Question

(6 5/6-5,375):7/48+2,75:(1,5-2/5)

Answer 1

(6 5/6-5,375)÷7/48+2,75÷(1,5-2/5)=12,5=(125/10)=(25/2)

1) 6(5/6)-5,375=(41/6)-(43/8)=(41×4-43×3)/24=(164-129)/24=(35/24)

2) (35/24)÷(7/48)=(35/24)×(48/7)=(5×7×2×24)/(24×7)=5×2=10

3) 1,5-(2/5)=(15/10)-(2/5)=(15-2×2)/10=(11/10)

4) 2,75÷(11/10)=(275/100)×(10/11)=(25×11×10)/(10×10×11)=(25/10)=2,5

5) 10+2,5=12,5=(125/10)=25/2

Answer 2

To solve the expression, follow the order of operations (PEMDAS/BODMAS):

P: Parentheses/Brackets E: Exponents/Orders MD: Multiplication and Division (from left to right) AS: Addition and Subtraction (from left to right)

Let's proceed step by step:

Step 1: Perform operations within the parentheses/brackets. (6 5/6 - 5,375) = (41/6 - 5.375)

Step 2: Convert the mixed number 6 5/6 to an improper fraction. 6 5/6 = (6 * 6 + 5)/6 = 41/6

So, the expression becomes: (41/6 - 5.375)

Step 3: Perform subtraction. (41/6 - 5.375) = (41/6 - 32/8) = (41/6 - 4) = (41 - 24)/6 = 17/6

Now, the expression is: (17/6)

Step 4: Perform the remaining operations outside the parentheses.

7/48 + 2.75 : (1.5 - 2/5)

Step 5: Perform subtraction within the parentheses. 1.5 - 2/5 = (7/5 - 2/5) = 5/5 = 1

Step 6: Perform division. 2.75 : 1 = 2.75

Now, the expression becomes: 7/48 + 2.75

Step 7: Find a common denominator to add the fractions. The common denominator for 48 and 6 is 48.

7/48 = (7 * 1)/48 = 7/48

Step 8: Add the fractions. 7/48 + 2.75 = 7/48 + 2.75 * (48/48) = 7/48 + 132/48 = (7 + 132)/48 = 139/48

So, the final result of the expression is:

17/6 + 139/48

To add these fractions, find a common denominator, which is 48:

17/6 + 139/48 = (17 * 8)/(6 * 8) + 139/48 = 136/48 + 139/48 = (136 + 139)/48 = 275/48

Therefore, the final answer is 275/48.