Lesson 4: Adding Fractions with Tenths and Hundredths

Property

A fraction with a denominator of 10 can be represented as a decimal in the tenths place. For example, $\frac{n}{10}$ can be written as 0.n. By adding a zero to the hundredths place, the tenths decimal becomes a hundredths decimal, 0.n0. This hundredths decimal can then be expressed as a fraction with denominator 100, $\frac{n0}{100}$. Therefore:

Examples

• $\frac{3}{10}$ can be written as 0.3. Adding a zero in the hundredths place gives 0.30, which can be written as $\frac{30}{100}$. Therefore, $\frac{3}{10} = \frac{30}{100}$.
• $\frac{7}{10}$ can be written as 0.7. Adding a zero in the hundredths place gives 0.70, which can be written as $\frac{70}{100}$. Therefore, $\frac{7}{10} = \frac{70}{100}$.
• $\frac{5}{10}$ can be written as 0.5. Adding a zero in the hundredths place gives 0.50, which can be written as $\frac{50}{100}$. Therefore, $\frac{5}{10} = \frac{50}{100}$.
• $\frac{8}{10}$ can be written as 0.8. Adding a zero in the hundredths place gives 0.80, which can be written as $\frac{80}{100}$. Therefore, $\frac{8}{10} = \frac{80}{100}$.

Explanation

This skill shows how tenths and hundredths are related. A fraction like $\frac{3}{10}$ represents three-tenths. By thinking of this as the decimal $0.3$, we can add a zero to the end without changing its value, making it $0.30$. This new decimal represents thirty-hundredths, which is written as the fraction $\frac{30}{100}$. Understanding this equivalence is the first step to adding fractions with tenths and hundredths.

Property

To add fractions with denominators of 10 and 100, you can use a model with 100 equal parts. On this model, one tenth is equivalent to ten hundredths.