Understanding ratios is super important in Year 9 math. Ratios help us work with fractions and percentages.

What is a Ratio?

A ratio compares two numbers. It tells us how much of one thing there is compared to another.

For instance, if a recipe needs 2 cups of flour and 3 cups of sugar, the ratio of flour to sugar is 2:3. This means for every 2 parts of flour, there are 3 parts of sugar.

Ratios, Fractions, and Percentages

Ratios as Fractions

You can write ratios as fractions too.

The ratio ( a:b ) can be shown as the fraction ( \frac{a}{b} ).

For our flour and sugar example:

• Ratio of flour to sugar: ( 2:3 )
• As a fraction: ( \frac{2}{3} )

So, if you have 5 total parts (2 parts of flour + 3 parts of sugar), 2 of those parts are flour.

Ratios and Percentages

Percentages show how much of something is out of 100.

To turn a ratio into a percentage, first change the ratio into a fraction, then multiply by 100.

Using our example:

1. Part of flour: 2
2. Part of sugar: 3
3. Total parts: ( 2 + 3 = 5 )
4. Fraction of flour: ( \frac{2}{5} )

To get the percentage of flour:

$$\left(\frac{2}{5}\right) \times 100 = 40\%$$

So, flour makes up 40% of the total mixture.

Now, to find out how much sugar is in the mixture:

1. Fraction of sugar: ( \frac{3}{5} )
2. Convert to percentage:

$$\left(\frac{3}{5}\right) \times 100 = 60\%$$

So, sugar makes up 60% of the mixture.

Real-Life Application

Knowing how ratios connect to fractions and percentages is super useful in real life.

Imagine sharing a pizza. If you have 2 pepperoni slices and 3 cheese slices, the ratio of pepperoni to cheese is 2:3.

Now, if we add up the slices (2 + 3), we get 5 total slices. To find out the percentage of pepperoni:

1. The fraction is ( \frac{2}{5} ).
2. Convert to percentage:

$$\left(\frac{2}{5}\right) \times 100 = 40\%$$

This means 40% of the pizza is pepperoni, and the other 60% is cheese.

Summary

In summary, understanding ratios is important for math and real life.

Remember:

• A ratio compares two amounts, like 2:3.
• A fraction comes from a ratio, such as ( \frac{2}{3} ).
• A percentage can be found from a fraction and shows how one part compares to the whole.

By mastering these ideas, Year 9 students can improve their math skills and better understand the world around them!