We are given the equation \(\frac{2}{5} = \frac{\square}{15}\). Our objective is to determine the unknown value, denoted by \(\square\), that makes the two fractions equivalent. Equivalent fractions represent the same portion of a whole. To find an equivalent fraction, we can multiply both the numerator and the denominator of the original fraction by the same non-zero number.
First, examine the denominators of the two fractions, which are \(5\) and \(15\). To turn the denominator \(5\) into \(15\), we must multiply it by \(3\), since \(5 \times 3 = 15\). To maintain the equivalence of the fractions, we must multiply the numerator of the first fraction by the same number, \(3\).
Now, apply this multiplier to the numerator of the first fraction:
\[2 \times 3 = 6\]
Thus, the unknown numerator \(\square\) is \(6\), and the equivalent fraction is \(\frac{6}{15}\). Checking our work: \(\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}\). The values are indeed equal.
Imagine you are sharing a delicious pizza. If you cut the pizza into 5 equal slices and take 2 of them, you have eaten \(\frac{2}{5}\) of the pizza. Now, imagine you cut that same pizza into 15 much smaller, equal slices. To have eaten the same amount of pizza, you would need to take 6 of those smaller slices. This shows that \(\frac{2}{5}\) is the same amount as \(\frac{6}{15}\). Understanding equivalent fractions helps in many real-life situations like cooking, dividing up supplies, or sharing items fairly among friends.