College

Add:

[tex]\frac{4}{10} + \frac{8}{100}[/tex]

Express your answer in simplest form.

A. [tex]\frac{3}{50}[/tex]
B. [tex]\frac{6}{55}[/tex]
C. [tex]\frac{3}{25}[/tex]
D. [tex]\frac{12}{25}[/tex]

Answer :

We are given the fractions

[tex]$$\frac{4}{10} \quad \text{and} \quad \frac{8}{100}.$$[/tex]

Step 1. Convert to a common denominator

Since the denominator [tex]$100$[/tex] is a multiple of [tex]$10$[/tex], we convert [tex]$\frac{4}{10}$[/tex] to an equivalent fraction with denominator [tex]$100$[/tex] by multiplying the numerator and denominator by [tex]$10$[/tex]:

[tex]$$\frac{4}{10} = \frac{4 \times 10}{10 \times 10} = \frac{40}{100}.$$[/tex]

Step 2. Add the fractions

Now that both fractions have the denominator [tex]$100$[/tex], we add the numerators:

[tex]$$\frac{40}{100} + \frac{8}{100} = \frac{40 + 8}{100} = \frac{48}{100}.$$[/tex]

Step 3. Simplify the result

To simplify [tex]$\frac{48}{100}$[/tex], find the greatest common divisor (GCD) of [tex]$48$[/tex] and [tex]$100$[/tex]. The GCD of [tex]$48$[/tex] and [tex]$100$[/tex] is [tex]$4$[/tex]. Divide both the numerator and the denominator by [tex]$4$[/tex]:

[tex]$$\frac{48 \div 4}{100 \div 4} = \frac{12}{25}.$$[/tex]

Thus, the simplified result is

[tex]$$\frac{12}{25}.$$[/tex]