Verified Answer :

  • Identify the equivalent fraction relationship: \(\frac{4}{5} = \frac{x}{25}\).
  • Multiply both sides by 25 to isolate \(x\): \(x = \frac{4}{5} \times 25\).
  • Simplify the expression: \(x = 4 \times 5 = 20\).
  • The missing value is \(\boxed{20}\).

Explanation

  1. Analysis of the problem

We are asked to find the missing value in the equation \(\frac{4}{5} = \frac{\boxed{\phantom{0}}}{25}\). This is a problem of finding an equivalent fraction. A fraction represents a ratio, and two fractions are equivalent if they represent the same ratio. In this case, we have a fraction \(\frac{4}{5}\) and we want to find a numerator \(x\) such that \(\frac{x}{25}\) is equal to \(\frac{4}{5}\).

  1. Setting up the equation and isolating the variable

To find the unknown value \(x\), we set up the equation:
\[\frac{4}{5} = \frac{x}{25}\]
Our goal is to isolate \(x\) on one side of the equation. We can do this by multiplying both sides of the equation by 25.
\[25 \times \frac{4}{5} = 25 \times \frac{x}{25}\]
\[25 \times \frac{4}{5} = x\]

  1. Calculating the missing value

Now, we perform the multiplication to find the value of \(x\):
\[x = \frac{25 \times 4}{5}\]
\[x = \frac{100}{5}\]
\[x = 20\]
Alternatively, we could simplify the expression by noting that \(\frac{25}{5} = 5\), so \(x = 5 \times 4 = 20\). Thus, the missing value is 20.

Examples

Imagine you are following a recipe that requires 4 cups of flour for every 5 cups of sugar. If you need to scale up your recipe and you decide to use 25 cups of sugar, you would need to calculate the amount of flour required. Using the ratio \(\frac{4}{5} = \frac{x}{25}\), you can find that you need 20 cups of flour to keep the recipe balanced. Knowing how to work with ratios and proportions is essential in cooking, construction, and many other daily tasks where scaling is involved.

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