Certainly! Let's subtract the mixed numbers [tex]\( 10 \frac{4}{5} \)[/tex] and [tex]\( 2 \frac{2}{10} \)[/tex] step by step.
### Step 1: Convert mixed numbers to improper fractions
First, we need to convert each mixed number into an improper fraction.
Convert [tex]\( 10 \frac{4}{5} \)[/tex]:
[tex]\[ 10 \frac{4}{5} = 10 + \frac{4}{5} \][/tex]
[tex]\[ 10 = \frac{50}{5} \][/tex]
[tex]\[ 10 \frac{4}{5} = \frac{50}{5} + \frac{4}{5} = \frac{54}{5} \][/tex]
Convert [tex]\( 2 \frac{2}{10} \)[/tex]:
[tex]\[ 2 \frac{2}{10} = 2 + \frac{2}{10} \][/tex]
[tex]\[ 2 = \frac{20}{10} \][/tex]
[tex]\[ 2 \frac{2}{10} = \frac{20}{10} + \frac{2}{10} = \frac{22}{10} \][/tex]
Next, simplify [tex]\( \frac{22}{10} \)[/tex] to its simplest form:
[tex]\[ \frac{22}{10} = \frac{11}{5} \][/tex]
So, we have:
[tex]\[ 10 \frac{4}{5} = \frac{54}{5} \][/tex]
[tex]\[ 2 \frac{2}{10} = \frac{11}{5} \][/tex]
### Step 2: Subtract the improper fractions
Now we need to subtract the two improper fractions:
[tex]\[ \frac{54}{5} - \frac{11}{5} \][/tex]
Since the denominators are the same, we can subtract the numerators directly:
[tex]\[ \frac{54 - 11}{5} = \frac{43}{5} \][/tex]
### Step 3: Simplify the result
The fraction [tex]\( \frac{43}{5} \)[/tex] can be converted to a mixed number:
[tex]\[ \frac{43}{5} = 8 \frac{3}{5} \][/tex]
or in decimal form:
[tex]\[ \frac{43}{5} = 8.6 \][/tex]
### Final Result
The result of subtracting the mixed numbers [tex]\( 10 \frac{4}{5} \)[/tex] and [tex]\( 2 \frac{2}{10} \)[/tex] is:
[tex]\[ \frac{43}{5} \text{ which is } 8.6 \][/tex]
