Question

(7:5/6-81/9)*2 2/5:((3/8+5/6+5/12)*8/25)=

Answer 1

1) 7: 5/6 = 7 * 6/5 = 42/5 = 8,4
2) 8,4 - 81/9 = 8,4 - 9 = -0,6
3) -0,6 * 2 2/5 = -0,6 * 2,4 = -1,44
4) 3/8 + 5/6 = 9/24 + 20/24 = 29/24
5) 29/24 + 5/12 = 29/24 + 10/24 = 39/24
6) 39/24 * 8/25 = 13/25
7) -1,44 : 13/25 = -144/100 * 25/13 = -36/13 = -2 10/13

Answer 2

Let's solve the given expression step by step:

Expression 1: (7:5/6 - 81/9) * 2

First, we need to simplify the division operation 7:5/6, which means dividing 7 by 5/6: 7 ÷ 5/6 = 7 * 6/5 = 42/5

Now we can substitute the simplified value into the expression: (42/5 - 81/9) * 2

Next, let's simplify the subtraction operation: 42/5 - 81/9

To subtract fractions, we need a common denominator. The least common multiple of 5 and 9 is 45. Converting both fractions to have a denominator of 45: (42/5) * (9/9) = 378/45 (81/9) * (5/5) = 405/45

Subtracting the fractions: 378/45 - 405/45 = (378 - 405)/45 = -27/45

Now we can substitute the simplified value into the expression: (-27/45) * 2

Multiplying the fractions: (-27/45) * 2 = -54/45

The simplified form of the first expression is -54/45.

Expression 2: 2 2/5 : ((3/8 + 5/6 + 5/12) * 8/25)

Inside the parentheses, we have an addition operation: 3/8 + 5/6 + 5/12

To add fractions, we need a common denominator. The least common multiple of 8, 6, and 12 is 24. Converting all fractions to have a denominator of 24: (3/8) * (3/3) = 9/24 (5/6) * (4/4) = 20/24 (5/12) * (2/2) = 10/24

Adding the fractions: 9/24 + 20/24 + 10/24 = 39/24

Now we can substitute the simplified value into the expression: 2 2/5 : (39/24 * 8/25)

Next, we need to simplify the division operation 2 2/5 : (39/24 * 8/25), which means dividing 2 2/5 by the product of (39/24 * 8/25): 2 2/5 ÷ (39/24 * 8/25)

To divide a mixed number, we convert it to an improper fraction: 2 2/5 = (5 * 2 + 2)/5 = 12/5

Substituting the values: 12/5 ÷ (39/24 * 8/25)

To divide fractions, we multiply by the reciprocal of the divisor: 12/5 * (24/39 * 25/8)

Now let's multiply the fractions: 12/5 * (600/312) = 12/5 * 25/13

Multiplying the fractions: (12 * 25)/(5 * 13) = 300/65

The simplified form of the second expression is 300/65.

To summarize: Expression 1: (7:5/6 - 81/9) * 2 = -54/45 Expression 2: 2 2/5 : ((3/8 + 5/6 + 5/12) * 8/25) = 300/65