# Subtracting Mixed Numbers

by Dynasty
(Spring, TX - Houston, TX)

Subtraction Arithmetic

Subtracting mixed numbers when:

1. the denominators of the two fractions are unlike denominators
2. it is necessary to borrow or create improper fractions

What is 14 1/3 minus 10 7/12 ?

### Comments for Subtracting Mixed Numbers

 Aug 17, 2013 Subtraction by: Staff Answer Part I (14 1/3) - (10 7/12) it might be easier to think about these mixed numbers like this: (14 + 1/3) - (10 + 7/12) convert each mixed number into an improper fraction convert the first mixed number 14 1/3 convert the integer portion of the mixed number to an improper fraction whose denominator is the same as the denominator of the fraction in this case, convert the 14 to a fraction whose denominator is 3 (14) * (3/3) = (14/1) * (3/3) = (14 * 3)/(1 * 3) = 42/3 replace the 14 with 42/3, and then add the two fractions 14 1/3 = 42/3 + 1/3 = (42 + 1)/3 = 43/3 -------------------------------------------------------------

 Aug 17, 2013 Subtraction by: Staff ------------------------------------------------------------- Part II convert the second mixed number 10 7/12 convert the integer portion of the mixed number to a fraction whose denominator is the same as the denominator of the fraction in this case, convert the 10 to an improper fraction whose denominator is 12 (10) * (12/12) = (10/1) * (12/12) = (10 * 12)/(1 * 12) = 120/12 replace the 10 with 120/12, and then add the two fractions 10 7/12 = 120/12 + 7/12 = (120 + 7)/12 = 127/12 replace the mixed number 14 1/3 with the improper fraction 43/3, and replace the mixed number 10 7/12 with the improper fraction 127/12 (14 1/3) - (10 7/12) = (43/3) - (127/12) -------------------------------------------------------------

 Aug 17, 2013 Subtraction by: Staff ------------------------------------------------------------- Part III the next step in the problem is to subtract the two improper fractions (43/3) - (127/12) since the two fractions have different denominators, the fractions must be changed so that both denominators are the same change the improper fraction 43/3 to a fraction with the denominator of 12 (43/3) * (4/4) = (43 * 4)/(3 * 4) = (43 * 4)/(3 * 4) = 172/12 replace the improper fraction 43/3 with the improper fraction 172/12 (43/3) - (127/12) = (172/12) - (127/12) the two fractions now have the same denominator subtract the two improper fractions (172/12) - (127/12) = (172 - 127)/12 = 45/12 = 15/4 -------------------------------------------------------------

 Aug 17, 2013 Subtraction by: Staff -------------------------------------------------------------Part IV convert the improper fraction to mixed number form:15/4= 15 ÷ 4= 3 R 3= 3 3/4 -------------------------------------------------------------

 Aug 17, 2013 Subtraction by: Staff ------------------------------------------------------------- Part V the final answer is: 45/12 or 3 3/4 Thanks for writing. Staff www.solving-math-problems.com