Question

Determine the value of the following expression.

$7\frac{3}{4}-4\frac{7}{10}$

Short answer

The value of the given expression is $\mathbf{3}\frac{\mathbf{1}}{\mathbf{20}}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$7\frac{3}{4}-4\frac{7}{10}$

Step 2. Write the concept.

To add or subtract the fraction, the denominator must be the same.

Step 3. Write a mixed fraction to fraction form.

The given expression can be written as in below:

$7\frac{3}{4}-4\frac{7}{10}=\frac{31}{4}-\frac{47}{10}$

Step 4. Solve the expression.

The expression $\frac{31}{4}-\frac{47}{10}$ can be solved below:

$\begin{array}{l}\frac{31}{4}-\frac{47}{10}=\frac{31\times 5}{4\times 5}-\frac{47\times 2}{10\times 2}\\ =\frac{155}{20}-\frac{94}{20}\\ =\frac{155-94}{20}\\ =\frac{61}{20}\end{array}$

Therefore,

$\begin{array}{l}7\frac{3}{4}-4\frac{7}{10}=\frac{61}{20}\\ =3\frac{1}{20}\end{array}$