
6 7/12+(5 3/40-4 8/15)


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Ответ:
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To solve the expression 6 7/12 + (5 3/40 - 4 8/15), we need to perform the operations in the parentheses first, and then add the result to 6 7/12.
Let's simplify the expression step by step:
Step 1: Solve the expression inside the parentheses.
5 3/40 - 4 8/15 To subtract mixed numbers, we need to convert them to improper fractions.
5 3/40 = (5 * 40 + 3)/40 = 203/40 4 8/15 = (4 * 15 + 8)/15 = 68/15
Now we have: 203/40 - 68/15
To subtract fractions, we need a common denominator. In this case, the least common multiple (LCM) of 40 and 15 is 120.
Now we can rewrite the expression with a common denominator:
(203/40) - (68/15) = (203 * 3)/(40 * 3) - (68 * 8)/(15 * 8) = 609/120 - 544/120 = (609 - 544)/120 = 65/120
Step 2: Add the result from the parentheses to 6 7/12.
6 7/12 + (65/120)
To add mixed numbers, we need to convert them to improper fractions.
6 7/12 = (6 * 12 + 7)/12 = 79/12
Now we have: 79/12 + 65/120
To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 12 and 120 is 120.
Now we can rewrite the expression with a common denominator:
(79/12) + (65/120) = (79 * 10)/(12 * 10) + (65 * 1)/(120 * 1) = 790/120 + 65/120 = (790 + 65)/120 = 855/120
The fraction 855/120 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 15.
855/120 = (855 ÷ 15)/(120 ÷ 15) = 57/8
Therefore, the simplified value of the expression 6 7/12 + (5 3/40 - 4 8/15) is 57/8.


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