Question

1.Выполните действия с дробями а) 6*(7/8+3/4)б) (7/8-5/16)*82.Найдите числа, обратные заданныма) 5/11б)4 3/83.Решите задачуВ первый день папа посадил 1/4 часть деревьев. Мама посадила 75% от того, что посадил папа. Сколько деревьев необходимо посадить, если в саду должно расти 20 деревьев? ​

Answer 1

1.

а)

$6 \times ( \frac{7}{8} + \frac{3}{4} ) = 6 \times ( \frac{7}{8} + \frac{6}{8} ) = 6 \times \frac{13}{8} = \frac{39}{4} = 9 \frac{3}{4}$

б)

$( \frac{7}{8} - \frac{5}{16} ) \times 8 = ( \frac{14}{16} - \frac{5}{16} ) \times 8 = \frac{9}{16} \times 8 = \frac{9}{2} = 4 \frac{1}{2}$

2.

а)

$\frac{11}{5}$

б)

$4 \frac{3}{8} = \frac{35}{8} = \frac{8}{35}$

3.

$a)20 \times \frac{1}{4} = 5 \\ b)5 \times \frac{3}{4} = 4 \\ c)20 - 5 - 4 = 11$

ответ:11

Answer 2

1. Выполнение действий с дробями: a) 6 * (7/8 + 3/4)

To add the fractions inside the parentheses, we need a common denominator, which is 8.

7/8 + 3/4 = (71 + 32) / 8 = (7 + 6) / 8 = 13/8

Now, we can multiply:

6 * (13/8) = 6 * 13 / 8 = 78 / 8 = 9 3/4

b) (7/8 - 5/16) * 82

Again, to subtract the fractions, we need a common denominator, which is 16.

7/8 - 5/16 = (72 - 51) / 16 = (14 - 5) / 16 = 9/16

Now, we can multiply:

(9/16) * 82 = 9/16 * 82 = (9 * 82) / 16 = 738 / 16 = 46 2/16 = 46 1/8

2. Найдите числа, обратные заданным: a) 5/11

The reciprocal (or the number's inverse) of a fraction is obtained by interchanging the numerator and the denominator.

Reciprocal of 5/11 = 11/5

b) 4 3/8

To find the reciprocal of a mixed number, we first convert it to an improper fraction:

4 3/8 = (4 * 8 + 3) / 8 = 35 / 8

Now, find the reciprocal:

Reciprocal of 4 3/8 = 8/35

3. Решение задачи:

Let's assume the number of trees to be planted is x.

In the first day, the father planted 1/4 of the trees, which is (1/4)x.

Then, the mother planted 75% of what the father planted, which is (75/100) * (1/4)x = (3/4) * (1/4)x = (3/16)x.

The total number of trees planted by both parents is the sum of what each planted:

(1/4)x + (3/16)x = (4/16)x + (3/16)x = (7/16)x

According to the problem, the total number of trees planted by both parents is 20:

(7/16)x = 20

To find x, we can isolate it by dividing both sides of the equation by (7/16):

x = 20 / (7/16) x = 20 * (16/7) x = 320 / 7 x ≈ 45.71

Rounded to the nearest whole number, they need to plant approximately 46 trees to have a total of 20 trees in the garden.