To find another method of computing the product of \(-5 \frac{1}{4} \times \left(-\frac{11}{12}\right)\), we first convert \(-5 \frac{1}{4}\) to an improper fraction.
\[ -5 \frac{1}{4} = -\frac{21}{4} \]
Now we can write the product as:
\[ -\frac{21}{4} \times \left(-\frac{11}{12}\right) \]
To find equivalent expressions, let's analyze the options provided:
A. \((-5 \frac{1}{4}) (11/12)\)
- This is not correct because it does not have the negative sign for \(-11/12\).
B. \(-5 \times \left(-\frac{11}{12}\right) + \left(-\frac{1}{4} \times \left(-\frac{11}{12}\right)\)
- This option separates the term into two parts, which can be computed but does not align with the expression we've started with.
C. \(-\frac{11}{12} \times (5 - 1/4)\)
- This simplifies to \(-\frac{11}{12} \times \left(\frac{20}{4} - \frac{1}{4}\right) = -\frac{11}{12} \times \frac{19}{4}\), which does not equal the original expression.
D. \((-1) (-5 \times \frac{11}{12}) + (-\frac{1}{4} \times \frac{11}{12})\)
- This splits the product into a sum involving \(-\frac{11}{12}\).
Upon reviewing the options in context of the original product \(-5 \frac{1}{4} \times \left(-\frac{11}{12}\right)\), the correct expression that corresponds to a legitimate method of splitting the terms is:
B. \(-5 \times \left(-\frac{11}{12}\right) + \left(-\frac{1}{4} \times \left(-\frac{11}{12}\right)\)
This option correctly represents a valid way to reorganize the multiplication into two separate parts that are added together.
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