The shaded region of the rectangular area model shown illustrates which of the following multiplicative expressions?

Rationale

¾ X ½ accurately represents the shaded region of the rectangular area model.

The rectangular area model visually illustrates the product of two fractions, where the shaded area corresponds to multiplying the two values. In this case, ¾ represents the width, and ½ represents the height of the shaded region, confirming that the expression ¾ X ½ is correct.

A (¾ X ½) CORRECT

This option correctly identifies the shaded area as the product of the fractions representing the dimensions of the rectangle. The width of the rectangle is ¾, and the height is ½. Thus, the area of the shaded region is indeed calculated as ¾ multiplied by ½.

B (¾ X ¾) YOUR ANSWER

This choice implies that both dimensions of the rectangle are ¾, which would result in an area of ¾ X ¾ = 9/16. However, this does not correspond to the shaded region, as the height is not equal to ¾, but rather to ½.

C (¾ X 3/2) YOUR ANSWER

This option suggests that the height of the rectangle is 3/2, leading to an area of ¾ X 3/2 = 9/8. This does not represent the shaded portion since the height of the shaded region is clearly ½, not 3/2.

D (¾ X 3) YOUR ANSWER

Here, the expression indicates the height is 3, resulting in an area of ¾ X 3 = 9/4. This choice incorrectly represents the dimensions of the shaded area, as the height is not 3 but ½.

Conclusion

The shaded region of the rectangular area model is accurately represented by the multiplicative expression ¾ X ½, matching the dimensions of the rectangle. The other choices either misrepresent the height or width, leading to incorrect area calculations that do not correspond to the shaded part of the model. Understanding the relationship between the dimensions and the area is essential for interpreting such models correctly.

The shaded region of the rectangular area model shown illustrates which of the following multiplicative expressions?

¾ X ½ accurately represents the shaded region of the rectangular area model.

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