Horse Racing

$3\frac{15}{16}$

Explanation

Analyze

• The Kentucky Derby is \(1\frac14\) miles long.
• The Preakness Stakes is \(1\frac{3}{16}\) miles long.
• The Belmont Stakes is \(1\frac{1}{2}\) miles long.
• What is the combined length of the three races

Form

The key phrases combined length indicates addition.  We translate the words of the problem to numbers and symbols

(The combined length of the three races) is equal to (The length of the Kentucky Derby) plus (the length of the Preakness Stakes) plus (The length of the Belmont Stakes)

The combined length of the three races = \(1\frac14 + 1\frac{3}{16} + 1\frac12\)

Solve

• Build \(\frac14\) and \(\frac12\) so that their denominators are 16
  • = \(1\frac14 \cdot \frac44 + 1\frac{3}{16} + 1\frac12 \cdot \frac88\)
• Add the fractions separately and whole numbers separately
  • = \(1\frac{4}{16} + 1\frac{3}{16} + 1\frac{8}{16} = 3\frac{15}{16}\)

State

The combined length of the three races of the Triple Crown is \(3\frac{15}{16}\) miles.

Check

We can estimate to check the result.  if we round \(1\frac14\) down to 1, round \(1\frac{3}{16}\) down to 1, and round \(1\frac12\) up to 2, the approximate combined length of the three races 1 + 1 + 2 = 4 miles.  Since \(3\frac{15}{16}\) is close to 4, the result seems reasonable.