Question

(7 1/12-k)-1 1/3=6 13/18-2 1/4

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve the equation, let's first simplify both sides step by step:

1. Simplify the left side of the equation: (7 1/12 - k) - 1 1/3

To subtract 1 1/3 from (7 1/12 - k), we need to find a common denominator for 12 and 3, which is 12.

(7 1/12 - k) - (1 1/3) = (7 + 1/12 - k) - (4/12) = (7 + 1/12 - k - 4/12) = (7 + 1/12 - 4/12 - k) = (7 - 3/12 - k) = (7 - 1/4 - k).

So, the left side of the equation becomes: (7 - 1/4 - k).

2. Simplify the right side of the equation: 6 13/18 - 2 1/4

To subtract 2 1/4 from 6 13/18, we need to find a common denominator for 18 and 4, which is 36.

6 13/18 - 2 1/4 = (6 + 13/18) - (2 + 9/36) = (6 + 13/18 - 2 - 9/36) = (6 + 13/18 - 2 - 1/4) = (6 + 13/18 - 9/18) = (6 + 4/18).

Now, let's find a common denominator for 18 and 36, which is 36.

6 + 4/18 = (6 * 36/36) + (4/18 * 2/2) = (216/36) + (8/36) = (216 + 8)/36 = 224/36.

Now, simplify 224/36 to the lowest terms:

224/36 = 112/18 = 56/9.

So, the right side of the equation becomes: 56/9.

Now, our equation becomes: (7 - 1/4 - k) = 56/9.

To isolate k, let's first combine the constant terms on the left side:

7 - 1/4 = (28/4) - (1/4) = 27/4.

Now, the equation is: (27/4 - k) = 56/9.

To isolate k, subtract (27/4) from both sides:

(27/4 - k) - (27/4) = (56/9) - (27/4).

The left side simplifies to: (27/4 - 27/4 - k) = (0 - k) = -k.

The right side simplifies to: (56/9) - (27/4).

To subtract (27/4) from (56/9), find a common denominator, which is 36.

(56/9) - (27/4) = (56/9 * 4/4) - (27/4 * 9/9) = (224/36) - (243/36).

Now, subtract the fractions: (224/36 - 243/36) = (-19/36).

So, the equation now becomes: -k = -19/36.

To solve for k, divide both sides by -1 (or multiply by -1):

k = 19/36.

Therefore, the solution to the equation is k = 19/36.