It's really cool how equivalent fractions connect to decimals and percentages, especially when you're in Year 7 math.

At first, fractions can seem a bit confusing, but once you understand equivalent fractions, everything starts to make sense!

What Are Equivalent Fractions?

Equivalent fractions are different fractions that show the same amount. For example, $1/2$ is the same as $2/4$ or $4/8$.

You can make equivalent fractions by multiplying or dividing the top number (numerator) and the bottom number (denominator) by the same number.

For example, if you take $1/3$ and multiply both the top and bottom by $2$, you get $2/6$. That means $2/6$ is equal to $1/3$.

How Do They Connect to Decimals?

Now, when we talk about decimals, it's easy to see how they connect to equivalent fractions. You can change a fraction into a decimal by dividing the top number by the bottom number.

For instance, for $1/2$, you divide $1$ by $2$ and get $0.5$. This decimal form is very useful because we see it a lot in everyday life, like with money or measurements.

Let’s look at the fraction $3/4$. If you divide $3$ by $4$, you get $0.75$. This shows how to turn that fraction into a decimal. We can also make equivalent fractions that have the same decimal form.

For example, $6/8$ is another way to show $3/4$. If you divide $6$ by $8$, you still get $0.75$. It’s like having different routes to reach the same place!

Percentage Connection

Now, percentages are just another way to show the same values but based on 100. To change a fraction into a percentage, you multiply the decimal by 100.

So, for the fraction $1/2$, its decimal form is $0.5$. To turn $0.5$ into a percentage, you do $0.5 \times 100 = 50\%$. This means that $1/2$ of something is the same as 50%.

For $3/4$, which is $0.75$ in decimal form, if you multiply by 100 you get $0.75 \times 100 = 75%.

Summary

To sum it all up:

1. Equivalent Fractions: Different fractions that mean the same part of a whole.
2. Decimals: You can turn fractions into decimals using division, and they show the same value.
3. Percentages: Percentages come from changing decimals (from fractions) into a scale of 100, making them easier to understand in everyday life.

Understanding how these ideas connect helps you solve problems with fractions, decimals, and percentages. They all fit together, and once you see how they link, you'll feel much more confident in your math skills!