/9 and 4/3: To find the LCD, we need to determine the smallest multiple that both 9 and 3 share. The multiples of 9 are 9, 18, 27, 36, ... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ... The smallest multiple that both 9 and 3 share is 9. Therefore, the LCD for 7/9 and 4/3 is 9.

b) 23/100 and 8/25: To find the LCD, we need to determine the smallest multiple that both 100 and 25 share. The multiples of 100 are 100, 200, 300, 400, ... and the multiples of 25 are 25, 50, 75, 100, 125, 150, 175, 200, ... The smallest multiple that both 100 and 25 share is 100. Therefore, the LCD for 23/100 and 8/25 is 100.

c) 5/16 and 5/8: To find the LCD, we need to determine the smallest multiple that both 16 and 8 share. The multiples of 16 are 16, 32, 48, 64, ... and the multiples of 8 are 8, 16, 24, 32, 40, 48, ... The smallest multiple that both 16 and 8 share is 16. Therefore, the LCD for 5/16 and 5/8 is 16.

d) 5/6 and 2/3: To find the LCD, we need to determine the smallest multiple that both 6 and 3 share. The multiples of 6 are 6, 12, 18, 24, ... and the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, ... The smallest multiple that both 6 and 3 share is 6. Therefore, the LCD for 5/6 and 2/3 is 6.

e) 5/2 and 19/10: To find the LCD, we need to determine the smallest multiple that both 2 and 10 share. The multiples of 2 are 2, 4, 6, 8, 10, 12, ... and the multiples of 10 are 10, 20, 30, 40, ... The smallest multiple that both 2 and 10 share is 10. Therefore, the LCD for 5/2 and 19/10 is 10.

f) 5/18 and 5/6: To find the LCD, we need to determine the smallest multiple that both 18 and 6 share. The multiples of 18 are 18, 36, 54, 72, ... and the multiples of 6 are 6, 12, 18, 24, 30, 36, ... The smallest multiple that both 18 and 6 share is 18. Therefore, the LCD for 5/18 and 5/6 is 18.

Converting Fractions to the Least Common Denominator

Now that we have determined the LCD for each pair of fractions, we can convert the fractions to have the same denominator.

a) 7/9 and 4/3: To convert 7/9 to have a denominator of 9, we multiply both the numerator and denominator by 1: 7/9 = (7 * 1)/(9 * 1) = 7/9. To convert 4/3 to have a denominator of 9, we multiply both the numerator and denominator by 3: 4/3 = (4 * 3)/(3 * 3) = 12/9.

b) 23/100 and 8/25: To convert 23/100 to have a denominator of 100, we multiply both the numerator and denominator by 1: 23/100 = (23 * 1)/(100 * 1) = 23/100. To convert 8/25 to have a denominator of 100, we multiply both the numerator and denominator by 4: 8/25 = (8 * 4)/(25 * 4) = 32/100.

c) 5/16 and 5/8: To convert 5/16 to have a denominator of 16, we multiply both the numerator and denominator by 1: 5/16 = (5 * 1)/(16 * 1) = 5/16. To convert 5/8 to have a denominator of 16, we multiply both the numerator and denominator by 2: 5/8 = (5 * 2)/(8 * 2) = 10/16.

d) 5/6 and 2/3: To convert 5/6 to have a denominator of 6, we multiply both the numerator and denominator by 1: 5/6 = (5 * 1)/(6 * 1) = 5/6. To convert 2/3 to have a denominator of 6, we multiply both the numerator and denominator by 2: 2/3 = (2 * 2)/(3 * 2) = 4/6.

e) 5/2 and 19/10: To convert 5/2 to have a denominator of 10, we multiply both the numerator and denominator by 5: 5/2 = (5 * 5)/(2 * 5) = 25/10. To convert 19/10 to have a denominator of 10, we multiply both the numerator and denominator by 1: 19/10 = (19 * 1)/(10 * 1) = 19/10.

f) 5/18 and 5/6: To convert 5/18 to have a denominator of 18, we multiply both the numerator and denominator by 1: 5/18 = (5 * 1)/(18 * 1) = 5/18. To convert 5/6 to have a denominator of 18, we multiply both the numerator and denominator by 3: 5/6 = (5 * 3)/(6 * 3) = 15/18.

Summary:

a) The least common denominator (LCD) for 7/9 and 4/3 is 9. The fractions can be converted to have a denominator of 9: 7/9 and 12/9. b) The LCD for 23/100 and 8/25 is 100. The fractions can be converted to have a denominator of 100: 23/100 and 32/100. c) The LCD for 5/16 and 5/8 is 16. The fractions can be converted to have a denominator of 16: 5/16 and 10/16. d) The LCD for 5/6 and 2/3 is 6. The fractions can be converted to have a denominator of 6: 5/6 and 4/6. e) The LCD for 5/2 and 19/10 is 10. The fractions can be converted to have a denominator of 10: 25/10 and 19/10. f) The LCD for 5/18 and 5/6 is 18. The fractions can be converted to have a denominator of 18: 5/18 and 15/18.

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