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Simplify: 52тАЛ┬аof┬а((43тАЛ├╖0.25)+21тАЛ)тИТ31тАЛ
1514тАЛ
1513тАЛ
1517тАЛ
1516тАЛ
1516тАЛ
Convert decimals to fractions early: 0.25=1/4. Then 3/4├╖1/4=3. The expression becomes 2/5├Ч(3+1/2)тИТ1/3.
An expression containing fractions and decimals: (2/5) of ((3/4 ├╖ 0.25) + 1/2) - 1/3
BODMAS=Brackets,Of,Division,Multiplication,Addition,Subtraction
Convert decimals to fractions early: 0.25=1/4. Then 3/4├╖1/4=3. The expression becomes 2/5├Ч(3+1/2)тИТ1/3.
Confusing the order of operations by performing subtraction before the 'of' (multiplication) operation.
Simplify inside the bracket
First, evaluate 3/4├╖0.25. Since 0.25=1/4, the division is 3/4├╖1/4=(3/4)├Ч(4/1)=3. Now add 1/2 to this result.
3+21тАЛ=26тАЛ+21тАЛ=27тАЛ
Evaluate the 'of' operation
Multiply the result by 2/5 as indicated by 'of'.
52тАЛ├Ч27тАЛ=57тАЛ
Perform the final subtraction
Subtract 1/3 from the result obtained in the previous step.
57тАЛтИТ31тАЛ=1521тАЛтИТ155тАЛ=1516тАЛ
D is correct because the final simplified value of the expression is 16/15.
This problem is a classic application of the BODMAS rule which is foundational for all simplification and algebra questions in competitive exams like RRB.