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Calculating the Expression
- To find the value of 2/5×(-3/7)-1/6×3/2+1/14×2/5, we need to follow the order of operations (PEMDAS).
- First, we will simplify the multiplication and division in the expression.

Multiplying Fractions
- To multiply fractions, we simply multiply the numerators together and the denominators together.
- For 2/5×(-3/7), we multiply 2 by -3 to get -6 in the numerator, and 5 by 7 to get 35 in the denominator. So, this simplifies to -6/35.
- For 1/6×3/2, we multiply 1 by 3 to get 3 in the numerator, and 6 by 2 to get 12 in the denominator. Thus, this becomes 3/12 which simplifies to 1/4.
- For 1/14×2/5, we multiply 1 by 2 to get 2 in the numerator, and 14 by 5 to get 70 in the denominator. This simplifies to 2/70, which further reduces to 1/35.

Calculating the Final Expression
- Now, we substitute these results back into the original expression: -6/35 - 1/4 + 1/35.
- To add or subtract fractions, we need a common denominator. Here, the least common multiple of 35 and 4 is 140.
- Rewriting the fractions with the common denominator: -24/140 - 35/140 + 4/140.
- Combining the fractions, we get -24 - 35 + 4 = -55.
- Therefore, the simplified value of the expression 2/5×(-3/7)-1/6×3/2+1/14×2/5 is -55/140 or -11/28.