Question

8/9×(-3 5/16)-4 5/9×(-7/58)​

Answer 1

Пошаговое объяснение:

.............................

Answer 2

To solve this expression, we'll follow the order of operations (PEMDAS/BODMAS):

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Let's start:

Step 1: Perform the operations inside parentheses/brackets (there are none in this expression).

Step 2: Perform any exponentiation if present (there are none in this expression).

Step 3: Perform multiplication and division from left to right:

1. 8/9 × (-3 5/16) = (8/9) × (-3 5/16) To multiply a fraction by a mixed number, first convert the mixed number to an improper fraction: -3 5/16 = -53/16

   Now, multiply: (8/9) × (-53/16) = -424/144 = -53/18

2. -4 5/9 × (-7/58) = (-4 5/9) × (-7/58) Convert the mixed number to an improper fraction: -4 5/9 = -41/9

   Now, multiply: (-41/9) × (-7/58) = 287/522

Step 4: Perform addition and subtraction from left to right:

Final step: (-53/18) - (287/522)

To subtract fractions, we need a common denominator. The least common multiple (LCM) of 18 and 522 is 522. So, let's convert both fractions to have a denominator of 522:

(-53/18) = (-53 * 29)/(18 * 29) = -1537/522

Now, the expression becomes: (-1537/522) - (287/522)

Now that the denominators are the same, we can combine the fractions:

= (-1537 - 287)/522 = -1824/522

To simplify the fraction, we can find the greatest common divisor (GCD) of the numerator and denominator and divide both by it:

GCD(1824, 522) = 6

= (-1824 ÷ 6) / (522 ÷ 6) = -304 / 87

So, the final result is: -304/87.