Finding the percentage of a fraction is simple and only takes a few steps. This is an important skill for Year 7 students, especially as they learn more about how fractions, decimals, and percentages are related. Knowing how these numbers work together can help in both math class and real-life situations.

What is a Fraction?

First, let’s talk about what a fraction is.

A fraction shows a part of something whole. It has two numbers with a slash (/) between them.

• The top number is called the numerator. This tells you how many parts you have.
• The bottom number is called the denominator. This shows how many equal parts the whole is divided into.

For example, in the fraction ( \frac{3}{4} ):

• The numerator is 3 (meaning you have 3 parts)
• The denominator is 4 (meaning there are 4 equal parts in total)

What is a Percentage?

When we use percentages, we are actually talking about a special kind of fraction.

A percentage means part per hundred.

So, (20%) means 20 out of 100, which can be written as ( \frac{20}{100} ).

Knowing how to turn fractions into percentages is really helpful.

Converting a Fraction to a Percentage

Here's how to change a fraction into a percentage:

1. Change the Fraction to a Decimal:
   To do this, divide the numerator by the denominator. So for ( \frac{3}{4} ):
   ( 3 \div 4 = 0.75 )

2. Change the Decimal to a Percentage:
   To convert a decimal to a percentage, multiply it by 100. Using our previous result:
   ( 0.75 \times 100 = 75% )

So, ( \frac{3}{4} ) equals ( 75% ).

Converting a Percentage to a Fraction

Now, let’s look at how to turn a percentage back into a fraction:

1. Write the Percentage as a Fraction Over 100:
   For example, to convert (40%), write it as ( \frac{40}{100} ).

2. Simplify the Fraction if You Can:
   Here, both the top and bottom can be divided by 20:
   ( \frac{40 \div 20}{100 \div 20} = \frac{2}{5} )

Now, (40%) is ( \frac{2}{5} ).

Examples

Let’s see a couple more examples to help understand these changes:

• Convert ( \frac{1}{2} ) to a percentage:

  1. First, find the decimal:
     ( 1 \div 2 = 0.5 )
  2. Next, convert it to a percentage:
     ( 0.5 \times 100 = 50% )

• Convert ( 25% ) to a fraction:

  1. Write it as a fraction over 100:
     ( \frac{25}{100} )
  2. Then simplify:
     ( \frac{25 \div 25}{100 \div 25} = \frac{1}{4} )

Why Is This Important?

Knowing how to change between fractions and percentages is useful in everyday life. Here are some real-life applications:

• Shopping Discounts: If a shirt costs £40 and is 25% off, you can find the discount by changing (25%) to a fraction or decimal and then multiplying it by the original price.

• Grades: When figuring out your grades, you might have fractions showing points earned out of possible points. Changing this to a percentage makes it easier to understand how well you did.

• Finances: Interest rates on loans and savings are shown as percentages. Knowing how to change these into fractions helps when calculating money matters.

Key Points to Remember

• To convert a fraction to a percentage:

  1. Divide the top number (numerator) by the bottom number (denominator).
  2. Multiply that result by 100.

• To convert a percentage to a fraction:

  1. Write the percentage as a fraction with 100 on the bottom.
  2. Simplify if you can.

Conclusion

Finding the percentage of a fraction is easy with just a few steps. Knowing how to do these conversions is a valuable skill, especially for Year 7 students. By practicing this, students can feel more confident with numbers. Understanding these basic ideas not only helps in math but also in making smart choices in everyday life, like managing money and checking grades.