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Recall the concept of unit rate and equivalent fractions.
See solution.
We want to find out how we can know if two ratios are equivalent. Let's explore two situations that can help us understand the two most common ways.
One dressing bottle has 6 milliliters of oil for every 3 milliliters of vinegar. Another bottle from the same brand has 18 milliliters of oil for every 9 milliliters of vinegar. We will write these ratios to check if they are the equivalent.
| First Dressing Bottle | Second Dressing Bottle |
|---|---|
| 6ml/3ml | 18ml/9ml |
First Dressing Bottle 6Ă· 3ml/3Ă· 3ml=2ml/1ml We can follow a similar process to find the unit rate of the second dressing bottle. Let's divide the numerator and denominator of this ratio by 9. Second Dressing Bottle 18Ă· 9ml/9Ă· 9ml=2ml/1ml Since the ratios have the same unit rate, they are equivalent.
In Spanish La Liga, the best player scored 7 penalties out of 13 attempts. In contrast, the top player in the English Premier League scored 21 out of 26 attempts. We will compare the ratios of these players.
| La Liga | English Premier League |
|---|---|
| 7/13 | 21/26 |
When we multiply the numerator of the first ratio by 3 and its numerator by 2, we obtain the second ratio. 7* 3/13* 2=21/26 However, we must multiply both the numerator and the denominator of a ratio by the same number to obtain an equivalent fraction. This means that in this case the ratios are not equivalent.
We can now state two ways of determining if two ratios are equivalent.
Note that there can be other ways to determine if two ratios are equivalent.
