Verified Answer :

  • Define the total number of apples as the variable \(a\).
  • Recognize that "divided equally" into seven parts signifies division by 7.
  • Construct the algebraic expression by placing \(a\) as the dividend and 7 as the divisor.
  • The correct expression is \(\boxed{\frac{a}{7}}\).

Explanation

  1. Analysis of the Problem

We define the variable \(a\) to represent the total number of apples. The problem describes a situation where these apples are distributed into seven boxes such that each box receives an equal amount. This action of dividing a total quantity into a specific number of equal parts corresponds to the division operation.

  1. Formulating the Algebraic Expression

To represent "divided equally into seven boxes," we take the total number of apples, \(a\), and divide this quantity by the number of boxes, which is 7. In algebra, this operation is expressed as a fraction, where the numerator is the total quantity and the denominator is the divisor. Thus, the total number of apples divided by 7 is written as:
\[\frac{a}{7}\]

  1. Selecting the Correct Expression

Comparing this result to the provided options:

  • \(7 + a\) represents the sum of 7 and \(a\).
  • \(7a\) represents the product of 7 and \(a\).
  • \(\frac{7}{a}\) represents 7 divided by \(a\).
  • \(\frac{a}{7}\) represents \(a\) divided by 7.

The correct expression is \(\frac{a}{7}\).

Examples

Algebraic expressions help us model real-world situations concisely. For instance, if you have a collection of \(\$a\) that you want to split equally among 7 friends, you can calculate each person's share using the expression \(\frac{a}{7}\). This allows you to quickly find the individual amount for any total sum just by substituting the value of \(a\). Understanding these translations is a fundamental skill for solving complex word problems in mathematics and science.

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