What is the value of the expression given below?
$26-7(3+5) \div 4+2$
Answer (1)
Evaluate the expression inside the parentheses: 3 + 5 = 8 .
Multiply 7 by the result: 7 × 8 = 56 .
Divide the result by 4: 56 ÷ 4 = 14 .
Perform subtraction and addition from left to right: 26 − 14 + 2 = 14 .
The final answer is 14 .
Explanation
Understanding the Expression We need to evaluate the expression 26 − 7 ( 3 + 5 ) d i v 4 + 2 . To do this, we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Evaluating Parentheses First, we evaluate the expression inside the parentheses: 3 + 5 = 8 . So the expression becomes 26 − 7 ( 8 ) d i v 4 + 2 .
Multiplication Next, we perform multiplication and division from left to right. First, we multiply 7 by 8: 7 t im es 8 = 56 . The expression becomes 26 − 56 d i v 4 + 2 .
Division Now, we divide 56 by 4: 56 d i v 4 = 14 . The expression becomes 26 − 14 + 2 .
Subtraction Finally, we perform addition and subtraction from left to right. First, we subtract 14 from 26: 26 − 14 = 12 . The expression becomes 12 + 2 .
Addition Then, we add 2 to 12: 12 + 2 = 14 .
Final Result Therefore, the value of the expression is 14.
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a series of actions. For example, imagine you are baking cookies. You need 2 cups of flour and 1 cup of sugar, and you want to triple the recipe. If you don't follow the correct order of operations, you might end up with the wrong amount of ingredients. The correct calculation is 3 t im es ( 2 + 1 ) = 3 t im es 3 = 9 cups total. If you calculated 3 t im es 2 + 1 = 6 + 1 = 7 , you would not have enough. This demonstrates how following the order of operations ensures accurate results in everyday tasks.
