Ratio
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Ratio |
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Ratio:
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Generally, in math, to describe a ratio, we separate two numbers in a ratio with a colon (:) or write the numbers in fraction form.
A ratio is used to show a relationship between two numbers. Earlier, we introduced a fraction to show a relation between two numbers. Previously, the fraction was introduced to relate a part to a whole ... ex. 3 of 8 parts; 3/8. However, fractions may be used to relate other pairs of numbers ... ex. ratio of 350 miles in 4 hours or the ratio of 3 inches to 5 feet. Normally, we refer to something in the format 17:20 as a ratio, but, it may be used interchangeable with 17/20 (normally thought of as a fraction).
Frequently, we will write a ratio in the form 4:8 as a fraction (4/8), reduce the fraction and return it to its original formation:
4:8 => 4/8 => 1/2 => 1:2 (showing 4:8 equals 1:2)
One difference between a fraction and a ratio is the way we deal with ratios that convert to an improper fraction (ex. 7:2 => 7/2). While we can be display a ratio as a fraction, if we display a ratio as an improper fraction (7/2), we will not convert it to a mixed number though we will try to reduce the fraction. Therefore:
15:1 => 15/1 => 15:1
15:3 => 15/3 => 5/1 => 5:1
16:6 => 16/6 => 8/3 => 8:3
Suppose we want to communicate the ratio of 7 and 12, we would write the ratio as 7:12 or 7/12. Regardless of the way it is written, we read the ratio as 7 to 12.
Ratios are used for many things and there are many phrases that imply communication of a ratio between people. The following are examples of phrases used to imply the communication of a ratio.
| Ratios | ||
| Comments | keywords | Mathematical Notation |
| ratio of 3 and 8 | 3:8 | 3:8 or 3/8 |
| ratio of 3 and 8 | 3/8 | 3:8 or 3/8 |
| 5 to 8 | 5 to 8 | 5:8 or 5/9 |
| 11 of 15 | 11 of 15 | 11:15 or 11/15 |
| 7 in 16 tries | 7 in 16 | 7:16 or 7/16 |
| a 3 by 5 flag | 3 by 5 | 3:5 or 3/5 |
| 4 out of 52 cards | 4 out of 52 | 4:52 or 4/52 |
| 11 miles per 60 minutes | 11 per 30 | 11:60 or 11/60 |
Check Your Understanding
Given the ratio below, identify the mathematical way of writing the ratio ....
1. 7 out of 10
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2. 16 to 30
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3. 11 in 20
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Check Your Understanding
