Question

|-17,6|•3,5-| 5 13/22|:|3/110 +|-196,4|=53 докажите тождество :

Answer 1

Тождеством называется полное сходство, то есть в нашем случае при решении выражения, которое находится в левой части, в ответе должно быть число равное числу в правой части равенства. Необходимо доказать данное тождество: |-17.6| * 3.5 - |-5 * (13/22)| / |3/110| + |-196.4| = 53.

Решим левую часть равенства:

|-17.6| * 3.5 - |-5 * (13/22)| / |3/110| + |-196.4| = 17.6 * 3.5 - (5 * (13/22)) / (3/110) + 196.4 =

= 61.6 - (123/22) / (3/110) + 196.4 = 61.6 - (123/22) * (110/3) + 196.4 = 61.6 - 205 + 196.4 = -143.4 +196.4 = 53.

Answer 2

To prove the given identity, let's break it down step by step:

Step 1: Evaluate each part of the expression.

|-17,6| means the absolute value of -17.6, which is 17.6. 3.5 is a constant and remains the same. |5 13/22| means the absolute value of 5 13/22, which is 5 13/22. Now, let's evaluate the expression inside the absolute value:

5 13/22 = (5 * 22 + 13)/22 = (110 + 13)/22 = 123/22. So, |5 13/22| = |123/22| = 123/22, as the absolute value of a positive fraction is the fraction itself.

Next, we have:

3/110 = 3 divided by 110. |-196,4| means the absolute value of -196.4, which is 196.4.

Step 2: Substitute the evaluated values back into the expression.

The original expression now becomes:

17.6 * 3.5 - 123/22 : 3/110 + 196.4 = 53.

Step 3: Simplify the expression.

Now, let's simplify the expression step by step:

1. 17.6 * 3.5 = 61.6.
2. 123/22 : 3/110 = (123/22) * (110/3) = 1230/66 = 1230/6 * (1/11) = 205 * (1/11) = 205/11.
3. 61.6 - 205/11 + 196.4.

Step 4: Convert all terms to fractions for easier calculations.

61.6 can be written as 61 6/10 = 61 3/5 = (61 * 5 + 3)/5 = 308/5. 196.4 can be written as 196 4/10 = 196 2/5 = (196 * 5 + 2)/5 = 982/5.

Now, the expression becomes:

308/5 - 205/11 + 982/5.

Step 5: Find a common denominator to combine the fractions.

The common denominator for 5 and 11 is 55. So, convert all fractions to have a denominator of 55:

(308/5) * (11/11) = 3388/55. (205/11) * (5/5) = 1025/55. (982/5) * (11/11) = 10802/55.

Now, the expression becomes:

3388/55 - 1025/55 + 10802/55.

Step 6: Combine the fractions.

3388/55 - 1025/55 + 10802/55 = (3388 - 1025 + 10802)/55 = 12947/55.

Step 7: Convert the result back to a mixed number.

12947/55 can be written as 235 42/55 = (235 * 55 + 42)/55 = 12947/55.

Now, the simplified expression is 12947/55.

Step 8: Check if the simplified expression equals 53.

Now, we need to check if 12947/55 equals 53:

12947/55 ≈ 235.4, which is not equal to 53.

Therefore, the given identity |-17,6| • 3,5 - |5 13/22| : |3/110| + |-196,4| = 53 is NOT true. The simplified expression evaluates to 12947/55 and not 53.