6. (19 - 5 × 2) ÷ 3 + 7
7. 11 + (4 × 9 - 6) ÷ 5
8. (18 + 3 × 4 ÷ 2) - 8 × 2
9. 10 + [7 × (9 + 8 - 6)] - 15
10. 15 + {4 × [5 × (8 - 3 + 9)] ÷ 7}
Answer (2)
Let's carefully break down each of the given mathematical expressions step-by-step, following the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Expression: ( 19 − 5 × 2 ) ÷ 3 + 7
Start with parentheses: 19 − 5 × 2 = 19 − 10 = 9
Division: 9 ÷ 3 = 3
Addition: 3 + 7 = 10
Expression: 11 + ( 4 × 9 − 6 ) ÷ 5
Start with parentheses: 4 × 9 = 36 36 − 6 = 30
Division: 30 ÷ 5 = 6
Addition: 11 + 6 = 17
Expression: 8 × ( 18 + 3 × 4 ÷ 2 ) − 8 × 2
Start with parentheses: 3 × 4 = 12 12 ÷ 2 = 6 18 + 6 = 24
Multiplication: 8 × 24 = 192 8 × 2 = 16
Subtraction: 192 − 16 = 176
Expression: 10 + [ 7 × ( 9 + 8 − 6 )] − 15
Start with innermost parentheses: 9 + 8 = 17 17 − 6 = 11
Multiplication inside brackets: 7 × 11 = 77
Addition and then subtraction: 10 + 77 = 87 87 − 15 = 72
Expression: 15 + { 4 × [ 5 × ( 8 − 3 + 9 )] ÷ 7 }
Start with innermost parentheses: 8 − 3 = 5 5 + 9 = 14
Multiplication inside brackets: 5 × 14 = 70
Further multiplication: 4 × 70 = 280
Division: 280 ÷ 7 = 40
Addition: 15 + 40 = 55
In each step, we have applied the order of operations properly, simplifying the expressions accurately. Each resulting value from these calculations reflects the step-by-step solution for the respective expression, ensuring clarity and correctness in solving mathematical problems.
We solved the five mathematical expressions step by step using the order of operations. Each expression was simplified correctly, leading to the final results of 10, 17, 8, 72, and 55 respectively. Following the order of operations ensures accurate calculations in mathematics.
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