Question

( 2,75+1 1/6):(2 1/3 • 3 1/7 - 7 1/4)​

Answer 1

(2,75 + 1 16) : (2 1/3 · 3 1/7 - 7 1/4) = 47

1) 2,75 + 1 1/6 = 2 3/4 + 1 1/6 = 2 9/12 + 1 2/12 = 3 11/12

2) 2 1/3 · 3 1/7 = 7/3 · 22/7 = 22/3 = 7 1/3

3) 7 1/3 - 7 1/4 = 7 4/12 - 7 3/12 = 1/12

4) 3 11/12 : 1/12 = 47/12 · 12/1 = 47

Ответ: 47.

Answer 2

To solve this expression, you should follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders (i.e., powers and square roots, etc.), Multiplication and Division (left-to-right), and Addition and Subtraction (left-to-right). In this case, we need to start by evaluating what's inside the parentheses first:

(2.75 + 1 1/6) ÷ (2 1/3 • 3 1/7 - 7 1/4)

First, let's deal with what's inside the parentheses:

2.75 + 1 1/6 = 2.75 + 1 + 1/6 Convert 1 to a fraction with the same denominator as 6: 2.75 + 6/6 + 1/6 = 2.75 + 7/6

Now, let's calculate the value inside the parentheses: 2.75 + 7/6 = (2.75 * 6/6) + 7/6 = 16.5/6 + 7/6 = (16.5 + 7)/6 = 23.5/6

Now, let's focus on the right side of the expression within the parentheses:

2 1/3 • 3 1/7 - 7 1/4

First, convert the mixed numbers to improper fractions:

2 1/3 = 7/3 3 1/7 = 22/7 7 1/4 = 29/4

Now, calculate the right side of the expression: (7/3) * (22/7) - (29/4)

Now, multiply and subtract:

(7/3) * (22/7) = (7 * 22) / (3 * 7) = 154/21

Now, subtract: (154/21) - (29/4)

To subtract fractions, they need a common denominator, which in this case is 84:

(154/21) * (4/4) - (29/4) * (21/21) = (616/84) - (609/84)

Now, subtract the fractions:

(616/84) - (609/84) = (616 - 609)/84 = 7/84

So, the right side of the expression simplifies to 7/84.

Now, we can put it all together:

(23.5/6) ÷ (7/84)

To divide by a fraction, you can multiply by its reciprocal:

(23.5/6) * (84/7)

Now, multiply:

(23.5 * 84) / (6 * 7) = 1974/42

Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6:

(1974/6) / (42/6) = 329/7

So, the final result is:

(2.75 + 1 1/6) ÷ (2 1/3 • 3 1/7 - 7 1/4) = 329/7