The value of x in 3 1/5 ÷ 2/7 × x/5 = 1 2/5 × 1 3/5 is:-

Concept: A mixed number such as 3 1/5 is first converted to an improper fraction, (whole×denominator+numerator) over denominator. When an expression contains only division and multiplication with no brackets, the operations are evaluated strictly left to right, since ÷ and × share the same precedence. Once both sides are reduced to single fractions, the unknown is isolated by equating the numerators over a common denominator.

Application:

1. Convert every mixed number to an improper fraction: 3 1/5 = 16/5, 1 2/5 = 7/5, 1 3/5 = 8/5.

2. Rewrite the equation using these improper fractions: 16/5 ÷ 2/7 × x/5 = 7/5 × 8/5.

3. Evaluate the left side strictly left to right, starting with the division: 16/5 ÷ 2/7 = 16/5 × 7/2 = 112/10 = 56/5.

4. Multiply this result by x/5: 56/5 × x/5 = 56x/25, so the equation becomes 56x/25 = 7/5 × 8/5.

5. Evaluate the right side: 7/5 × 8/5 = 56/25.

6. The equation now reads 56x/25 = 56/25.

7. Multiply both sides by 25/56 to isolate x: x = 56/25 × 25/56 = 1.

Cross-check: Substituting x = 1 back into the original left side, 3 1/5 ÷ 2/7 × 1/5 = 16/5 × 7/2 × 1/5 = 112/50 = 56/25, which equals the right side 1 2/5 × 1 3/5 = 7/5 × 8/5 = 56/25, confirming the solution independently.

Result: x = 1.