Understanding Fractions and Decimals in Year 8 Math

In Year 8 math, it's really important to know how fractions and decimals work together. Both of these are ways to show parts of a whole. Understanding how they connect helps you do different math problems better.

Changing Fractions to Decimals and Vice Versa

To see how fractions and decimals relate, you should learn how to change one into the other.

For example, let’s take the fraction $\frac{3}{4}$.

To turn this fraction into a decimal, you divide the top number by the bottom number:

$$\frac{3}{4} = 3 \div 4 = 0.75$$

Now, if you look at a decimal like $0.5$, you can turn it into a fraction.

$0.5$ is the same as $\frac{5}{10}$, which you can make simpler to get $\frac{1}{2}$.

Adding and Subtracting Fractions and Decimals

When you want to add or subtract fractions, it can be easier to first change them to decimals.

Let’s say you want to add $\frac{1}{2}$ and $\frac{1}{4}$:

1. Change $\frac{1}{2}$ to a decimal: $\frac{1}{2} = 0.5$.
2. Change $\frac{1}{4}$ to a decimal: $\frac{1}{4} = 0.25$.
3. Now add them together: $0.5 + 0.25 = 0.75$.

If you want the answer back in fraction form, you can change $0.75$ back to a fraction, which gives you $\frac{3}{4}$.

Multiplying and Dividing

When you multiply decimals, you can either multiply them directly or change them into fractions first.

For example, to multiply $0.6 \times 0.3$, you can write these decimals as fractions:

$$0.6 = \frac{6}{10} \quad \text{and} \quad 0.3 = \frac{3}{10}$$

Now you can multiply:

$$\frac{6}{10} \times \frac{3}{10} = \frac{18}{100} = 0.18$$

The Big Picture

In short, fractions and decimals are very similar. Knowing how to switch between them helps you improve your math skills. This knowledge makes it easier to solve a variety of math problems.