Subtract mixed numbers

  2. Basic Math Decoded
  3. Subtract mixed numbers
 
  4     5
3 — - 2 —
  7     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.
 
  2 × 9 + 4   2 × 9 + 5
= ————————— - —————————
      7           9    
 
  25   23
= —— - ——
   7    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: 1
Least Common Denominator: (7 × 9) ÷ 1 = 63
 
Divide the Least Common Denominator by each denominator and multiply the result by the corresponding numerator. Subtract the results of both multiplications and place the answer over the Least Common Denominator.
 
  9 × 25 - 7 × 23
= ———————————————
         63      
 
Partial multiplications
 
  25
×  9
 225
 
  23
×  7
 161
 
  225 - 161
= —————————
      63   
 
Partial subtraction
 
  225
- 161
   64
 
  64
= ——
  63
 
 
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.
 
    1 R 1
63)64
   63
    1
 
Final answer
 
   1
1 ——
  63
 
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