Question

fractions as quotients and fraction multiplication: end - of - unit assessment

1. find the area of the shaded region. explain or show your reasoning.
2. select all of the expressions that represent the area of the shaded region.

a. (5×3)-(5×1/4)
b. 5×11
c. 11/4×5
d. 55×1/4
e. 2 3/4×5
f. 5×2 + 5/4

Explanation:

Step1: Analyze the first - part of the problem

The rectangle has length 4 units and width 1 unit. If we assume the whole rectangle is divided into equal - sized parts and we want to find the area of the shaded region. But the first figure's shading details are not clear enough to calculate precisely from the description. Let's focus on the second part.

Step2: Analyze the second - part of the problem

The large rectangle has length 5 units and width 3 units. The non - shaded part is a small rectangle with length 5 units and width $\frac{1}{4}$ unit. The area of the large rectangle is $A_{total}=5\times3 = 15$ square units. The area of the non - shaded part is $A_{non - shaded}=5\times\frac{1}{4}=\frac{5}{4}$ square units. The area of the shaded region is $A = 5\times3-5\times\frac{1}{4}=(5\times3)-(5\times\frac{1}{4})$. Also, $5\times3 - 5\times\frac{1}{4}=5\times(3 - \frac{1}{4})=5\times\frac{11}{4}=\frac{11}{4}\times5 = 5\times2\frac{3}{4}=2\frac{3}{4}\times5=5\times2+\frac{5}{4}$.

Answer:

A. $(5\times3)-(5\times\frac{1}{4})$
C. $\frac{11}{4}\times5$
D. $55\times\frac{1}{4}$ (since $5\times\frac{11}{4}=\frac{55}{4}=55\times\frac{1}{4}$)
E. $2\frac{3}{4}\times5$
F. $5\times2+\frac{5}{4}$