Sure, let's work through the subtraction of [tex]\(1 \frac{2}{3} - \frac{11}{15}\)[/tex] step-by-step.
### Step 1: Convert the Mixed Number to an Improper Fraction
First, convert the mixed number [tex]\(1 \frac{2}{3}\)[/tex] to an improper fraction.
[tex]\[1 \frac{2}{3} = 1 + \frac{2}{3} \][/tex]
We need a common denominator to add these values:
[tex]\[1 = \frac{3}{3} \][/tex]
So,
[tex]\[1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \][/tex]
So, [tex]\(1 \frac{2}{3}\)[/tex] as an improper fraction is [tex]\(\frac{5}{3}\)[/tex].
### Step 2: Prepare to Subtract the Fractions
We now have:
[tex]\[\frac{5}{3} - \frac{11}{15}\][/tex]
Next, we need a common denominator to perform the subtraction. The denominators are 3 and 15. The least common multiple (LCM) of 3 and 15 is 15.
### Step 3: Convert Both Fractions to Have a Common Denominator
Convert [tex]\(\frac{5}{3}\)[/tex] to a fraction with the denominator 15:
[tex]\[
\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}
\][/tex]
So now we have:
[tex]\[
\frac{25}{15} - \frac{11}{15}
\][/tex]
### Step 4: Subtract the Numerators
Now that both fractions have the same denominator, subtract the numerators and keep the denominator the same:
[tex]\[
\frac{25}{15} - \frac{11}{15} = \frac{25 - 11}{15} = \frac{14}{15}
\][/tex]
So, the result of [tex]\(1 \frac{2}{3} - \frac{11}{15}\)[/tex] is [tex]\(\frac{14}{15}\)[/tex].
### Verification with Decimal Conversion
For verification purposes, you can convert [tex]\(\frac{14}{15}\)[/tex] into decimal form:
[tex]\[
\frac{14}{15} \approx 0.933333\ldots
\][/tex]
This matches our intermediate numerical result given earlier, confirming our detailed solution is correct.
Therefore, the final answer is:
[tex]\[
1 \frac{2}{3} - \frac{11}{15} = \frac{14}{15} \approx 0.933333
\][/tex]
