Question

48 3/5 :6 3/4×5/12-2 5/6+2 3/4×(1 1/2×1/3-13×26)​

Answer 1

Пошаговое объяснение:

1) 1 1/2 * 1/3 = 3/2 * 1/3 = 1/2 * 1/1 = 1/2

2) 13 * 26 = 338

3) 1/2 - 338 = -337 1/2

4) 2 3/4 * (-337 1/2) = 11/4 * (-675/2) = -7425/8 = -928 1/8

5) 48 3/5 : 6 3/4 = 243/5 : 27/4 = 243/5 * 4/27 = 9/5 * 4/1 = 36/5

6) 36/5 * 5/12 = 3/1 * 1/1 = 3/1 = 3

7) 3 - 2 5/6 = 2 6/6 - 2 5/6 = 1/6

8) 1/6 + (-928 1/8) = 4/24 - 928 3/24 = 4/24 - 927 27/24 = -927 23/24

Answer 2

To solve the expression 48 3/5 : 6 3/4 × 5/12 - 2 5/6 + 2 3/4 × (1 1/2 × 1/3 - 13 × 26), let's break it down step by step:

Step 1: Convert mixed numbers to improper fractions: 48 3/5 becomes (48 × 5 + 3) / 5 = 243/5 6 3/4 becomes (6 × 4 + 3) / 4 = 27/4 2 5/6 becomes (2 × 6 + 5) / 6 = 17/6 1 1/2 becomes (1 × 2 + 1) / 2 = 3/2

Step 2: Simplify the expression inside the parentheses: 1 1/2 × 1/3 - 13 × 26

1 1/2 × 1/3 = (3/2) × (1/3) = 3/6 = 1/2

-13 × 26 = -338

So, the expression inside the parentheses simplifies to 1/2 - 338.

Step 3: Simplify the multiplication and subtraction in the main expression: 48 3/5 : 6 3/4 × 5/12 - 2 5/6 + 2 3/4 × (1/2 - 338)

48 3/5 : 6 3/4 = (243/5) : (27/4) = (243/5) × (4/27) = 972/135 = 72/10 = 36/5

2 3/4 × (1/2 - 338) = (11/4) × (-337 1/2) = (11/4) × (-675/2) = -7425/8

Now, the expression becomes: 36/5 × 5/12 - 17/6 + (-7425/8)

Step 4: Perform the remaining calculations: 36/5 × 5/12 = (36 × 5) / (5 × 12) = 180/60 = 3

Therefore, the final expression is: 3 - 17/6 - 7425/8

To subtract fractions, we need a common denominator: 3 = (3 × 48/48) = 144/48 17/6 = (17 × 8/8) = 136/48

Now, the expression becomes: 144/48 - 136/48 - 7425/8

Subtracting the fractions: (144 - 136)/48 = 8/48 = 1/6

So, the simplified value of the expression is 1/6.