Question

1) (1-7/10)х=2 1/4 2) (5/7-2/3):(4/9-5/12)

Answer 1

1) (1-7/10)х=2 1/4
значит: (1-7/10)*х=2 1/4
(10/10-7/10)*х=2 1/4
3/10*х=2 1/4
х=2 1/4:3/10
х=7 5/12
Ответ: х=7 5/12

Answer 2

Let's solve each of the equations step by step:

1. (1 - 7/10) * x = 2 1/4

First, simplify the expression inside the parentheses: (1 - 7/10) = (10/10 - 7/10) = 3/10

Now the equation becomes: (3/10) * x = 2 1/4

To simplify the right side, convert the mixed number into an improper fraction: 2 1/4 = (2 * 4 + 1) / 4 = 9/4

The equation now becomes: (3/10) * x = 9/4

To solve for x, we can multiply both sides of the equation by the reciprocal of (3/10), which is (10/3): x = (9/4) * (10/3)

Multiply the numerators and the denominators separately: x = (9 * 10) / (4 * 3) = 90/12 = 7.5

Therefore, the solution for x is 7.5.

2. (5/7 - 2/3) / (4/9 - 5/12)

To simplify the expression, let's find a common denominator for both fractions in the numerator and the denominator:

The common denominator for 7 and 3 is 21 (7 * 3). The common denominator for 9 and 12 is 36 (9 * 4).

Now rewrite the expression with the common denominators: [(5/7) * (3/3) - (2/3) * (7/7)] / [(4/9) * (4/4) - (5/12) * (3/3)]

Simplify: [(15/21) - (14/21)] / [(16/36) - (15/36)]

Combine the fractions in the numerator: (1/21) / (1/36)

To divide fractions, we invert the second fraction and multiply: (1/21) * (36/1)

Multiply the numerators and the denominators separately: (1 * 36) / (21 * 1) = 36/21

The fraction 36/21 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3: (36/3) / (21/3) = 12/7

Therefore, the solution to the expression (5/7 - 2/3) / (4/9 - 5/12) is 12/7.