Add mixed numbers

  2. Basic Math Decoded
  3. Add mixed numbers
 
   7     5
3 —— + 2 —
  12     9
 
Convert mixed numbers to fractions. Multiply the integer portion by the denominator and add the numerator, the result will be the numerator of the fraction, keeping the same denominator.
 
  3 × 12 + 7   2 × 9 + 5
= —————————— + —————————
      12           9    
 
  43   23
= —— + ——
  12    9
 
 
The fractions have different denominators. Find the Least Common Denominator (LCD) of the fractions. It is the smallest positive integer that is a multiple of the denominators, and can be calculated as the product of the denominators divided by the Greatest Common Factor.
 
 
Greatest Common Factor: 3
Least Common Denominator: (12 × 9) ÷ 3 = 36
 
Divide the Least Common Denominator by each denominator and multiply the result by the corresponding numerator. Add the results of both multiplications and place the sum over the Least Common Denominator.
 
  3 × 43 + 4 × 23
= ———————————————
         36      
 
Partial multiplications
 
  43
×  3
 129
 
  23
×  4
  92
 
  129 + 92
= ————————
     36   
 
Partial sum
 
  129
+  92
  221
 
  221
= ———
   36
 
 
Fraction cannot be simplified.
 
 
This fraction is improper (numerator larger than or equal to the denominator). Convert it to a mixed number. The integer portion is the quotient when dividing the numerator by the denominator, the numerator of the fraction portion is the rest of that division, and keeps the same denominator.
 
     6 R 5
36)221
   216
     5
 
Final answer
 
   5
6 ——
  36
 
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