Add the following

$253\frac{41}{63}$

Explanation

We will write each mixed number as the sum of a whole number and a fraction. Then we will add the whole numbers and the fractions separately.  If we change each mixed number to an improper fraction, build equivalent fractions, and add, the resulting numerators will be very large and difficult to work with.

• Write each mixed number as the sum of whole number and a fraction
  • \(168\frac37 + 85\frac29 = 168 + \frac37 + 85 + \frac29\)
• Use the commutative property of addition to change the order of the addition so that the whole numbers are together and the fractions are together.
  • =\(168 + 85 + \frac37 + \frac29\)
• Add the whole numbers
  • = \(253 + \frac37 + \frac29\)
• Prepare to add the fractions.  To build \(\frac37\) and \(\frac29\) so that their denominators are 63, multiply each by a form of 1.
  • = \(253 + \frac37 \cdot \frac99 + \frac29 \cdot \frac77 \)
• Multiply the numerators.  Multiply the denominators
  • =\(253 + \frac{27}{63} + \frac{14}{63}\)
• Add the numerators and write the sum over the common denominator 63.
  • =\( 253 + \frac{41}{63}\)
• Write the sum as a mixed number
  • = \(253\frac{41}{63}\)