Question

Сравните дроби: а) 6/7 и 7/8 б) 11/30 и 7/24 в) 5/6 и 8/9 г)11/20 и 9/16

Answer 1

6/7>7/8 11/30<7/24 5/6>8/9 11/20<9/16

Answer 2

Сравнение дробей:

а) 6/7 и 7/8:

To compare the fractions 6/7 and 7/8, we can use a common denominator. The least common multiple (LCM) of 7 and 8 is 56, so we can convert both fractions to have a denominator of 56.

Multiplying the numerator and denominator of 6/7 by 8, we get (6 * 8) / (7 * 8) = 48/56. Similarly, multiplying the numerator and denominator of 7/8 by 7, we get (7 * 7) / (8 * 7) = 49/56.

Now that both fractions have the same denominator, we can compare their numerators. In this case, 49/56 is greater than 48/56. Therefore, 7/8 is greater than 6/7.

б) 11/30 и 7/24:

To compare the fractions 11/30 and 7/24, we can again find a common denominator. The LCM of 30 and 24 is 120, so we can convert both fractions to have a denominator of 120.

Multiplying the numerator and denominator of 11/30 by 4, we get (11 * 4) / (30 * 4) = 44/120. Similarly, multiplying the numerator and denominator of 7/24 by 5, we get (7 * 5) / (24 * 5) = 35/120.

Since both fractions have the same denominator, we can compare their numerators. In this case, 44/120 is greater than 35/120. Therefore, 11/30 is greater than 7/24.

в) 5/6 и 8/9:

To compare the fractions 5/6 and 8/9, we can once again find a common denominator. The LCM of 6 and 9 is 18, so we can convert both fractions to have a denominator of 18.

Multiplying the numerator and denominator of 5/6 by 3, we get (5 * 3) / (6 * 3) = 15/18. Similarly, multiplying the numerator and denominator of 8/9 by 2, we get (8 * 2) / (9 * 2) = 16/18.

Now that both fractions have the same denominator, we can compare their numerators. In this case, 16/18 is greater than 15/18. Therefore, 8/9 is greater than 5/6.

г) 11/20 и 9/16:

To compare the fractions 11/20 and 9/16, we can find a common denominator. The LCM of 20 and 16 is 80, so we can convert both fractions to have a denominator of 80.

Multiplying the numerator and denominator of 11/20 by 4, we get (11 * 4) / (20 * 4) = 44/80. Similarly, multiplying the numerator and denominator of 9/16 by 5, we get (9 * 5) / (16 * 5) = 45/80.

Since both fractions have the same denominator, we can compare their numerators. In this case, 45/80 is greater than 44/80. Therefore, 9/16 is greater than 11/20.

In summary: - 7/8 > 6/7 - 11/30 > 7/24 - 8/9 > 5/6 - 9/16 > 11/20

Remember, when comparing fractions, it's important to find a common denominator so that the numerators can be compared accurately.