Question

(1 3/4+1 1/42):(2 2/9*3 3/16-7 1/14)=

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To simplify the expression, let's convert the mixed numbers into improper fractions first.

1 3/4 can be written as (4 * 1 + 3) / 4 = 7/4.

1 1/42 can be written as (42 * 1 + 1) / 42 = 43/42.

2 2/9 can be written as (9 * 2 + 2) / 9 = 20/9.

3 3/16 can be written as (16 * 3 + 3) / 16 = 51/16.

7 1/14 can be written as (14 * 7 + 1) / 14 = 99/14.

Now, let's simplify the expression:

(7/4 + 43/42) : (20/9 * 51/16 - 99/14)

To simplify further, let's find the common denominator for the fractions in the denominator:

Denominator: 9 * 16 * 14 = 2016.

Now, let's calculate the numerator:

Numerator: (7/4 + 43/42) : (20/9 * 51/16 - 99/14)

Numerator: [(7 * 42 + 4 * 43) / (4 * 42)] : [(20 * 16 * 14 * 51) / (9 * 16 * 14) - (99 * 9 * 16) / (14 * 9)]

Numerator: [294 + 172] / 168 : [287040 / 2016 - 14256 / 14]

Numerator: 466 / 168 : 142224 / 2016 - 14256 / 14

Numerator: 466 / 168 : 142224 / 2016 - 10176 / 2016

Now, let's find the common denominator for the fractions in the numerator:

Denominator: 168 * 2016 = 337,728.

Now, let's calculate the numerator:

Numerator: (466 * 2016) / 168 - (142224 - 10176) / 2016

Numerator: 937,056 / 168 - 132,048 / 2016

Numerator: 937,056 / 168 - 65,52 / 168

Numerator: (937,056 - 65,520) / 168

Numerator: 871,536 / 168

Finally, let's simplify the fraction:

871,536 / 168 = 5184.

Therefore, the simplified expression is 5184.