Question

Evaluate the following expression and name the property used in each step:

$4\frac{4}{9}+7\frac{2}{9}$

Short answer

The value of the expression is: $\mathbf{4}\frac{\mathbf{4}}{\mathbf{9}}\mathbf{+}\mathbf{7}\frac{\mathbf{2}}{\mathbf{9}}\mathbf{=}\mathbf{11}\frac{\mathbf{2}}{\mathbf{3}}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$4\frac{4}{9}+7\frac{2}{9}$

Step 2. Write the concept.

The substitution property for multiplication, addition, and subtraction is:

$\begin{array}{c}a\cdot b=c\\ a÷b=c\\ a\pm b=c\end{array}$

Also, to add or subtract the fraction, the denominator must be the same.

Step 3. Write mixed fraction to fraction.

$\begin{array}{c}4\frac{4}{9}=\frac{40}{9}\\ 7\frac{2}{9}=\frac{65}{9}\end{array}$

Step 4. Evaluate the expression.

The expression $4\frac{4}{9}+7\frac{2}{9}$ can be written as in below:

$4\frac{4}{9}+7\frac{2}{9}=\frac{40}{9}+\frac{65}{9}$

Here denominator of both fractions is the same.

Then,

$\begin{array}{l}4\frac{4}{9}+7\frac{2}{9}=\frac{40}{9}+\frac{65}{9}\\ =\frac{40+65}{9}\\ =\frac{105}{9}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\left(\text{Substitution\hspace{0.17em}\hspace{0.17em}Property}\right)\\ =11\frac{2}{3}\end{array}$