Question

1. use the model to help write a fraction equivalent to \\(\frac{2}{6}\\). explain.

Explanation:

Step1: Recall Equivalent Fraction Rule

To find an equivalent fraction, we multiply or divide the numerator and denominator by the same non - zero number. For the fraction \(\frac{2}{6}\), we can simplify it by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 2 and 6 is 2.

Step2: Simplify the Fraction

Divide the numerator \(2\) by \(2\): \(2\div2 = 1\).
Divide the denominator \(6\) by \(2\): \(6\div2=3\).
So, \(\frac{2\div2}{6\div2}=\frac{1}{3}\).
We can also think about the model: the rectangle is divided into 6 equal parts, and 2 are shaded. If we group the 6 parts into groups of 2, we will have 3 groups, and 1 of those groups is shaded, which represents \(\frac{1}{3}\).

Answer:

A fraction equivalent to \(\frac{2}{6}\) is \(\frac{1}{3}\) (we can also have other equivalents like \(\frac{4}{12}\) by multiplying numerator and denominator by 2, but \(\frac{1}{3}\) is a simplified equivalent. The explanation for \(\frac{1}{3}\) is that when we divide both the numerator and denominator of \(\frac{2}{6}\) by their greatest common factor (2), we get \(\frac{1}{3}\), and the model also shows that if we re - group the 6 parts into 3 equal groups (each group having 2 original parts), 1 group is shaded, representing \(\frac{1}{3}\)).