How to Simplify Ratios in Year 7 Math

When students learn about ratios in Year 7 Mathematics, they can use an easy method to simplify them. Ratios show the relationship between two or more things. For example, how many of one thing there are compared to another. Making ratios simpler helps us understand them better.

Steps to Simplify Ratios

1. Know the Ratio: A ratio looks like $a:b$, where $a$ and $b$ are whole numbers. For example, if the ratio of cats to dogs is 4:2, that means there are 4 cats for every 2 dogs.

2. Find Common Factors: To simplify, first find the greatest common divisor (GCD) of the two numbers. The GCD is the biggest number that can divide both numbers without leaving a remainder. For the ratio 4:2, the GCD is 2.

3. Divide by the GCD: Next, divide both numbers in the ratio by the GCD to make it as simple as possible. So for our example, dividing both parts by 2 gives us:

   $\frac{4}{2} : \frac{2}{2} = 2:1$

   This means the simplified ratio of cats to dogs is 2:1.

Examples of Simplifying Ratios

• Example 1: Simplifying 10:15

  • The GCD of 10 and 15 is 5.
  • Dividing both parts by 5: $10 \div 5 : 15 \div 5 = 2:3$

• Example 2: Simplifying 8:12

  • The GCD of 8 and 12 is 4.
  • Dividing both parts by 4: $8 \div 4 : 12 \div 4 = 2:3$

• Example 3: Simplifying 9:27

  • The GCD of 9 and 27 is 9.
  • Dividing both parts by 9: $9 \div 9 : 27 \div 9 = 1:3$

Important Things to Remember

• More Than Two Parts: Sometimes, ratios can have three or more parts, like 10:20:30. To simplify, find the GCD for all parts. Here, the GCD is 10. Dividing gives:

  $10 \div 10 : 20 \div 10 : 30 \div 10 = 1:2:3$

• Using Fractions: Ratios can also look like fractions. Simplifying the fraction can help simplify the ratio. For example, the ratio 1:4 is the same as the fraction $\frac{1}{4}$.

Practice Makes Perfect

To get really good at simplifying ratios, students should practice with different ratios. Here are some practice problems:

• Ratio Practice Problems:
  • Simplify these ratios:
    • 16:24
    • 14:42
    • 5:15
    • 100:250

Practicing these problems is important. It helps with understanding ratios better and builds confidence. Knowing how to simplify ratios is helpful in math and everyday life—like cooking and budgeting—making this skill very useful!