Verified Answer :

  • Define the total number of paintbrushes as \(p\).
  • Identify the number of groups (classrooms) as 12.
  • Express the equal distribution as a division of the total by the number of groups: \(\frac{p}{12}\).
  • Select the matching option: \(\boxed{\frac{p}{12}}\).

Explanation

  1. Analyzing the Problem

We have a total quantity of items represented by the variable \(p\), which stands for the number of paintbrushes. These paintbrushes are being distributed equally into 12 classrooms. In mathematics, when we distribute a total amount into a specific number of equal groups, we use the operation of division.

  1. Formulating the Expression

To represent this division algebraically, we place the total amount, \(p\), in the numerator (the dividend) and the number of groups, 12, in the denominator (the divisor). This gives us the expression \(\frac{p}{12}\). This expression represents the number of paintbrushes that each classroom receives.

  1. Selecting the Final Option

Comparing our formulated expression \(\frac{p}{12}\) with the given options:

  • \(12 + p\) (Addition)
  • \(12p\) (Multiplication)
  • \(\frac{12}{p}\) (Dividing 12 by \(p\))
  • \(\frac{p}{12}\) (Dividing \(p\) by 12)

The correct expression is \(\frac{p}{12}\), which corresponds to the final option. Therefore, \(\boxed{\frac{p}{12}}\).

Examples

Imagine you are a teacher organizing a classroom art project with 60 paintbrushes to share among 12 students. To find out how many brushes each student receives, you would divide the total number of brushes by the number of students: \(\frac{60}{12} = 5\). This is the same principle applied to the variable \(p\), where \(\frac{p}{12}\) allows you to calculate the portion per group regardless of the total number of paintbrushes available.

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