Verified Answer :

  • Set up the equation using a variable: \(\frac{2}{5} = \frac{x}{50}\).
  • Identify the multiplier for the denominator: \(50 \div 5 = 10\).
  • Apply the same multiplier to the numerator: \(2 \times 10 = 20\).
  • State the final missing value: \(\boxed{20}\).

Explanation

  1. Analyzing the Problem

The problem asks to find the missing value \(\square\) in the equation \(\frac{2}{5} = \frac{\square}{50}\). This is a question about equivalent fractions, where two fractions represent the same quantity even if they have different numerators and denominators. We can denote the unknown value with the variable \(x\), transforming the equation into \(\frac{2}{5} = \frac{x}{50}\).

  1. Finding the Equivalent Fraction

To determine the value of \(x\), we can observe the relationship between the denominators. We know that \(\frac{2}{5} = \frac{x}{50}\). Since the denominator of the first fraction is \(5\) and the denominator of the second is \(50\), we look for a multiplier \(k\) such that \(5 \times k = 50\). Dividing 50 by 5, we find that \(k = 10\). To keep the fractions equal, we must multiply both the numerator and the denominator of the first fraction by the same factor of 10.

  1. Calculating the Missing Value

We apply the multiplication factor:
\[ \frac{2 \times 10}{5 \times 10} = \frac{20}{50} \]
Comparing this result to \(\frac{x}{50}\), we can see that \(x = 20\). Therefore, the missing value that satisfies the equation \(\frac{2}{5} = \frac{\square}{50}\) is \(20\).

Examples

Equivalent fractions are essential in everyday life, such as in cooking where measurements need to be scaled. For example, if a recipe calls for \(\frac{2}{5}\) of a cup of sugar but your measuring cup is marked in fiftieths, you would use \(\frac{20}{50}\) of a cup to get the same amount. Understanding this concept helps maintain proportions in everything from construction projects to financial ratios.

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