Question

5/9+ 1 5/7 *(4 2/3 - 2 5/8) : 1 3/4 =

Answer 1

⁵/₉+ 1 ⁵/₇ ×(4 ²/₃ - 2 ⁵/₈) : 1 ³/₄ =1⁵/₉

1) 4 ²/₃ - 2 ⁵/₈=¹⁴/₃-²¹/₈=¹⁴ˣ⁸/₂₄ - ²¹ˣ³/₂₄=¹¹²/₂₄-⁶³/₂₄=¹¹²⁻⁶³/₂₄=⁴⁹/₂₄

2) 1⁵/₇×⁴⁹/₂₄=¹²/₇×⁴⁹/₂₄=¹²ˣ⁴⁹/₇ₓ₂₄=¹ˣ⁷/₁ₓ₂=⁷/₂

3) ⁷/₂ : 1 ³/₄ =⁷/₂ : ⁷/₄ =⁷/₂ײ/₇=⁷ˣ²/₂ₓ₇=¹/₁=1

4) ⁵/₉+1=1⁵/₉

Answer 2

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

P - Parentheses/Brackets E - Exponents/Orders (i.e., powers and square roots, etc.) MD - Multiplication and Division (left-to-right) AS - Addition and Subtraction (left-to-right)

Let's break down the expression step by step:

1. First, deal with the subtraction inside the parentheses: 4 2/3 - 2 5/8 = (4 + 2/3) - (2 + 5/8)

   To subtract mixed numbers, find a common denominator, which in this case is 24. (4 + 2/3) - (2 + 5/8) = (424/3 + 224/3) - (224/8 + 524/8)

   Now, simplify: (96/3 + 48/3) - (48/8 + 120/8) = (144/3) - (168/8)

   Reduce fractions: (48) - (21)

2. Next, multiply and divide from left to right: 5/9 + 1 5/7 * 27/8 / 1 3/4

   Multiply: 1 5/7 * 27/8 = (7 + 5/7) * 27/8 = (7*8/7 + 5/7) * 27/8 = (56/7 + 5/7) * 27/8 = (61/7) * 27/8

   Now, divide: (61/7) * 27/8 = (61 * 27) / (7 * 8)

   Multiply and divide: (61 * 27) / (7 * 8) = (1647) / (56)

   Reduce the fraction: (3 * 547) / (3 * 19) = 547/19

3. Finally, add and subtract from left to right: 5/9 + 547/19 / 1 3/4

   Add: 5/9 + 547/19 = (5/9 * 19/19) + (547/19)

   Common denominator for addition is 171: (5 * 19/9 * 19) + (547 * 9/19 * 9) / 171

   Now, simplify: (95 + 4923) / 171 = 5018 / 171

   Reduce the fraction: 5018/171 = 294/10.982...

Rounded to two decimal places: Approximately 26.80