Answer:
The correct answer is
[tex]2\frac{2}{9}[/tex]
Step-by-step explanation:
Method 1
We want to simplify,
[tex]-2\frac{1}{9} -(-4\frac{1}{3})[/tex]
The double negatives becomes positive,
[tex]=-2\frac{1}{9} +4\frac{1}{3}[/tex]
We now add the whole number parts and the fractions separately
[tex]=-2+4-\frac{1}{9} +\frac{1}{3}[/tex]
This will give us,
[tex]=2-\frac{1}{9} +\frac{1}{3}[/tex]
The least common denominator for the fractional parts is 9.
[tex]=2+\frac{-1+3\times1}{9}[/tex]
[tex]=2+\frac{-1+3}{9}[/tex]
[tex]=2+\frac{2}{9}[/tex]
[tex]=2\frac{2}{9}[/tex]
Method 2
We want to simplify,
[tex]-2\frac{1}{9} -(-4\frac{1}{3})[/tex]
The double negatives becomes positive,
[tex]=-2\frac{1}{9} +4\frac{1}{3}[/tex]
We first convert the mixed numbers to improper fractions to obtain,
[tex]=-\frac{2\times9+1}{9} +\frac{4\times3+1}{3}[/tex]
We carry out the multiplication in the numerator to get,
[tex]=-\frac{18+1}{9} +\frac{12+1}{3}[/tex]
We add in the numerator to get,
[tex]=-\frac{19}{9} +\frac{13}{3}[/tex]
The least common denominator is [tex]9[/tex].
[tex]=\frac{-19+13\times3}{9}[/tex]
[tex]=\frac{-19+39}{9}[/tex]
[tex]=\frac{20}{9}[/tex]
We convert back to mixed numbers to get,
[tex]=2\frac{2}{9}[/tex]
