# Alegbra 1A - Mixed Numbers

-6 - 7 3/4 + (-2 2/3)=

Convert each mixed number to a fraction with the same denominator, add (or subtract) the fractions, and then convert the total back into a mixed number.

### Comments for Alegbra 1A - Mixed Numbers

 Aug 28, 2011 Adding Mixed Numbers by: Staff -------------------------------------- Part II Convert the fraction 31/4 to a fraction with a denominator of 12 The denominator of the fraction (31)/4 is 4. To convert the denominator of 4 to a denominator of 12, we are going to multiply the 4 by 3. As before, we cannot change the value of the fraction. We are going to multiply the numerator AND the denominator by 3. In other words, the fraction 31/4 will be multiplied by another fraction: 3/3. Note that 3/3 = 1, so we are actually multiplying by 1. The decimal value of the fraction (31)/4 will not change. = (31/4)*(3/3) When multiplying two fractions, multiply the two numerators and multiply the two denominators: = (31*3)/(4*3) 7 3/4 = (31)/4 = (93)/12 Convert the fraction 8/3 to a fraction with a denominator of 12 The denominator of the fraction 8/3 is 3. To convert the denominator of 3 to a denominator of 12, we are going to multiply the 3 by 4. As before, we cannot change the value of the fraction. We are going to multiply the numerator AND the denominator by 4. In other words, the fraction 8/3 will be multiplied by another fraction: 4/4. Note that 4/4 = 1, so we are actually multiplying by 1. The decimal value of the fraction 8/3 will not change. = (8/3)*(4/4) When multiplying two fractions, multiply the two numerators and multiply the two denominators: = (8*4)/(3*4) 2 2/3 = 8/3 = (32)/12 This is a summary of the steps which have completed so far: Original problem: = - 6 - 7 3/4 + (-2 2/3) Problem after converting the mixed numbers to improper fractions: = - 6/1 - 31/4 - 8/3 Problem after converting the improper fractions to fractions with a common denominator: = - (72)/12 - (93)/12 - (32)/12 Since each fraction has the same denominator, the fractions can finally be added. When adding fractions, only the numerators are added. = (- 72 - 93 - 32)/12 = (-197)/12 This fraction cannot be reduced, but it can be converted into a mixed number. To convert (-197)/12 to a mixed number, divide -197 by 12 = (-197)/12 = (-197) ÷ 12 = -16, remainder 5 = -16 5/12 The final answer is: -16 5/12 [or (-197)/12 or -16.4167] Check the answer with a calculator: = -6 - 7 3/4 + (-2 2/3) = -6 - 7.75 + (-2.6667) = -16.4167 Since -16.4167 is the same answer obtained by converting -16 5/12 to its decimal equivalent, the answer of -16 5/12 is correct. Thanks for writing. Staff www.solving-math-problems.com