Question

Выполните действия: а) 4 5/6+2 3/8 б) 7 15/8-1 7/12 в) 3 4/9+ 2 2/7 г) 5 3/14-1 1/12 срочно дам 30 балов ​

Answer 1

а) 6 = 2 · 3; 8 = 2³; НОК (6 и 8) = 2³ · 3 = 24

24 : 6 = 4 - доп. множ. к 5/6 = 20/24

24 : 8 = 3 - доп. множ. к 3/8 = 9/24

4 5/6 + 2 3/8 = 4 20/24 + 2 9/24 = 6 29/24 = 7 целых 5/24;

б) 8 = 2³; 12 = 2² · 3; НОК (8 и 12) = 2³ · 3 = 24

24 : 8 = 3 - доп. множ. к 15/8 = 45/24

24 : 12 = 2 - доп. множ. к 7/12 = 14/24

7 15/8 - 1 7/12 = 7 45/24 - 1 14/24 = 6 31/24 = 7 целых 7/24;

в) 9 = 3²; 7 - простое число; НОК (9 и 7) = 3² · 7 = 63

63 : 9 = 7 - доп. множ. к 4/9 = 28/63

63 : 7 = 9 - доп. множ. к 2/7 = 18/63

3 4/9 + 2 2/7 = 3 28/63 + 2 18/63 = 5 целых 46/63;

г) 14 = 2 · 7; 12 = 2² · 3; НОК (14 и 12) = 2² · 3 · 7 = 84

84 : 14 = 6 - доп. множ. к 3/14 = 18/84

84 : 12 = 7 - доп. множ. к 1/12 = 7/84

5 3/14 - 1 1/12 = 5 18/84 - 1 7/84 = 4 целых 11/84.

Answer 2

Ответ:

Пошаговое объяснение:

А)

4. 5/6 + 2. 3/8 =

4. 20/24 + 2. 9/24 =

6. 29/24 = 7. 5/24

Б)

7. 15/8 - 1. 7/12 =

7. 45/24 - 1. 14/24 =

6. 31/24 = 7. 7/24

В)

3. 4/9 + 2. 2/7 =

3. 28/63 + 2. 18/63 = 5. 46/63

Г)

5. 3/14 - 1. 1/12 =

5. 18/84 - 1. 7/84 = 4. 11/84

Answer 3

a) 4 5/6 + 2 3/8

To add the fractions 4 5/6 and 2 3/8, we need to find a common denominator. The common denominator of 6 and 8 is 24.

Converting the mixed numbers to improper fractions: 4 5/6 = (4 * 6 + 5) / 6 = 29/6 2 3/8 = (2 * 8 + 3) / 8 = 19/8

Now, we can add the fractions: 29/6 + 19/8 = (29 * 8 + 19 * 6) / (6 * 8) = 232/48

Simplifying the fraction: 232/48 = 29/6

Therefore, 4 5/6 + 2 3/8 = 29/6.

б) 7 15/8 - 1 7/12

To subtract the fractions 7 15/8 and 1 7/12, we need to find a common denominator. The common denominator of 8 and 12 is 24.

Converting the mixed numbers to improper fractions: 7 15/8 = (7 * 8 + 15) / 8 = 71/8 1 7/12 = (1 * 12 + 7) / 12 = 19/12

Now, we can subtract the fractions: 71/8 - 19/12 = (71 * 3 - 19 * 2) / (8 * 3) = 193/24

Simplifying the fraction: 193/24 = 8 1/24

Therefore, 7 15/8 - 1 7/12 = 8 1/24.

в) 3 4/9 + 2 2/7

To add the fractions 3 4/9 and 2 2/7, we need to find a common denominator. The common denominator of 9 and 7 is 63.

Converting the mixed numbers to improper fractions: 3 4/9 = (3 * 9 + 4) / 9 = 31/9 2 2/7 = (2 * 7 + 2) / 7 = 16/7

Now, we can add the fractions: 31/9 + 16/7 = (31 * 7 + 16 * 9) / (9 * 7) = 307/63

Simplifying the fraction: 307/63 = 4 55/63

Therefore, 3 4/9 + 2 2/7 = 4 55/63.

г) 5 3/14 - 1 1/12

To subtract the fractions 5 3/14 and 1 1/12, we need to find a common denominator. The common denominator of 14 and 12 is 168.

Converting the mixed numbers to improper fractions: 5 3/14 = (5 * 14 + 3) / 14 = 73/14 1 1/12 = (1 * 12 + 1) / 12 = 13/12

Now, we can subtract the fractions: 73/14 - 13/12 = (73 * 12 - 13 * 14) / (14 * 12) = 751/168

Simplifying the fraction: 751/168 = 4 119/168

Therefore, 5 3/14 - 1 1/12 = 4 119/168.