Add the following

$6\frac{83}{12}$

Explanation

Strategy We will write each mixed number as an improper fraction, and then use the rule for adding two fractions that have different denominators.  We cannot add the mixed numbers as they are; their fractional parts are not similar objects.

Solution

• Write \(4\frac16\) and \(2\frac34\) as improper fractions
  • \(4\frac16 + 2\frac34 = \frac{25}{6} + \frac{11}{4}\)

By inspection, we see that the lowest common denominator is 12.

• To build \(\frac{25}{6}\) and \(\frac{11}{4}\) so that their denominators are 12, multiply each by a form of 1.
  • = \(\frac{25 \cdot 2}{6 \cdot 2} + \frac{11 \cdot 3}{4 \cdot 3}\)
• Multiply the numerators.  Multiply the denominators.
  • = \(\frac{50}{12} + \frac{33}{12}\)
• Add the numerators and write the sum over the common denominator 12.  The result is an improper fraction.
  • =\(\frac{83}{12}\)
• Write the improper fraction \(\frac{83}{12}\) as a mixed number
  • =\(6\frac{11}{12}\)