Question

(-3 2/3 + 5 7/9) - (2 1/8 - 3 7/12)

Answer 1

Ответ:

$7 \times \frac{59}{72}$

(Тобто 7 цілих 59/72)

Answer 2

To solve the expression (-3 2/3 + 5 7/9) - (2 1/8 - 3 7/12), you can break it down into several steps:

Step 1: Add the fractions within each set of parentheses.

For the first set of parentheses (-3 2/3 + 5 7/9):

• Convert the mixed numbers to improper fractions:
  • -3 2/3 = -11/3
  • 5 7/9 = 52/9
• Now add the fractions:
  • (-11/3 + 52/9)

For the second set of parentheses (2 1/8 - 3 7/12):

• Convert the mixed numbers to improper fractions:
  • 2 1/8 = 17/8
  • 3 7/12 = 43/12
• Now subtract the fractions:
  • (17/8 - 43/12)

Step 2: Find a common denominator for each set of fractions.

For the first set of parentheses, the common denominator is 9:

• (-11/3 + 52/9) = (-33/9 + 52/9)

For the second set of parentheses, the common denominator is 24 (the least common multiple of 8 and 12):

• (17/8 - 43/12) = (51/24 - 86/24)

Step 3: Perform the addition and subtraction with the common denominators.

For the first set of parentheses:

• (-33/9 + 52/9) = (19/9)

For the second set of parentheses:

• (51/24 - 86/24) = (-35/24)

Step 4: Subtract the results of the second set of parentheses from the first set:

(19/9) - (-35/24)

Step 5: To subtract fractions, find a common denominator, which is 9 * 24 = 216:

(19/9) * (24/24) - (-35/24) * (9/9)

Step 6: Continue simplifying:

(19 * 24/216) + (35 * 9/216)

Step 7: Add the fractions:

(456/216) + (315/216)

Step 8: Combine the fractions:

(456 + 315)/216

Step 9: Find the final result:

771/216

Step 10: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

(771/9) / (216/9) = 85/24

So, the final result is 85/24.