Solve the equation: a) 5\frac{4}{27} - x = 1\frac{8}{9};

Task: Solve the equation 5 4/27 - x = 1 8/9.

Solution:

1. Convert mixed numbers to improper fractions:
   • 5 4/27 = (5 * 27 + 4) / 27 = 139/27
   • 1 8/9 = (1 * 9 + 8) / 9 = 17/9
2. Rewrite the equation with improper fractions:
   • 139/27 - x = 17/9
3. Isolate 'x':
   • Subtract 17/9 from both sides and add x to both sides:
   • 139/27 - 17/9 = x
4. Find a common denominator for 27 and 9, which is 27:
   • 17/9 = (17 * 3) / (9 * 3) = 51/27
5. Perform the subtraction:
   • x = 139/27 - 51/27
   • x = (139 - 51) / 27
   • x = 88/27
6. Convert the improper fraction to a mixed number:
   • 88 divided by 27 is 3 with a remainder of 7 (3 * 27 = 81; 88 - 81 = 7).
   • x = 3 7/27

Answer: x = 3 7/27