Pregunta
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Select all eypressions that are equivalent to the following calculation. Add 43 and 25 and then multply ty 8 . (1) \( (25+43) \times 8 \) a \( 43+25 \times 8 \) \( 08 \times 43+25 \) a \( 8 \times(43+25) \) \( 043+(25 \times 8) \)

Ask by Powers Boone. in the United States
Mar 13,2025

Solución de inteligencia artificial de Upstudy

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Responder

The expressions equivalent to "Add 43 and 25 and then multiply by 8" are: 1. \( (25 + 43) \times 8 \) 2. \( 8 \times (43 + 25) \)

Solución

Let's denote the original calculation as \[ 8 \times (43 + 25). \] Now we check each option: 1. \(\ (25+43) \times 8 \) This expression adds \(25\) and \(43\) first and then multiplies by \(8\), which is equivalent to \(8 \times (43+25)\). 2. \(\ 43+25 \times 8 \) Here, multiplication is performed before addition, yielding \(43 + (25 \times 8)\). Since \(25 \times 8 = 200\) and \(43+200=243\), this is not equivalent to the original calculation (which evaluates to \(8 \times 68 = 544\)). 3. \(\ 08 \times 43+25 \) This is interpreted as \((8 \times 43) + 25\). Multiplying \(8\) and \(43\) gives \(344\) and adding \(25\) yields \(369\), so it is not equivalent. 4. \(\ 8 \times(43+25) \) This exactly follows the intended order of operations by first adding \(43\) and \(25\) and then multiplying by \(8\), which is equivalent. 5. \(\ 043+(25 \times 8) \) Here, \(043\) is just another form of \(43\). The multiplication \(25 \times 8\) is performed first, giving \(200\), then added to \(43\) gives \(243\). This is not equivalent. Thus, the expressions equivalent to the original calculation are: \[ (25+43) \times 8 \quad \text{and} \quad 8 \times(43+25). \]

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Beyond the Answer

Let's break it down! The calculation you're performing is \( (43 + 25) \times 8 \). To determine which of the expressions provided are equivalent, we can focus on the order of operations and the properties of addition and multiplication. For example, both \( (25 + 43) \times 8 \) and \( 8 \times (43 + 25) \) work because addition is commutative, meaning it doesn't matter the order you add them in. Hence, both yield the correct result of \( 8 \times 68 \). As for \( 43 + 25 \times 8 \) and \( 043 + (25 \times 8) \), these aren’t equivalent as they imply a different order of operations due to the multiplication taking precedence. So, watch out for those pesky PEMDAS rules! Additionally, expressions like \( 08 \times 43 + 25 \) also introduce operations that jumble the original calculation. Reading through those calculations can sometimes get tricky, but you've caught on to the right sequences! Always remember to keep the operations in line for accurate results!

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