How to Simplify Ratios: An Easy Guide for Year 7 Math

Simplifying ratios might sound tricky, but it can be simple if you follow these easy steps. Let's break it down so anyone can understand!

Step 1: Know What a Ratio Is

A ratio compares two or more amounts. For example, if you have 4 apples and 2 oranges, the ratio of apples to oranges is 4:2. This means there are 4 apples for every 2 oranges.

Step 2: Spot the Numbers

Look at the numbers in the ratio. In our example of 4:2, the numbers are 4 and 2.

Step 3: Find the Biggest Number That Fits

To simplify the ratio, we need to find the Greatest Common Factor (GCF) of the two numbers. The GCF is the largest number that can divide both numbers without leaving a remainder.

For 4 and 2, let’s list the factors:

• Factors of 4: 1, 2, 4
• Factors of 2: 1, 2

The biggest number in both lists is 2. So, the GCF is 2.

Step 4: Divide Both Numbers by the GCF

Now, divide both numbers in the ratio by the GCF.

For the ratio 4:2:

• ( 4 \div 2 = 2 )
• ( 2 \div 2 = 1 )

So, the simplified ratio is 2:1.

Step 5: Check Your Work

Make sure the simplified ratio still shows the same relationship as the original. Here, there are still twice as many apples as oranges, which is correct!

Extra Tips:

• You can also show ratios as fractions. The ratio 4:2 can be written as ( \frac{4}{2} ), which simplifies to ( \frac{2}{1} ). This means the same thing as 2:1.
• If you have bigger numbers, you can also use the prime factorization method to find the GCF.
• Practice with different ratios to get more comfortable with this process.

Conclusion:

By following these 5 steps—understanding the ratio, spotting the numbers, finding the GCF, dividing by the GCF, and checking your answer—you can easily simplify any ratio. With regular practice, you'll get better at working with ratios in all kinds of situations!