Alright! Let's break down this mathematical expression step-by-step.
Given expression:
[tex]\[ 9 - 3 \div \frac{1}{3} + 1 \][/tex]
1. Division Operation:
The first step is to perform the division. We need to divide [tex]\(3\)[/tex] by [tex]\(\frac{1}{3}\)[/tex].
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{1}{3}\)[/tex] is [tex]\(3\)[/tex]. So,
[tex]\[ 3 \div \frac{1}{3} = 3 \times 3 = 9 \][/tex]
2. Substitution:
Now replace the division part in the original expression with the result:
[tex]\[ 9 - 9 + 1 \][/tex]
3. Subtraction:
Next, we perform the subtraction:
[tex]\[ 9 - 9 = 0 \][/tex]
4. Addition:
Finally, we add [tex]\(1\)[/tex] to the result of the subtraction:
[tex]\[ 0 + 1 = 1 \][/tex]
So the final result of the expression [tex]\(9 - 3 \div \frac{1}{3} + 1\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
