Evaluate:
a) $23 \times 17-23 \times 7$
b) $20-(9 \div 3)+8 \times 1$
Answer (2)
For expression a), apply the distributive property: 23 × 17 − 23 × 7 = 23 × ( 17 − 7 ) = 23 × 10 = 230 .
For expression b), follow the order of operations: 20 − ( 9 \tdiv 3 ) + 8 × 1 = 20 − 3 + 8 = 17 + 8 = 25 .
The result of expression a) is 230 .
The result of expression b) is 25 .
230 , 25
Explanation
Understanding the Problem We are asked to evaluate two expressions. The first involves multiplication and subtraction, and the second involves parentheses, division, addition, and multiplication. We will use the order of operations (PEMDAS/BODMAS) to solve these.
Evaluating Expression a a) To evaluate 23 × 17 − 23 × 7 , we can use the distributive property to simplify the expression. The distributive property states that a × c − a × b = a × ( c − b ) . In this case, a = 23 , c = 17 , and b = 7 . So we have: 23 × 17 − 23 × 7 = 23 × ( 17 − 7 ) Now, we calculate the difference within the parentheses: 17 − 7 = 10 Finally, we multiply the result by 23: 23 × 10 = 230
Evaluating Expression b b) To evaluate 20 − ( 9 \tdiv 3 ) + 8 × 1 , we follow the order of operations (PEMDAS/BODMAS):
Parentheses: ( 9 \tdiv 3 ) = 3
Multiplication: 8 × 1 = 8
Now the expression is 20 − 3 + 8
Subtraction and Addition (from left to right): 20 − 3 = 17 , then 17 + 8 = 25 So, 20 − ( 9 \tdiv 3 ) + 8 × 1 = 25
Final Answer Therefore, the results are: a) 23 × 17 − 23 × 7 = 230 b) 20 − ( 9 \tdiv 3 ) + 8 × 1 = 25
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses or managing budgets. For example, if you buy several items at a store and have a coupon, you need to apply the coupon (subtraction) before calculating the sales tax (multiplication). Similarly, when calculating the total cost of a project with fixed costs and variable costs, you need to perform the multiplication (variable costs) before adding the fixed costs. These basic arithmetic operations are fundamental to financial literacy and everyday problem-solving.
The result of expression a) is 230, using the distributive property. The result of expression b) is 25, following the order of operations. Both evaluations are essential for understanding basic arithmetic operations.
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