Understanding Fractions with Denominators of 10 and 100

Fractions with denominators of 10 (tenths) and 100 (hundredths) are special because they are the building blocks of the decimal system. Learning how to work with them makes adding fractions and understanding decimals incredibly easy!

Equivalent Fractions: Changing Tenths to Hundredths

You cannot easily add fractions if their bottom numbers (denominators) are different. To add tenths and hundredths together, you first need to turn the tenths into hundredths.

To write a fraction like $\frac{7}{10}$ as an equivalent fraction with a denominator of 100, you simply multiply both the top (numerator) and the bottom (denominator) by 10.

$\frac{7 \times 10}{10 \times 10} = \frac{70}{100}$

So, $\frac{7}{10}$ represents exactly the same amount as $\frac{70}{100}$.

Adding Tenths and Hundredths

Let's look at an example: Add $\frac{3}{10} + \frac{25}{100}$.

Step 1: Make the denominators the same. Convert $\frac{3}{10}$ into hundredths by multiplying the top and bottom by 10. $\frac{3 \times 10}{10 \times 10} = \frac{30}{100}$

Step 2: Add the numerators. Now that both fractions are in hundredths, the denominators match, and you can just add the top numbers! $\frac{30}{100} + \frac{25}{100} = \frac{55}{100}$

Connecting Fractions to Decimals

Because our number system is based on tens, fractions over 10 and 100 can be written directly as decimals.

• Tenths: $\frac{3}{10}$ is written as $0.3$ (read as "three tenths").
• Hundredths: $\frac{45}{100}$ is written as $0.45$ (read as "forty-five hundredths").

If you have $\frac{7}{10}$, it is written as $0.7$ in decimal form. Because we know that $\frac{7}{10} = \frac{70}{100}$, this also proves that $0.7$ is exactly the same as $0.70$!