Simplify the following numerical expressions:
(a) $30+4 \div 2+5-1 \times 3$
(b) $42+(2 \times 16 \div 2)-1$
(c) $12-[3+\{7-(4+1)\}]$
Answer (2)
Apply the order of operations (PEMDAS/BODMAS) to expression (a): 30 + 4 ÷ 2 + 5 − 1 × 3 = 30 + 2 + 5 − 3 = 34 .
Apply the order of operations to expression (b): 42 + ( 2 × 16 ÷ 2 ) − 1 = 42 + ( 32 ÷ 2 ) − 1 = 42 + 16 − 1 = 57 .
Apply the order of operations to expression (c): 12 − [ 3 + { 7 − ( 4 + 1 )}] = 12 − [ 3 + { 7 − 5 }] = 12 − [ 3 + 2 ] = 12 − 5 = 7 .
The simplified expressions are 34 , 57 , 7 .
Explanation
Understanding the Problem We are asked to simplify three numerical expressions using the order of operations (PEMDAS/BODMAS). This means we need to perform operations in the following order: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Simplifying Expression (a) For expression (a), 30 + 4 ÷ 2 + 5 − 1 × 3 , we first perform the division and multiplication: 4 ÷ 2 = 2 and 1 × 3 = 3 . Then, we perform the addition and subtraction from left to right: 30 + 2 + 5 − 3 = 34 .
Simplifying Expression (b) For expression (b), 42 + ( 2 × 16 ÷ 2 ) − 1 , we first perform the multiplication: 2 × 16 = 32 . Then, we perform the division: 32 ÷ 2 = 16 . Finally, we perform the addition and subtraction from left to right: 42 + 16 − 1 = 57 .
Simplifying Expression (c) For expression (c), 12 − [ 3 + { 7 − ( 4 + 1 )}] , we first simplify the innermost parentheses: 4 + 1 = 5 . Then, we simplify the curly braces: 7 − 5 = 2 . Next, we simplify the square brackets: 3 + 2 = 5 . Finally, we perform the subtraction: 12 − 5 = 7 .
Final Answer Therefore, the simplified expressions are: (a) 34 (b) 57 (c) 7
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses, managing budgets, or even following recipes. For example, if you are calculating the total cost of items with discounts and taxes, you need to apply the operations in the correct order to get the accurate final amount. Similarly, in cooking, adding ingredients in the right sequence ensures the dish turns out as expected. These basic arithmetic skills are fundamental to everyday problem-solving.
The simplified results for the expressions are 34 for (a), 57 for (b), and 7 for (c) after applying the order of operations. This method ensures the correct order of calculations is followed. Each step involves clear mathematical operations as per standard rules.
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