Question

Simplify negative 2 and 1 over 9 – negative 4 and 1 over 3.

Answer 1

Answer:

The correct answer is

$2\frac{2}{9}$

Step-by-step explanation:

Method 1

We want to simplify,

$-2\frac{1}{9} -(-4\frac{1}{3})$

The double negatives becomes positive,

$=-2\frac{1}{9} +4\frac{1}{3}$

We now add the whole number parts and the fractions separately

$=-2+4-\frac{1}{9} +\frac{1}{3}$

This will give us,

$=2-\frac{1}{9} +\frac{1}{3}$

The least common denominator for the fractional parts is 9.

$=2+\frac{-1+3\times1}{9}$

$=2+\frac{-1+3}{9}$

$=2+\frac{2}{9}$

$=2\frac{2}{9}$

Method 2

We want to simplify,

$-2\frac{1}{9} -(-4\frac{1}{3})$

The double negatives becomes positive,

$=-2\frac{1}{9} +4\frac{1}{3}$

We first convert the mixed numbers to improper fractions to obtain,

$=-\frac{2\times9+1}{9} +\frac{4\times3+1}{3}$

We carry out the multiplication in the numerator to get,

$=-\frac{18+1}{9} +\frac{12+1}{3}$

We add in the numerator to get,

$=-\frac{19}{9} +\frac{13}{3}$

The least common denominator is $9$.

$=\frac{-19+13\times3}{9}$

$=\frac{-19+39}{9}$

$=\frac{20}{9}$

We convert back to mixed numbers to get,

$=2\frac{2}{9}$