Minimum Notes

Published on: September 29, 2026

This Minimum Calculator finds the smallest value in a list and shows the working line by line. Sorting the values from smallest to largest brings the answer to the front, where nothing comes before it. Negative values sort below zero, which is where a quick scan of an unsorted list most often goes wrong. Following the same pattern every time is what makes the minimum easy to check and repeat for any list of numbers.

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the first value in the sorted list.
See Example 1 Hide Example 1

Problem

\(5,\; 8,\; 12,\; 15\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the first value in the sorted list.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the smallest of the values \(5,\; 8,\; 12,\; 15\).

\(5,\; 8,\; 12,\; 15\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(5,\; 8,\; 12,\; 15\).

\(5,\; 8,\; 12,\; 15\)

Step 3

Step 3 - Take the first value in the sorted list.

In this problem: Nothing in the sorted list comes before \(5\), so that is the smallest value.

\(\text{Minimum} = 5\)

Final Answer

\(\text{Minimum} = 5\)
See Example 2 Hide Example 2

Problem

\(6,\; 6,\; 7,\; 10\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the first value in the sorted list.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the smallest of the values \(6,\; 6,\; 7,\; 10\).

\(6,\; 6,\; 7,\; 10\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(6,\; 6,\; 7,\; 10\).

\(6,\; 6,\; 7,\; 10\)

Step 3

Step 3 - Take the first value in the sorted list.

In this problem: Nothing in the sorted list comes before \(6\), so that is the smallest value.

\(\text{Minimum} = 6\)

Final Answer

\(\text{Minimum} = 6\)
See Example 3 Hide Example 3

Problem

\(4,\; 9,\; 11,\; 16\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the first value in the sorted list.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the smallest of the values \(4,\; 9,\; 11,\; 16\).

\(4,\; 9,\; 11,\; 16\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(4,\; 9,\; 11,\; 16\).

\(4,\; 9,\; 11,\; 16\)

Step 3

Step 3 - Take the first value in the sorted list.

In this problem: Nothing in the sorted list comes before \(4\), so that is the smallest value.

\(\text{Minimum} = 4\)

Final Answer

\(\text{Minimum} = 4\)
See Example 4 Hide Example 4

Problem

\(13,\; 2,\; 21,\; 8,\; 17\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the first value in the sorted list.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the smallest of the values \(13,\; 2,\; 21,\; 8,\; 17\).

\(13,\; 2,\; 21,\; 8,\; 17\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(2,\; 8,\; 13,\; 17,\; 21\).

\(2,\; 8,\; 13,\; 17,\; 21\)

Step 3

Step 3 - Take the first value in the sorted list.

In this problem: Nothing in the sorted list comes before \(2\), so that is the smallest value.

\(\text{Minimum} = 2\)

Final Answer

\(\text{Minimum} = 2\)