Question

Выполните действия: 1) 25целых7/32 - 21целых1/24; 2) 19целых7/20 - 9целых1/30; 3) 41целых9/28 - 15целых2/21; 4) 73целых5/24 - 58целых19/36; 5) 91целых37/54 - 47целых11/45;

Answer 1

Дроби, почему-то не сократились... Но в правильности я уверен...

Answer 2

1) 25 целых 7/32 - 21 целых 1/24

To subtract mixed fractions, we need to convert them into improper fractions first.

For the first fraction, 25 целых 7/32, the whole number 25 can be written as an improper fraction by multiplying it by the denominator of the fraction and adding the numerator. So, 25 целых 7/32 is equal to (25 * 32 + 7)/32 = 807/32.

For the second fraction, 21 целых 1/24, the whole number 21 can be written as an improper fraction by multiplying it by the denominator of the fraction and adding the numerator. So, 21 целых 1/24 is equal to (21 * 24 + 1)/24 = 505/24.

Now, we can subtract the two fractions:

807/32 - 505/24

To subtract fractions, we need to have a common denominator. In this case, the common denominator is 32 * 24 = 768.

So, we need to convert both fractions to have a denominator of 768:

(807/32) * (24/24) = 19368/768

(505/24) * (32/32) = 16160/768

Now, we can subtract the two fractions:

19368/768 - 16160/768 = (19368 - 16160)/768 = 3208/768

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 8:

(3208/8) / (768/8) = 401/96

So, the result of the subtraction is 401/96.

2) 19 целых 7/20 - 9 целых 1/30

Following the same steps as above, let's convert the mixed fractions to improper fractions:

19 целых 7/20 = (19 * 20 + 7)/20 = 387/20

9 целых 1/30 = (9 * 30 + 1)/30 = 271/30

Now, we can subtract the two fractions:

387/20 - 271/30

To subtract fractions, we need a common denominator. The common denominator here is 20 * 30 = 600.

So, we convert both fractions to have a denominator of 600:

(387/20) * (30/30) = 11610/600

(271/30) * (20/20) = 5420/600

Now, we can subtract the two fractions:

11610/600 - 5420/600 = (11610 - 5420)/600 = 6190/600

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 10:

(6190/10) / (600/10) = 619/60

Therefore, the result of the subtraction is 619/60.

3) 41 целых 9/28 - 15 целых 2/21

Converting the mixed fractions to improper fractions:

41 целых 9/28 = (41 * 28 + 9)/28 = 1157/28

15 целых 2/21 = (15 * 21 + 2)/21 = 317/21

Subtracting the two fractions:

1157/28 - 317/21

The common denominator is 28 * 21 = 588.

Converting both fractions to have a denominator of 588:

(1157/28) * (21/21) = 24357/588

(317/21) * (28/28) = 8852/588

Subtracting the two fractions:

24357/588 - 8852/588 = (24357 - 8852)/588 = 15405/588

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 147:

(15405/147) / (588/147) = 105/4

Therefore, the result of the subtraction is 105/4.

4) 73 целых 5/24 - 58 целых 19/36

Converting the mixed fractions to improper fractions:

73 целых 5/24 = (73 * 24 + 5)/24 = 1765/24

58 целых 19/36 = (58 * 36 + 19)/36 = 2107/36

Subtracting the two fractions:

1765/24 - 2107/36

The common denominator is 24 * 36 = 864.

Converting both fractions to have a denominator of 864:

(1765/24) * (36/36) = 63540/864

(2107/36) * (24/24) = 50688/864

Subtracting the two fractions:

63540/864 - 50688/864 = (63540 - 50688)/864 = 12852/864

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 12:

(12852/12) / (864/12) = 1071/72

Therefore, the result of the subtraction is 1071/72.

5) 91 целых 37/54 - 47 целых 11/45

Converting the mixed fractions to improper fractions:

91 целых 37/54 = (91 * 54 + 37)/54 = 4933/54

47 целых 11/45 = (47 * 45 + 11)/45 = 2126/45

Subtracting the two fractions:

4933/54 - 2126/45

The common denominator is 54 * 45 = 2430.

Converting both fractions to have a denominator of 2430:

(4933/54) * (45/45) = 221985/2430

(2126/45) * (54/54) = 114804/2430

Subtracting the two fractions:

221985/2430 - 114804/2430 = (221985 - 114804)/2430 = 107181/2430

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 27:

(107181/27) / (2430/27) = 3977/90

Therefore, the result of the subtraction is 3977/90.