Certainly! Let's subtract the mixed numbers [tex]\(19 \frac{6}{7} - 9 \frac{4}{7}\)[/tex].
### Step 1: Convert the mixed numbers to improper fractions.
First, we need to convert each mixed number into an improper fraction.
For [tex]\(19 \frac{6}{7}\)[/tex]:
- The whole number part is 19.
- The fractional part is [tex]\(\frac{6}{7}\)[/tex].
To convert it to an improper fraction:
[tex]\[
19 \frac{6}{7} = \frac{19 \times 7 + 6}{7} = \frac{133 + 6}{7} = \frac{139}{7}
\][/tex]
For [tex]\(9 \frac{4}{7}\)[/tex]:
- The whole number part is 9.
- The fractional part is [tex]\(\frac{4}{7}\)[/tex].
To convert it to an improper fraction:
[tex]\[
9 \frac{4}{7} = \frac{9 \times 7 + 4}{7} = \frac{63 + 4}{7} = \frac{67}{7}
\][/tex]
### Step 2: Subtract the improper fractions.
Now that we have the improper fractions, we can subtract them:
[tex]\[
\frac{139}{7} - \frac{67}{7}
\][/tex]
Since the denominators are the same, we just subtract the numerators:
[tex]\[
\frac{139 - 67}{7} = \frac{72}{7}
\][/tex]
### Step 3: Convert the result back to a mixed number.
Next, we need to convert [tex]\(\frac{72}{7}\)[/tex] back to a mixed number.
To do this, divide 72 by 7:
- 72 divided by 7 gives a quotient of 10 and a remainder of 2.
So:
[tex]\[
\frac{72}{7} = 10 \frac{2}{7}
\][/tex]
### Final Answer:
The result of subtracting [tex]\(19 \frac{6}{7}\)[/tex] and [tex]\(9 \frac{4}{7}\)[/tex] is:
[tex]\[
10 \frac{2}{7}
\][/tex]
