Which of these expressions is equal to [tex]$6+(2+3) \times 5$[/tex]?

A. [tex]$(4 \times 5)+3$[/tex]
B. [tex]$1+10 \times 3$[/tex]
C. [tex]$9 \times 5+10$[/tex]
D. [tex]$5+4 \times(5-6)$[/tex]

Evaluate the expression 6 + ( 2 + 3 ) × 5 using the order of operations: 6 + ( 5 ) × 5 = 6 + 25 = 31 .
Evaluate the expression ( 4 × 5 ) + 3 : 20 + 3 = 23 .
Evaluate the expression 1 + 10 × 3 : 1 + 30 = 31 .
Evaluate the expression 9 × 5 + 10 : 45 + 10 = 55 .
Evaluate the expression 5 + 4 × ( 5 − 6 ) : 5 + 4 × ( − 1 ) = 5 − 4 = 1 .
The expression equal to 6 + ( 2 + 3 ) × 5 is 1 + 10 × 3 .
1 + 10 × 3 ​

Explanation

Understanding the Problem We need to determine which of the given expressions is equal to 6 + ( 2 + 3 ) × 5 . To do this, we will evaluate each expression using the order of operations (PEMDAS/BODMAS).

Evaluating the Original Expression First, let's evaluate the expression 6 + ( 2 + 3 ) × 5 . Following the order of operations, we first evaluate the expression inside the parentheses: 2 + 3 = 5 . Then, we perform the multiplication: 5 × 5 = 25 . Finally, we perform the addition: 6 + 25 = 31 . So, 6 + ( 2 + 3 ) × 5 = 31 .

Evaluating the First Option Now, let's evaluate the first option: ( 4 × 5 ) + 3 . First, we perform the multiplication: 4 × 5 = 20 . Then, we perform the addition: 20 + 3 = 23 . So, ( 4 × 5 ) + 3 = 23 .

Evaluating the Second Option Next, let's evaluate the second option: 1 + 10 × 3 . First, we perform the multiplication: 10 × 3 = 30 . Then, we perform the addition: 1 + 30 = 31 . So, 1 + 10 × 3 = 31 .

Evaluating the Third Option Now, let's evaluate the third option: 9 × 5 + 10 . First, we perform the multiplication: 9 × 5 = 45 . Then, we perform the addition: 45 + 10 = 55 . So, 9 × 5 + 10 = 55 .

Evaluating the Fourth Option Finally, let's evaluate the fourth option: 5 + 4 × ( 5 − 6 ) . First, we evaluate the expression inside the parentheses: 5 − 6 = − 1 . Then, we perform the multiplication: 4 × ( − 1 ) = − 4 . Finally, we perform the addition: 5 + ( − 4 ) = 1 . So, 5 + 4 × ( 5 − 6 ) = 1 .

Finding the Matching Expression Comparing the results, we see that 6 + ( 2 + 3 ) × 5 = 31 and 1 + 10 × 3 = 31 . Therefore, the expression 1 + 10 × 3 is equal to 6 + ( 2 + 3 ) × 5 .


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 events. For example, if you buy 6 items that cost $3 each and then use a coupon for $5 off your entire purchase, the total cost can be calculated as 6 × 3 − 5 = 13 . This is different from 6 × ( 3 − 5 ) = − 12 , which doesn't make sense in this context. The order of operations ensures that we perform the calculations in the correct sequence to arrive at the correct result.

Answered by GinnyAnswer | 2025-07-03

The expression that equals 6 + ( 2 + 3 ) × 5 is 1 + 10 × 3 since both evaluate to 31. We confirmed this through step-by-step calculations. Therefore, the correct answer is Option B.
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Answered by Anonymous | 2025-07-04