Question

Which expression represents another method of computing the product given below?
-5 1/4 x (-11/12)


A. (-5 1/4) (11/12)

B. -5 x (-11/12) + (-1/4 x (-11/12)

C. -11/12 x (5 - 1/4)

D. (-1) (-5 x 11/12) + (-1/4 x 11/12)

Answer 1

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.