to find an expression equivalent to 20(9+5).
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The question asks to find an expression equivalent to $20(9+5)$.
Step 1: Understand the original expression.
The expression $20(9+5)$ means 20 multiplied by the sum of 9 and 5.
Using the order of operations (PEMDAS/BODMAS), we first calculate the sum inside the parentheses:
$$9+5 = 14$$
Then, we multiply by 20:
$$20 \times 14 = 280$$
Step 2: Evaluate each option.
A) $9(20+5)$
$$9(20+5) = 9(25) = 225$$
This is not equal to 280.
B) $20(5+9)$
Using the commutative property of addition, $9+5$ is equivalent to $5+9$.
$$20(5+9) = 20(14) = 280$$
This is equal to 280.
C) $20(9)+5$
$$20(9)+5 = 180+5 = 185$$
This is not equal to 280.
D) $(20+9)5$
$$(20+9)5 = (29)5 = 145$$
This is not equal to 280.
E) $20+(9)(5)$
$$20+(9)(5) = 20+45 = 65$$
This is not equal to 280.
Comparing the values, only option B is equivalent to the original expression.
The final answer is $\boxed{\text{B}}$.
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