Solve: (-12 1/6) + (+10 1/3) Mixed Number Addition

Question

(1216)+(+1013)= (-12\frac{1}{6})+(+10\frac{1}{3})=

Video Solution

Solution Steps

00:00 Solve
00:15 We'll use the substitution method and arrange the exercise
00:24 We'll multiply the fraction by 2 to get a common denominator
00:34 We'll convert from 12 sixths to 11 and 7 sixths
00:44 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert the mixed numbers to improper fractions.
  • Step 2: Find a common denominator and add the fractions.
  • Step 3: Convert the resulting improper fraction back into a mixed number.

Let's begin by converting the mixed numbers into improper fractions:

The mixed number 1216 -12\frac{1}{6} can be converted as follows:

1216=(12×6+16)=736 -12\frac{1}{6} = -\left(\frac{12 \times 6 + 1}{6}\right) = -\frac{73}{6}

The mixed number +1013 +10\frac{1}{3} can be converted as follows:

1013=10×3+13=313 10\frac{1}{3} = \frac{10 \times 3 + 1}{3} = \frac{31}{3}

Next, we need a common denominator to add these fractions together. The denominators are 6 and 3, and the least common denominator is 6.

Convert 313\frac{31}{3} to have the denominator of 6:

313=31×23×2=626 \frac{31}{3} = \frac{31 \times 2}{3 \times 2} = \frac{62}{6}

Now, we add the fractions:

736+626=73+626=116 -\frac{73}{6} + \frac{62}{6} = \frac{-73 + 62}{6} = \frac{-11}{6}

Convert 116\frac{-11}{6} back into a mixed number:

116=156 \frac{-11}{6} = -1\frac{5}{6} (since 11÷6=1 11 \div 6 = 1 with a remainder of 5)

Therefore, the solution to the problem is 156 -1\frac{5}{6} .

Answer

156 -1\frac{5}{6}