Finding equivalent ratios can be easy for Year 10 students if they use some simple methods. Knowing these methods helps with calculations and builds a good understanding of ratios and proportions.
First, let's talk about what a ratio is.
A ratio compares two amounts. For example, it can show how many boys there are compared to girls in a class.
If there are 8 boys and 12 girls, we can write the ratio as 8:12.
One important way to find equivalent ratios is by simplifying them.
To simplify a ratio, you need to divide both parts by the biggest number that can divide them both evenly, called the greatest common divisor (GCD).
Example:
For the ratio 8:12, the GCD is 4.
So if we divide both numbers by 4, we get:
8 ÷ 4 = 2
12 ÷ 4 = 3
This means that 8:12 is the same as 2:3.
You can also find equivalent ratios by multiplying both parts of a ratio by the same number.
Example:
Start with the simplified ratio 2:3.
If we multiply both parts by 2, we get 4:6.
Another good way is to create a table of equivalent ratios.
For example, for the ratio 1:2, you can write down:
| Scale Factor | Ratio | |--------------|--------| | 1 | 1:2 | | 2 | 2:4 | | 3 | 3:6 | | 4 | 4:8 |
Finally, when you want to compare two ratios, you can use cross multiplication to see if they are equivalent.
For example, for ratios a:b and c:d, you can check if a × d = b × c.
By using these methods, Year 10 students can easily find and understand equivalent ratios. This makes learning about ratios much simpler!
Finding equivalent ratios can be easy for Year 10 students if they use some simple methods. Knowing these methods helps with calculations and builds a good understanding of ratios and proportions.
First, let's talk about what a ratio is.
A ratio compares two amounts. For example, it can show how many boys there are compared to girls in a class.
If there are 8 boys and 12 girls, we can write the ratio as 8:12.
One important way to find equivalent ratios is by simplifying them.
To simplify a ratio, you need to divide both parts by the biggest number that can divide them both evenly, called the greatest common divisor (GCD).
Example:
For the ratio 8:12, the GCD is 4.
So if we divide both numbers by 4, we get:
8 ÷ 4 = 2
12 ÷ 4 = 3
This means that 8:12 is the same as 2:3.
You can also find equivalent ratios by multiplying both parts of a ratio by the same number.
Example:
Start with the simplified ratio 2:3.
If we multiply both parts by 2, we get 4:6.
Another good way is to create a table of equivalent ratios.
For example, for the ratio 1:2, you can write down:
| Scale Factor | Ratio | |--------------|--------| | 1 | 1:2 | | 2 | 2:4 | | 3 | 3:6 | | 4 | 4:8 |
Finally, when you want to compare two ratios, you can use cross multiplication to see if they are equivalent.
For example, for ratios a:b and c:d, you can check if a × d = b × c.
By using these methods, Year 10 students can easily find and understand equivalent ratios. This makes learning about ratios much simpler!