Question

(3 5/21 -2 9/19)×1 13/15:(1 1/6+ 1 1/3

Answer 1

(3 5/21 -2 9/19) × 1 13/15 : (1 1/6 + 1 1/3)

Давайте посчитаем это выражение шаг за шагом.

1) Найдем разность (3 5/21 - 2 9/19):

Для начала приведем оба числа к общему знаменателю, который в данном случае равен 21 × 19 = 399.

3 5/21 = (3 × 21 + 5) / 21 = 68 / 21
2 9/19 = (2 × 19 + 9) / 19 = 47 / 19

Теперь вычтем полученные дроби:
68/21 - 47/19 = (68 × 19 - 47 × 21) / (21 × 19) = (1292 - 987) / 399 = 305 / 399

2) Далее умножим полученную разность на дробь 1 13/15:

Переведем 1 13/15 в неправильную дробь:
1 13/15 = (1 × 15 + 13) / 15 = 28/15

Умножим 305/399 на 28/15:
(305/399) × (28/15) = (305 × 28) / (399 × 15) = 8540 / 5985

3) Наконец, разделим полученную дробь на сумму 1 1/6 и 1 1/3:

Переведем каждую дробь в неправильный вид:
1 1/6 = (1 × 6 + 1) / 6 = 7/6
1 1/3 = (1 × 3 + 1) / 3 = 4/3

Выполним сложение:
7/6 + 4/3 = (7 × 3 + 4 × 6) / (6 × 3) = 43/18

Теперь разделим 8540/5985 на 43/18:
(8540/5985) ÷ (43/18) = (8540 × 18) / (5985 × 43) ≈ 1.572

Таким образом, результат данного выражения примерно равен 1.572.

Answer 2

Пришу прям подробно

(68/21-37/14)* 13/15÷((1+1)+(1/6 + 1/3)

25/42 * 13/15-((1+1)+(1/6 + 1/3)

25/42 13/15 ((2)+(1/6 + 1/3)

25/42 13/15 (2 + 1/2)

25/42 13/15 = 2 1/2

25/42 * 13/15 ÷ 5/2

25/42 13/15 * 2/5

Сокращаем на 5 числа 25 и 5

5/42 13/15 * 2

Сокращаем на 2 числа 42 и 2

5/21* 13/15

Сокращаем на 5 числа 5 и 15

1/21* 13/3

Умножаем дроби

13/63 ответ

Answer 3

To solve the given expression, let's break it down step by step, following the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Step 1: Simplify the fractions and perform the subtraction

• $3 \frac{5}{21} - 2 \frac{9}{19}$

To perform the subtraction, we need to have a common denominator. The common denominator is the least common multiple (LCM) of 21 and 19, which is 399.

Converting the fractions to have a denominator of 399:

• $3 \times \frac{399}{21} - 2 \times \frac{399}{19}$
• $57 - 42\frac{18}{19}$

Now, let's simplify $42\frac{18}{19}$:

• $42\frac{18}{19} = 42 + \frac{18}{19}$

Step 2: Perform the division and addition

• $\frac{57}{1} - \left(42 + \frac{18}{19}\right)$

Now, let's add the whole numbers and fractions separately:

• $42 + \frac{18}{19} = \frac{42 \times 19 + 18}{19}$
• $42\frac{342}{19}$

Now, subtract this from 57:

• $\frac{57}{1} - 42\frac{342}{19}$

To subtract, we need a common denominator. The common denominator is 19.

• $\frac{57 \times 19}{1 \times 19} - \frac{42 \times 19 + 342}{19}$
• $\frac{1083 - 864}{19}$
• $\frac{219}{19}$

Step 3: Perform the final division

• $\frac{219}{19} \div 1 \frac{13}{15}$

To divide fractions, we invert the divisor and multiply:

• $\frac{219}{19} \times \frac{15}{13}$

Now, let's perform the multiplication:

• $=\frac{219 \times 15}{19 \times 13}$
• $=\frac{3285}{247}$

So, the result of the given expression is approximately $\frac{3285}{247}$ or $13 \frac{164}{247}$ as a mixed fraction.