Question

Порівняйте дроби 5/12 5/7 8/9 17/18 6/7 17/21 7/12 11/15 5/9 4/7 7/15 13/18 4/36 5/42 7/64 9/72

Answer 1

Ответ:

Для порівняння дробів, можна використати метод перетворення обох дробів до спільного знаменника та порівняти їхні чисельники.

1. 5/12 < 5/7, бо 5/12 ≈ 0.42, а 5/7 ≈ 0.71.

2. 8/9 < 17/18, бо 8/9 ≈ 0.89, а 17/18 ≈ 0.94.

3. 6/7 < 17/21, бо 6/7 ≈ 0.86, а 17/21 ≈ 0.81.

4. 7/12 < 11/15, бо 7/12 ≈ 0.58, а 11/15 ≈ 0.73.

5. 5/9 > 4/7, бо 5/9 ≈ 0.56, а 4/7 ≈ 0.57.

6. 7/15 < 13/18, бо 7/15 ≈ 0.47, а 13/18 ≈ 0.72.

7. 4/36 > 5/42, бо 4/36 ≈ 0.11, а 5/42 ≈ 0.12.

8. 7/64 < 9/72, бо 7/64 ≈ 0.11, а 9/72 ≈ 0.12.

Остаточна порядковість дробів від найменшого до найбільшого:

4/36 < 5/42 < 7/64 < 5/9 < 7/15 < 5/12 < 6/7 < 7/12 < 8/9 < 9/72 < 11/15 < 13/18 < 17/21 < 17/18.

Пошаговое объяснение:

Answer 2

Comparing Fractions

Let's compare the given fractions:

1. 5/12 and 5/7: To compare these fractions, we can find a common denominator. The least common multiple (LCM) of 12 and 7 is 84. Converting both fractions to have a denominator of 84, we get: - 5/12 = 35/84 - 5/7 = 60/84

Since 35/84 is less than 60/84, 5/12 is less than 5/7.

2. 8/9 and 17/18: Again, we can find a common denominator. The LCM of 9 and 18 is 18. Converting both fractions to have a denominator of 18, we get: - 8/9 = 16/18 - 17/18 = 17/18

Since 16/18 is less than 17/18, 8/9 is less than 17/18.

3. 6/7 and 17/21: We can find a common denominator by multiplying the denominators together. The product of 7 and 21 is 147. Converting both fractions to have a denominator of 147, we get: - 6/7 = 126/147 - 17/21 = 119/147

Since 126/147 is greater than 119/147, 6/7 is greater than 17/21.

4. 7/12 and 11/15: We can find a common denominator by multiplying the denominators together. The product of 12 and 15 is 180. Converting both fractions to have a denominator of 180, we get: - 7/12 = 105/180 - 11/15 = 132/180

Since 105/180 is less than 132/180, 7/12 is less than 11/15.

5. 5/9 and 4/7: We can find a common denominator by multiplying the denominators together. The product of 9 and 7 is 63. Converting both fractions to have a denominator of 63, we get: - 5/9 = 35/63 - 4/7 = 36/63

Since 35/63 is less than 36/63, 5/9 is less than 4/7.

6. 7/15 and 13/18: We can find a common denominator by multiplying the denominators together. The product of 15 and 18 is 270. Converting both fractions to have a denominator of 270, we get: - 7/15 = 126/270 - 13/18 = 195/270

Since 126/270 is less than 195/270, 7/15 is less than 13/18.

7. 4/36 and 5/42: We can find a common denominator by multiplying the denominators together. The product of 36 and 42 is 1512. Converting both fractions to have a denominator of 1512, we get: - 4/36 = 168/1512 - 5/42 = 180/1512

Since 168/1512 is less than 180/1512, 4/36 is less than 5/42.

8. 7/64 and 9/72: We can find a common denominator by multiplying the denominators together. The product of 64 and 72 is 4608. Converting both fractions to have a denominator of 4608, we get: - 7/64 = 315/4608 - 9/72 = 126/4608

Since 315/4608 is greater than 126/4608, 7/64 is greater than 9/72.

To summarize the comparisons:

- 5/12 < 5/7 - 8/9 < 17/18 - 6/7 > 17/21 - 7/12 < 11/15 - 5/9 < 4/7 - 7/15 < 13/18 - 4/36 < 5/42 - 7/64 > 9/72