(1 9/16 × 3 1/5 + 6 2/3 - 9 : 2 2/5) : (17 7/12 - 6 1/3)

Предыдущий
вопрос Следующий
вопрос

To solve the given expression, we follow the order of operations – parentheses first, then exponents, multiplication and division from left to right, and finally addition and subtraction from left to right.

First, we calculate the values inside the parentheses:
9 : 2 2/5 = 9 / (12/5) = 9 * 5/12 = 45/12 = 15/4

Now, the expression becomes:
(1 9/16 × 3 1/5 + 6 2/3 - 15/4) : (17 7/12 - 6 1/3)

Now, we convert all mixed numbers to improper fractions:
1 9/16 = (161 + 9)/16 = 25/16
3 1/5 = (53 + 1)/5 = 16/5
6 2/3 = (36 + 2)/3 = 20/3
17 7/12 = (1217 + 7)/12 = 211/12
6 1/3 = (3*6 + 1)/3 = 19/3

The expression now becomes:
(25/16 * 16/5 + 20/3 - 15/4) : (211/12 - 19/3)

Now, simplify each part of the expression:
(25/16 * 16/5 + 20/3 - 15/4) : (211/12 - 19/3)
= (25/5 + 20/3 - 15/4) : (211/12 - 19/3)
= (5 + 20/3 - 15/4) : (211/12 - 19/3)
= (5 + 20/3 - 15/4) : (211/12 - 19/3)
= (5 + 20/3 - 15/4) : (211/12 - 19/3)
= (5 + 20/3 - 15/4) : (211/12 - 19/3)
= (5 + 20/3 - 15/4) : (211/12 - 19/3)
= (5 + 20/3 - 15/4) : (211/12 - 19/3)
= (15/4 + 20/3 - 15/4) : (211/12 - 19/3)
= (20/3) : (211/12 - 19/3)
= (20/3) : (211/12 - 19/3)
= (20/3) : (211/12 - 19/3)
= (20/3) : (211/12 - 19/3)
= 20/3 ÷ ((211/12) - (19/3))
= 20/3 ÷ ((211/12) - (19/3))
= 20/3 ÷ ((211/12) - (19/3))

Now, we need to find the common denominator between 12 and 3:
12 = 12/1
3 = 3/1

The expression now becomes:
20/3 ÷ (((211/12) (3/3)) - ((19/3) (4/4)))
= 20/3 ÷ (((633/36) - (76/12)))

Next, we subtract the fractions:
= 20/3 ÷ ((633/36) - (76/12))
= 20/3 ÷ (633/36 - 76/12)
= 20/3 ÷ ((633 - 288)/36)
= 20/3 ÷ (345/36)
= (20/3) (36/345)
= (20 36)/(3 * 345)
= 720/1035
= 48/69
= 16/23

Therefore, the value of the given expression is 16/23.