Explanation:
3 1/7 × [3 1/3 × (2/3 + 1/6) - 1 5/18] ÷ 2 3/7
well, first we have to bring everything to true fractions.
then we need to bring all fractions we need to add or subtract to the same denominators.
and then we simply calculate.
3 1/7 = (3×7 + 1)/7 = 22/7
3 1/3 = (3×3 + 1)/3 = 10/3
1 5/18 = (1×18 + 5)/18 = 23/18
2 3/7 = (2×7 + 3)/7 = 17/7
22/7 × [10/3 × (2/3 + 1/6) - 23/18] ÷ 17/7
to be able to add 2/3 and 1/6 we need to bring the to the same denominator, with its simply 6.
2/3 + 1/6 = 2/2 × 2/3 + 1/6 = 4/6 + 1/6 = 5/6
22/7 × [10/3 × 5/6 - 23/18] ÷ 17/7
22/7 × [50/18 - 23/18] ÷ 17/7
22/7 × 27/18 ÷ 17/7
22/7 × 27/18 × 7/17
22/17 × 27/18 = 22/17 × 3/2 = 66/34 = 33/17
so, the result is 33/17 = 1 16/17