Sure, let's break down the problem step-by-step:
We need to divide the fraction [tex]\(-\frac{26}{18}\)[/tex] by [tex]\(\frac{1}{3}\)[/tex].
Step 1: Understand the Problem
Dividing one fraction by another fraction is the same as multiplying the first fraction by the reciprocal of the second fraction.
Step 2: Find the Reciprocal
The reciprocal of [tex]\(\frac{1}{3}\)[/tex] is [tex]\(\frac{3}{1}\)[/tex] or simply [tex]\(3\)[/tex].
Step 3: Set Up the Multiplication
Now, we should multiply [tex]\(-\frac{26}{18}\)[/tex] by [tex]\(3\)[/tex]:
[tex]\[
-\frac{26}{18} \times 3
\][/tex]
Step 4: Perform the Multiplication
When you multiply a fraction by a whole number, you multiply the numerator by that whole number while keeping the denominator the same:
[tex]\[
-\frac{26 \times 3}{18} = -\frac{78}{18}
\][/tex]
Step 5: Simplify the Result
To simplify the fraction [tex]\(-\frac{78}{18}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 78 and 18 is 6:
[tex]\[
-\frac{78 \div 6}{18 \div 6} = -\frac{13}{3}
\][/tex]
Step 6: Convert to Decimal (Optional):
If we wish to express [tex]\(-\frac{13}{3}\)[/tex] as a decimal, we can perform the division:
[tex]\[
-\frac{13}{3} \approx -4.333333333333333
\][/tex]
Thus, the solution to [tex]\(\left(-\frac{26}{18}\right) \div \frac{1}{3}\)[/tex] is approximately [tex]\(-4.333333333333333\)[/tex] in decimal form.
