- A comparison of two numbers by division is called a Ratio.
- A ratio can be expressed in three different ways: .
- A ratio is read as "a ratio of a to b".
- A ratio is a fraction that can be simplified.
- Two ratios are called equal ratios or equivalent ratios if are equal.
- and are equal ratios as (numerator and denominator are multiplied by the same number).
- A table of equivalent ratios is called a ratio table.
2 4 6 8 10 5 10 15 20 25
- All ratios in the ratio table are equivalent.
- Two ratios are said to be in proportion if their cross-product are equal.
- are in proportion if .
1. Find the ratio of 7 to 10.
The ratio of 7 to 10 is
2. Find the ratio of 16 oranges to 21 apples.
The ratio of 16 to 21 is
3. Complete the following ratio table:
|Number of Lemons||5||10||?|
|Glasses of Lemonade||10||?||30|
To keep the ratio table equal, the top and the bottom numbers should be multiplied by the same number.
|Number of Lemons||5||10 ()||15 ()|
|Glasses of Lemonade||10||20 ()||30 ()|
4. Do the following ratios form a proportion: ?
The cross-product should be the same for the ratios to form a proportion. Since , the ratios are not in proportion.
5. 6 pastries cost $5. What should 18 pastries cost?
Put the provided information as a proportion: .
Since 6 is multiplied by 3 to get 18, 5 must be multiplied by 3.
The answer is $15.
- The quantity that comes first in the ratio statement becomes the numerator in the ratio fraction.
- A proportion consists of 4 terms. It is a comparison of two ratios.
- If the numerator and denominator of a ratio are multiplied by the same number, the resulting ratio is equivalent to the first one.
- Their cross-product should be the same for the ratios to be in proportion.
- In the case of word problems, pay attention to which value goes as a numerator and which one goes as a denominator.
- Not all ratios are in proportion.