Question

Представьте неправильные дроби в виде смешанных чисел и приведите их к наименьшему общему знаменателю;27/8и17/12;43/6и23/9;13/12и25/18;93/25и52/15;71/30и41/25; 51/25и93/20. ПОЖАЛУЙСТА!!!!

Answer 1

Converting Improper Fractions to Mixed Numbers and Finding the Least Common Denominator

To convert improper fractions to mixed numbers, we divide the numerator by the denominator. The whole number part of the result is the whole number in the mixed number, and the remainder becomes the numerator of the fractional part. The denominator remains the same.

To find the least common denominator (LCD) of two fractions, we need to find the smallest multiple that both denominators share. Once we have the LCD, we can convert the fractions to have the same denominator by multiplying the numerator and denominator of each fraction by the appropriate factor.

Let's apply these steps to the given fractions:

1. 27/8 and 17/12:

To convert 27/8 to a mixed number, we divide 27 by 8. The quotient is 3 with a remainder of 3. Therefore, 27/8 can be written as 3 3/8.

To convert 17/12 to a mixed number, we divide 17 by 12. The quotient is 1 with a remainder of 5. Therefore, 17/12 can be written as 1 5/12.

To find the LCD of 8 and 12, we can list the multiples of each denominator: 8, 16, 24, 32, 40, 48, 56, 64... and 12, 24, 36, 48, 60, 72, 84, 96... The least common multiple is 24, so we can convert both fractions to have a denominator of 24.

Converting 27/8 to have a denominator of 24, we multiply both the numerator and denominator by 3. The result is 81/24.

Converting 17/12 to have a denominator of 24, we multiply both the numerator and denominator by 2. The result is 34/24.

Therefore, the fractions 27/8 and 17/12, when converted to have the same denominator, become 81/24 and 34/24 respectively.

2. 43/6 and 23/9:

To convert 43/6 to a mixed number, we divide 43 by 6. The quotient is 7 with a remainder of 1. Therefore, 43/6 can be written as 7 1/6.

To convert 23/9 to a mixed number, we divide 23 by 9. The quotient is 2 with a remainder of 5. Therefore, 23/9 can be written as 2 5/9.

To find the LCD of 6 and 9, we can list the multiples of each denominator: 6, 12, 18, 24, 30, 36, 42, 48... and 9, 18, 27, 36, 45, 54, 63, 72... The least common multiple is 18, so we can convert both fractions to have a denominator of 18.

Converting 43/6 to have a denominator of 18, we multiply both the numerator and denominator by 3. The result is 129/18.

Converting 23/9 to have a denominator of 18, we multiply both the numerator and denominator by 2. The result is 46/18.

Therefore, the fractions 43/6 and 23/9, when converted to have the same denominator, become 129/18 and 46/18 respectively.

3. 13/12 and 25/18:

To convert 13/12 to a mixed number, we divide 13 by 12. The quotient is 1 with a remainder of 1. Therefore, 13/12 can be written as 1 1/12.

To convert 25/18 to a mixed number, we divide 25 by 18. The quotient is 1 with a remainder of 7. Therefore, 25/18 can be written as 1 7/18.

To find the LCD of 12 and 18, we can list the multiples of each denominator: 12, 24, 36, 48, 60, 72, 84, 96... and 18, 36, 54, 72, 90, 108, 126, 144... The least common multiple is 36, so we can convert both fractions to have a denominator of 36.

Converting 13/12 to have a denominator of 36, we multiply both the numerator and denominator by 3. The result is 39/36.

Converting 25/18 to have a denominator of 36, we multiply both the numerator and denominator by 2. The result is 50/36.

Therefore, the fractions 13/12 and 25/18, when converted to have the same denominator, become 39/36 and 50/36 respectively.

4. 93/25 and 52/15:

To convert 93/25 to a mixed number, we divide 93 by 25. The quotient is 3 with a remainder of 18. Therefore, 93/25 can be written as 3 18/25.

To convert 52/15 to a mixed number, we divide 52 by 15. The quotient is 3 with a remainder of 7. Therefore, 52/15 can be written as 3 7/15.

To find the LCD of 25 and 15, we can list the multiples of each denominator: 25, 50, 75, 100, 125, 150, 175, 200... and 15, 30, 45, 60, 75, 90, 105, 120... The least common multiple is 75, so we can convert both fractions to have a denominator of 75.

Converting 93/25 to have a denominator of 75, we multiply both the numerator and denominator by 3. The result is 279/75.

Converting 52/15 to have a denominator of 75, we multiply both the numerator and denominator by 5. The result is 260/75.

Therefore, the fractions 93/25 and 52/15, when converted to have the same denominator, become 279/75 and 260/75 respectively.

5. 71/30 and 41/25:

To convert 71/30 to a mixed number, we divide 71 by 30. The quotient is 2 with a remainder of 11. Therefore, 71/30 can be written as 2 11/30.

To convert 41/25 to a mixed number, we divide 41 by 25. The quotient is 1 with a remainder of 16. Therefore, 41/25 can be written as 1 16/25.

To find the LCD of 30 and 25, we can list the multiples of each denominator: 30, 60, 90, 120, 150, 180, 210, 240... and 25, 50, 75, 100, 125, 150, 175, 200... The least common multiple is 150, so we can convert both fractions to have a denominator of 150.

Converting 71/30 to have a denominator of 150, we multiply both the numerator and denominator by 5. The result is 355/150.

Converting 41/25 to have a denominator of 150, we multiply both the numerator and denominator by 6. The result is 246/150.

Therefore, the fractions 71/30 and 41/25, when converted to have the same denominator, become 355/150 and 246/150 respectively.

6. 51/25 and 93/20:

To convert 51/25 to a mixed number, we divide 51 by 25. The quotient is 2 with a remainder of 1. Therefore, 51/25 can be written as 2 1/25.

To convert 93/20 to a mixed number, we divide 93 by 20. The quotient is 4 with a remainder of 13. Therefore, 93/20 can be written as 4 13/20.

To find the LCD of 25 and 20, we can list the multiples of each denominator: 25, 50, 75, 100, 125, 150, 175, 200... and 20, 40, 60, 80, 100, 120, 140, 160... The least common multiple is 100, so we can convert both fractions to have a denominator of 100.

Converting 51/25 to have a denominator of 100, we multiply both the numerator and denominator by 4. The result is 204/100.

Converting 93/20 to have a denominator of 100, we multiply both the numerator and denominator by 5. The result is 465/100.

Therefore, the fractions 51/25 and 93/20, when converted to have the same denominator, become 204/100 and 465/100 respectively.

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