To solve this expression, we follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right):
Given expression: 4×8/9 + 6×7/9 ÷ (5×11/12 - 3×5/9) × 1×2/3
Simplify inside the parentheses first:5×11/12 = 55/123×5/9 = 15/9 = 5/3
Subtracting them: 55/12 - 5/3 = (55/12) - (20/12) = 35/12
Now, calculate the division in the parentheses:6×7/9 ÷ (35/12) = 42/9 ÷ (35/12) = 14/3 ÷ (35/12)
To divide by a fraction, we invert and multiply: 14/3 12/35 = (1412)/(3*35) = 168/105
Therefore, the expression in the parentheses simplifies to 168/105.
Now, substitute back into the original expression:4×8/9 + 168/105 × 1×2/3
Multiplying/dividing: 32/9 + 336/105To add them, we find a common denominator, which is 315:
(32/9) + (336/105) = (3235/935) + (3363/1053) = 1120/315 + 1008/315= (1120 + 1008)/315 = 2128/315
Therefore, the final answer is 2128/315.
To solve this expression, we follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right):
Given expression: 4×8/9 + 6×7/9 ÷ (5×11/12 - 3×5/9) × 1×2/3
Simplify inside the parentheses first:
5×11/12 = 55/12
3×5/9 = 15/9 = 5/3
Subtracting them: 55/12 - 5/3 = (55/12) - (20/12) = 35/12
Now, calculate the division in the parentheses:
6×7/9 ÷ (35/12) = 42/9 ÷ (35/12) = 14/3 ÷ (35/12)
To divide by a fraction, we invert and multiply: 14/3 12/35 = (1412)/(3*35) = 168/105
Therefore, the expression in the parentheses simplifies to 168/105.
Now, substitute back into the original expression:
4×8/9 + 168/105 × 1×2/3
Multiplying/dividing: 32/9 + 336/105
To add them, we find a common denominator, which is 315:
(32/9) + (336/105) = (3235/935) + (3363/1053) = 1120/315 + 1008/315
= (1120 + 1008)/315 = 2128/315
Therefore, the final answer is 2128/315.