Question

for each of the following four squares, write a fraction to describe the shaded portion. what property of fractions does the diagram
a.
b.
c.
d.
a. the fraction illustrated by the shaded region is \\(\square\\).
(type an integer or a simplified fraction.)
b. the fraction illustrated by the shaded region is \\(\square\\).
(type an integer or a simplified fraction.)
c. the fraction illustrated by the shaded region is \\(\square\\).
(type an integer or a simplified fraction.)
d. the fraction illustrated by the shaded region is \\(\square\\).
(type an integer or a simplified fraction.)
what property of fractions does this illustrate?
\\(\bigcirc\\) equality of fractions
\\(\bigcirc\\) the definition of simplest form
\\(\bigcirc\\) the definition of rational numbers
\\(\bigcirc\\) the fundamental law of fractions

Explanation:

Step1: Analyze Square a

The square is divided into 4 equal parts, and 1 part is shaded. So the fraction is $\frac{1}{4}$.

Step2: Analyze Square b

The square is divided into 8 equal parts (4 columns and 2 rows), and 2 parts are shaded. Simplifying $\frac{2}{8}$ gives $\frac{1}{4}$.

Step3: Analyze Square c

The square is divided into 12 equal parts (4 columns and 3 rows), and 3 parts are shaded. Simplifying $\frac{3}{12}$ gives $\frac{1}{4}$.

Step4: Analyze Square d

The square is divided into 16 equal parts (4 columns and 4 rows), and 4 parts are shaded. Simplifying $\frac{4}{16}$ gives $\frac{1}{4}$.

Step5: Determine the Fraction Property

All these fractions simplify to the same value ($\frac{1}{4}$), which illustrates the Equality of fractions (or also relates to the Fundamental Law of Fractions as we're multiplying numerator and denominator by the same non - zero number, but the key here is showing equal fractions).

Answer:

a. $\frac{1}{4}$
b. $\frac{2}{8}=\frac{1}{4}$
c. $\frac{3}{12}=\frac{1}{4}$
d. $\frac{4}{16}=\frac{1}{4}$
Property: Equality of fractions (or The Fundamental Law of Fractions, but the option given with Equality of fractions is appropriate here)
For the multiple - choice question, the answer is: Equality of fractions (the option with this text)