Question

Решите |-5\3|+2\7= 3\4+|-2\6|= -1 7\9 + |-3 2\3|=

Answer 1

1)41/21=1 целых 20/21
2) 13/12=1 целых 1/12
3)17/9=1 целых 8/9

Answer 2

We can solve this equation by breaking it down into smaller parts and simplifying each part.

Starting with the left-hand side:

|-5/3| + 2/7

Since |-5/3| is the absolute value of a negative number, we can rewrite it as:

|-5/3| = 5/3

Therefore:

|-5/3| + 2/7 = 5/3 + 2/7

To add these fractions, we need to find a common denominator. The least common multiple of 3 and 7 is 21:

5/3 * 7/7 = 35/21

2/7 * 3/3 = 6/21

Therefore:

5/3 + 2/7 = 35/21 + 6/21 = 41/21

Moving on to the right-hand side:

3/4 + |-2/6|

Since |-2/6| is the absolute value of a negative number, we can rewrite it as:

|-2/6| = 2/6 = 1/3

Therefore:

3/4 + |-2/6| = 3/4 + 1/3

To add these fractions, we need to find a common denominator. The least common multiple of 4 and 3 is 12:

3/4 * 3/3 = 9/12

1/3 * 4/4 = 4/12

Therefore:

3/4 + 1/3 = 9/12 + 4/12 = 13/12

Finally, we need to simplify the third part of the equation:

-1 7/9 + |-3 2/3|

Since |-3 2/3| is the absolute value of a negative number, we can rewrite it as:

|-3 2/3| = 3 2/3

Therefore:

-1 7/9 + |-3 2/3| = -1 7/9 + 3 2/3

To add these mixed numbers, we need to convert them to improper fractions:

-1 7/9 = -16/9

3 2/3 = 11/3

Therefore:

-1 7/9 + 3 2/3 = -16/9 + 11/3

To add these fractions, we need to find a common denominator. The least common multiple of 9 and 3 is 9:

-16/9 * 1/1 = -16/9

11/3 * 3/3 = 33/9

Therefore:

-16/9 + 11/3 = -16/9 + 33/9 = 17/9

Now we can rewrite the original equation with the simplified expressions:

41/21 = 13/12 + 17/9

To solve for the variable, we need to get all the terms on one side of the equation:

41/21 - 13/12 - 17/9 = 0

To add these fractions, we need to find a common denominator. The least common multiple of 21, 12, and 9 is 252:

41/21 * 12/12 = 492/252

13/12 * 21/21 = 273/252

17/9 * 28/28 = 476/252

Therefore:

41/21 - 13/12 - 17/9 = 492/252 - 273/252 - 476/252 = -257/252

Therefore, the solution to the equation is:

|-5/3| + 2/7 = 3/