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Zorluk: Çok zorSimplification and BODMAS Rule

What value is obtained upon simplifying the mathematical expression given below using the correct order of operations (BODMAS)?

87.5% of 120−[225×{24.5−(4.5÷2.4−0.9‾×1.6+115)}]87.5\% \text{ of } 120 - \left[ 2 \frac{2}{5} \times \left\{ 24.5 - \left( 4.5 \div \overline{2.4 - 0.9} \times 1.6 + 1 \frac{1}{5} \right) \right\} \right]
  1. 60.660.6Cevap
  2. B
    66.3666.36
  3. C
    53.5853.58
  4. D
    52.252.2

Cevap

60.660.6
The correct result 60.660.6 is achieved by systematically resolving operations from the innermost group outward: first the bar/vinculum, followed by division and multiplication inside the parentheses, subtraction in the curly brackets, multiplication in the square brackets, and finally subtracting this total from 87.5%87.5\% of 120120.

Adım Adım Çözüm

1
Evaluate the expression under the vinculum (bar)
2.4−0.9‾=1.5\overline{2.4 - 0.9} = 1.5
The vinculum has the highest priority among grouping symbols.
2
Evaluate the terms inside the parentheses (...)(...) using BODMAS
4.5÷1.5×1.6+115=3×1.6+1.2=4.8+1.2=6.04.5 \div 1.5 \times 1.6 + 1 \frac{1}{5} = 3 \times 1.6 + 1.2 = 4.8 + 1.2 = 6.0
Perform division first (4.5÷1.5=34.5 \div 1.5 = 3), then multiplication (3×1.6=4.83 \times 1.6 = 4.8), and finally addition (4.8+1.2=6.04.8 + 1.2 = 6.0).
3
Simplify the expression inside the curly brackets {...}\{...\}
24.5−6.0=18.524.5 - 6.0 = 18.5
Subtract the result of the parentheses from 24.524.5.
4
Simplify the expression inside the square brackets [...][...]
225×18.5=2.4×18.5=44.42 \frac{2}{5} \times 18.5 = 2.4 \times 18.5 = 44.4
Convert the mixed fraction 2252 \frac{2}{5} to decimal 2.42.4 and multiply by 18.518.5.
5
Calculate the percentage value
87.5% of 120=78×120=10587.5\% \text{ of } 120 = \frac{7}{8} \times 120 = 105
Convert 87.5%87.5\% to the equivalent fraction 78\frac{7}{8} and multiply by 120120.
6
Perform the final subtraction
105−44.4=60.6105 - 44.4 = 60.6
Subtract the value of the square brackets from the percentage result.

Anahtar Kavram

Strict evaluation of nested brackets (vinculum, round, curly, square) and mixed operators (percentage, fraction, division, multiplication) using the BODMAS rule.
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Konular

Simplification and BODMAS Rule

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