Step 1. Add the whole numbers first.
[tex]3+ \frac{5}{6} + \frac{2}{11} [/tex]
Step 2. Find the Least Common Denominator (LCD) of [tex] \frac{5}{6} [/tex] , [tex] \frac{2}{11} [/tex]
Method 1: By Listing MultiplesList out all multiples of each denominator, and find the first common one.
Multiples of 6 : 6, 12, 18 ... 54, 60, 66, ...
Multiples of 11 : 11, 22, 33, 44, 55, 66, ...
Therefore, the LCD is 66.
Method 2: By Prime FactorsList all prime factors of each denominator, and find the union of these
primes.
Prime Factors of 6: 2,3
Prime Factors of 11: 11
Therefore, the LCD is 2 x 3 x 11 = 66.
LCD = 66
Step 3. Make the denominators the same as the LCD
[tex]3+ \frac{5*11}{6*11} + \frac{2*6}{11*6} [/tex]
Step 4. Simplify. Denominators are now the same
[tex]3+ \frac{55}{66} + \frac{12}{66} [/tex]
Step 5. Join the denominators
[tex]3+ \frac{55+12}{66} [/tex]
Step 6. Simplify
[tex]3+ \frac{67}{66} [/tex]
Step 7. Convert [tex] \frac{67}{66} [/tex] into a mixed fraction
[tex]3+1 \frac{1}{66} [/tex]
Step 8. Simplify
[tex]4 \frac{1}{66} [/tex]
Done! :) Hope This Helps! :) ♥♥♥
Decimal Form If Needed: 4.015152
