Understanding Percentages, Fractions, and Decimals in Year 7 Math

In Year 7 math, it's important to understand how percentages, fractions, and decimals are connected.

These three ideas are just different ways to show parts of a whole. Knowing how they relate to each other can make math easier and more fun!

The Basics: What are Percentages, Fractions, and Decimals?

• Fractions show part of a whole using two numbers, like $a/b$. The top number ($a$) is called the numerator, and the bottom number ($b$) is the denominator. For example, the fraction $1/4$ means one part out of four total parts.

• Decimals are another way to show fractions, especially when the bottom number is 10, 100, and so on. For instance, $1/4$ can also be written as $0.25$. This means that one part out of four equals 0.25 of the whole.

• Percentages are a special kind of fraction where the whole is always 100. A percentage shows how much of something there is out of 100. So, $25\%$ means $25$ out of $100$. This can also be written as the fraction $25/100$ or the decimal $0.25$.

How to Change Between Them

From Percentage to Fraction

To change a percentage to a fraction, put the percentage over 100 and simplify. For example, to change $30\%$ to a fraction:

1. Write it as $\frac{30}{100}$.
2. Simplify it to $\frac{3}{10}$.

From Percentage to Decimal

To turn a percentage into a decimal, divide by 100. For $30\%$:

1. Divide $30$ by $100$, which equals $0.30$.

From Fraction to Percentage

To change a fraction to a percentage, multiply by 100. For instance, turning $3/4$ into a percentage:

1. Multiply $3/4$ by $100$, which gives $75$.
2. So, $3/4 = 75\%$.

From Decimal to Percentage

To convert a decimal to a percentage, multiply by 100. For example:

• For $0.45$, multiply by $100$ to get $45\%$.

Calculating Percentages

Calculating percentages can be useful in real life, like figuring out sales tax, discounts, and scores!

Finding a Percentage of a Number

To find a percentage of a number, change the percentage into a decimal and multiply. For example, to find $20\%$ of $50$:

1. Change $20\%$ to a decimal: $0.20$.
2. Now multiply: $0.20 \times 50 = 10$.

So, $20\%$ of $50$ is $10$.

Percentage Increase and Decrease

These calculations help in everyday life.

• Percentage Increase: To find out how much a price increases by $15\%$:

1. Assume the original price is $200$.
2. Calculate $15\%$ of $200$: $0.15 \times 200 = 30$.
3. Add that to the original price: $200 + 30 = 230$.

So the new price is $230$.

• Percentage Decrease: If something decreases by $20\%$:

1. Start with the original price of $200$.
2. Calculate $20\%$: $0.20 \times 200 = 40$.
3. Subtract that from the original price: $200 - 40 = 160$.

Now the new price is $160$.

Finding the Whole from a Percentage

Sometimes you know a percentage of a number and want to find the whole. If $25\%$ of a number is $50$, you can set up the equation:

$0.25 \times X = 50$

To solve for $X$, divide both sides by $0.25$:

$X = \frac{50}{0.25} = 200$

So the whole amount is $200$.

Conclusion

Percentages, fractions, and decimals are all connected. Understanding how they relate can help you with math in everyday situations, budgeting, and solving problems in Year 7 math. Mastering these ideas will give you a strong base for more advanced topics later on. Happy calculating!