Question
Which expression represents another method of computing the product given below?
- 5 1/4 * (- 11/12)
○A. (- 1)(- 5 * 11/12) + (- 1/4 * 11/12)
○B. (- 5 1/4)(11/12)
OC. - 11/12 * (5 - 1/4)
OD. (- 5(- 11/12)) + (- 1/4 * (- 11/12))
- 5 1/4 * (- 11/12)
○A. (- 1)(- 5 * 11/12) + (- 1/4 * 11/12)
○B. (- 5 1/4)(11/12)
OC. - 11/12 * (5 - 1/4)
OD. (- 5(- 11/12)) + (- 1/4 * (- 11/12))
Answers
GPT-4o mini
To find an alternative method for computing the product \( 5 \frac{1}{4} \times \left(- \frac{11}{12}\right) \), we begin by converting \( 5 \frac{1}{4} \) into an improper fraction.
\[
5 \frac{1}{4} = \frac{21}{4}
\]
Now we need to compute:
\[
\frac{21}{4} \times \left(- \frac{11}{12}\right)
\]
To assess each option given:
**Option A:**
\[
(-1)(-5 \times \frac{11}{12}) + (-\frac{1}{4} \times \frac{11}{12})
\]
This doesn't directly represent our original product, but let's evaluate whether it's mathematically correct but involves various operations similar to our original product.
**Option B:**
\[
(-5 \frac{1}{4})(\frac{11}{12})
\]
This is equivalent to the original product but does not provide a different computing method, as it just restates the product.
**Option C:**
\[
-\frac{11}{12}(5 - \frac{1}{4}) = -\frac{11}{12} (\frac{20}{4} - \frac{1}{4}) = -\frac{11}{12} \times \frac{19}{4}
\]
This is a different way to break down \( 5 \frac{1}{4} \) but results in a different product since it simplifies to a different multiplication than the original.
**Option D:**
This option represents breaking \( 5 \frac{1}{4} \) into two parts:
\[
(-5)(-\frac{11}{12}) + (-\frac{1}{4})(-\frac{11}{12}) = -\frac{5 \times 11}{12} + \frac{1 \times 11}{48} = -\frac{55}{12} + \frac{11}{48}
\]
That is similarly a breakdown but ends up complicating the computation.
Among the options provided, only option B \( (-5 \frac{1}{4})(\frac{11}{12}) \) directly matches the original operation.
The most fitting restatement that offers a different angle while maintaining correctness in representation for computing the product:
**The best alternative expression in terms of rewriting without introducing unnecessary complexity would still be alluding to redefining its numerical components, as the expression specializes in the original concept. Thus, A can be argued as an expression manipulating elements toward computation, while B retains factual numerical data alignment and C changing the internal structure leads us to requirements of being cautious with interpretations.**
Hence, the answer is **the original method itself as represented via option B**, maintaining the essence of the arithmetic operation.
\[
5 \frac{1}{4} = \frac{21}{4}
\]
Now we need to compute:
\[
\frac{21}{4} \times \left(- \frac{11}{12}\right)
\]
To assess each option given:
**Option A:**
\[
(-1)(-5 \times \frac{11}{12}) + (-\frac{1}{4} \times \frac{11}{12})
\]
This doesn't directly represent our original product, but let's evaluate whether it's mathematically correct but involves various operations similar to our original product.
**Option B:**
\[
(-5 \frac{1}{4})(\frac{11}{12})
\]
This is equivalent to the original product but does not provide a different computing method, as it just restates the product.
**Option C:**
\[
-\frac{11}{12}(5 - \frac{1}{4}) = -\frac{11}{12} (\frac{20}{4} - \frac{1}{4}) = -\frac{11}{12} \times \frac{19}{4}
\]
This is a different way to break down \( 5 \frac{1}{4} \) but results in a different product since it simplifies to a different multiplication than the original.
**Option D:**
This option represents breaking \( 5 \frac{1}{4} \) into two parts:
\[
(-5)(-\frac{11}{12}) + (-\frac{1}{4})(-\frac{11}{12}) = -\frac{5 \times 11}{12} + \frac{1 \times 11}{48} = -\frac{55}{12} + \frac{11}{48}
\]
That is similarly a breakdown but ends up complicating the computation.
Among the options provided, only option B \( (-5 \frac{1}{4})(\frac{11}{12}) \) directly matches the original operation.
The most fitting restatement that offers a different angle while maintaining correctness in representation for computing the product:
**The best alternative expression in terms of rewriting without introducing unnecessary complexity would still be alluding to redefining its numerical components, as the expression specializes in the original concept. Thus, A can be argued as an expression manipulating elements toward computation, while B retains factual numerical data alignment and C changing the internal structure leads us to requirements of being cautious with interpretations.**
Hence, the answer is **the original method itself as represented via option B**, maintaining the essence of the arithmetic operation.