Option A: [tex]\frac{3}{12} \times \frac{3}{6}[/tex]
Option C: [tex]\frac{1}{4} \times \frac{1}{2}[/tex]
Solution:
To find the area of the shaded region:
Number of squares in one row = 12
Number of squares in one column = 6
Note that:
Number of squares shaded in one row = 3
Number of squares shaded in one column = 3
Option A: [tex]\frac{3}{12} \times \frac{3}{6}[/tex]
Area of the shaded region [tex]$=\frac{\text {Number of squares shaded in row}}{\text { Total square in row }} \times \frac{\text { Number of squares shaded in column}}{\text { Total square in row }}[/tex][tex]=\frac{3}{12} \times \frac{3}{6}[/tex]
Hence it is true.
Option B: [tex]\frac{3}{10} \times \frac{1}{2}[/tex]
Already proved in option A.
Hence it is not true.
Option C: [tex]\frac{1}{4} \times \frac{1}{2}[/tex]
By option A,
Area of the shaded region = [tex]\frac{3}{12} \times \frac{3}{6}[/tex]
Divide the numerator and denominator by the common factor.
[tex]=\frac{3\div3}{12\div3} \times \frac{3\div3}{6\div3}[/tex]
[tex]=\frac{1}{4} \times \frac{1}{2}[/tex]
Hence it is true.
Option D: [tex]\frac{1}{4} \times \frac{1}{3}[/tex]
Already proved in option C.
Hence it is not true.
Option E: [tex]\frac{4}{12} \times \frac{3}{6}[/tex]
Here, the number of squares shaded in row indicated as 4.
But the shaded squares in row wise is 3.
Hence it is not true.
Therefore Option A and Option C are true.
[tex]\frac{3}{12} \times \frac{3}{6}[/tex] and [tex]\frac{1}{4} \times \frac{1}{2}[/tex] are true.
