Express each decimal as a fraction. Then, add. Express the answer as a decimal.

Steps to Solve

1. Convert 0.4 to a Fraction

To convert the decimal $0.4$ into a fraction, recognize that $0.4$ can be expressed as $\frac{4}{10}$.

Next, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is $2$: $$ \frac{4 \div 2}{10 \div 2} = \frac{2}{5} $$

2. Convert 0.16 to a Fraction

For $0.16$, write it as $\frac{16}{100}$.

Then simplify the fraction by dividing both the numerator and the denominator by their GCD, which is $4$: $$ \frac{16 \div 4}{100 \div 4} = \frac{4}{25} $$

3. Add the Fractions

Now, we need to add $\frac{2}{5}$ and $\frac{4}{25}$. First, find a common denominator. The least common multiple (LCM) of $5$ and $25$ is $25$. Rewrite $\frac{2}{5}$ with a denominator of $25$: $$ \frac{2}{5} = \frac{2 \times 5}{5 \times 5} = \frac{10}{25} $$

Now add: $$ \frac{10}{25} + \frac{4}{25} = \frac{10 + 4}{25} = \frac{14}{25} $$

4. Convert the Result to Decimal

To express $\frac{14}{25}$ as a decimal, divide the numerator by the denominator: $$ 14 \div 25 = 0.56 $$