Question

А) 4целых1/2+2/3*3целых6/7-5целых3/4 б) -2целых1/4*(-1/3)2в квадрате

Answer 1

А)4 1/2+2/3 * 3 6/7-5 3/4=9/2+2/3 * 27/7-23/4=9/2+18/7-23/4=
    =126/28+72/28-161/28=37/28=1 9/28
б) -2 1/4*(-1/3)^2=-9/4 * 1/9=- 1/4

Answer 2

а) To solve the expression 4 and 1/2 + 2/3 * 3 and 6/7 - 5 and 3/4, we can follow the order of operations, which is parentheses, multiplication/division (from left to right), and addition/subtraction (from left to right).

First, let's simplify the multiplication and division:

2/3 * 3 and 6/7 = (2/3) * (3 + 6/7) = (2/3) * (21/7 + 6/7) = (2/3) * (27/7) = (2 * 27) / (3 * 7) = 54/21 = 18/7

Now we can substitute the simplified values back into the expression:

4 and 1/2 + 18/7 - 5 and 3/4

Next, let's convert the mixed numbers to improper fractions:

4 and 1/2 = (4 * 2 + 1) / 2 = 9/2 5 and 3/4 = (5 * 4 + 3) / 4 = 23/4

Now the expression becomes:

9/2 + 18/7 - 23/4

To add or subtract fractions, we need a common denominator. The common denominator of 2, 7, and 4 is 28.

Converting each fraction to have a denominator of 28:

(9/2) * (14/14) = 126/28 (18/7) * (4/4) = 72/28 (23/4) * (7/7) = 161/28

Now the expression becomes:

126/28 + 72/28 - 161/28

Combining the fractions:

(126 + 72 - 161) / 28 = 37/28

So the final result of the expression 4 and 1/2 + 2/3 * 3 and 6/7 - 5 and 3/4 is 37/28.

b) To simplify the expression -2 and 1/4 * (-1/3) ^ 2, we follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

First, let's simplify the exponent:

(-1/3) ^ 2 = (-1/3) * (-1/3) = 1/9

Now the expression becomes:

-2 and 1/4 * 1/9

Next, let's convert the mixed number to an improper fraction:

-2 and 1/4 = (-2 * 4 + 1) / 4 = -7/4

Now the expression becomes:

-7/4 * 1/9

Multiplying the fractions:

(-7/4) * (1/9) = (-7 * 1) / (4 * 9) = -7/36

So the final result of the expression -2 and 1/4 * (-1/3) ^ 2 is -7/36.