The ratio of apples to oranges in a fruit basket is 2 to 5. Determine if each of the ratios below are equivalent.
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The ratio is 2 to 5 or 2:5 or 2/5. All these describe the ratio in different forms of fractions. The ratio can consequently be expressed as fractions or as a decimal. 2:5 in decimals is 0.4.
Yes
To determine if the ratios are equivalent, we need to simplify each ratio and see if they result in the same simplified form.
The given ratio is 2 to 5.
Ratio 1: 4 to 10
To simplify this ratio, we can divide both terms by their greatest common factor, which is 2.
Ratio 1 Simplified: 2 to 5
Since the simplified form of Ratio 1 is the same as the given ratio, Ratio 1 is equivalent.
Ratio 2: 6 to 15
To simplify this ratio, we can divide both terms by their greatest common factor, which is 3.
Ratio 2 Simplified: 2 to 5
Since the simplified form of Ratio 2 is the same as the given ratio, Ratio 2 is equivalent.
Therefore, both Ratio 1 and Ratio 2 are equivalent to the given ratio of 2 to 5.
To determine if the ratios are equivalent, we compare the two ratios and simplify them if needed.
The given ratio of apples to oranges is 2 to 5, which can be written as 2:5.
Let's check the following ratios:
1) 3 to 7
To compare this ratio with the given ratio, we need to determine if there is an equal scaling factor that can be applied to both ratios to make them equivalent.
To do this, we check if the ratio of the first term (apples) in the given ratio (2) to the first term (apples) in the new ratio (3) is equal to the ratio of the second term (oranges) in the given ratio (5) to the second term (oranges) in the new ratio (7).
2/5 = 3/7
To make it easier to compare, we can cross multiply:
2 * 7 = 5 * 3
14 = 15
Since the result is not equal (14 is not equal to 15), the ratio 3:7 is not equivalent to the given ratio of 2:5.
2) 4 to 10
Again, we compare the ratio of the first term:
2/4 = 5/10
Cross multiplying:
2 * 10 = 4 * 5
20 = 20
Since the result is equal (20 is equal to 20), the ratio 4:10 is equivalent to the given ratio of 2:5.
Therefore, the ratios 3:7 is not equivalent, while the ratio 4:10 is equivalent to the original ratio of 2:5.