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 figure for area calculation

The large rectangle has dimensions 5 (horizontal) and 3 (vertical). The un - shaded part at the bottom is a rectangle with height $\frac{1}{4}$ and length 5.

Step2: Calculate the area of the large rectangle

The area of a rectangle is $A = l\times w$. For the large rectangle with $l = 5$ and $w = 3$, the area $A_{total}=5\times3$.

Step3: Calculate the area of the un - shaded part

The un - shaded part has $l = 5$ and $w=\frac{1}{4}$, so its area $A_{un - shaded}=5\times\frac{1}{4}$.

Step4: Calculate the area of the shaded part

The area of the shaded part $A_{shaded}=A_{total}-A_{un - shaded}=(5\times3)-(5\times\frac{1}{4})$. Also, we can consider the height of the shaded part as $3-\frac{1}{4}=\frac{12 - 1}{4}=\frac{11}{4}$. Then the area of the shaded part using the rectangle area formula $A = l\times w$ with $l = 5$ and $w=\frac{11}{4}$ is $A=\frac{11}{4}\times5$. And $\frac{11}{4}\times5=\frac{55}{4}=55\times\frac{1}{4}$. Also, $2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}$, so $2\frac{3}{4}\times5=\frac{11}{4}\times5$. And $5\times2+\frac{5}{4}=\frac{40 + 5}{4}=\frac{45}{4}
eq\frac{55}{4}$. And $5\times11 = 55
eq\frac{55}{4}$.

Answer:

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