Question 31

The shaded region of the rectangular area model illustrates the expression ¾ X ½.

The shaded area represents the product of ¾ and ½, indicating a multiplication of fractions that results in a smaller area within the rectangle.

A) ¾ X ½

This option is correct as it directly corresponds to the shaded region depicted in the rectangular area model. The multiplication of ¾ by ½ represents the area of a rectangle where the length is ¾ of the total length and the width is ½ of the total width, accurately illustrating the shaded portion.

B) ¾ X ¾

This option is incorrect as it suggests multiplying ¾ by itself. The resultant area would represent a square with sides of length ¾, which does not align with the shaded area shown in the model.

C) ¾ X 3/2

This option is incorrect because multiplying ¾ by 3/2 would yield a larger area than what is represented by the shaded region. The result would imply a rectangle that exceeds the dimensions of the original model, contradicting the visual representation.

D) ¾ X 3

This option is also incorrect. The multiplication of ¾ by 3 indicates a larger area than what is depicted by the shaded region, suggesting a rectangle that is three times longer than the original length, which does not match the model's shaded area.

Conclusion

The expression ¾ X ½ is definitively correct as it accurately reflects the dimensions of the shaded area in the rectangular model. All other options suggest areas that either exceed or do not correspond to the shaded region, thereby confirming that A is the only valid choice based on the context provided.