Which ratio forms a proportion with Start Fraction 20 over 30 End Fraction? Use equivalent ratios to test each ratio.
To form a proportion with the ratio Start Fraction 20 over 30, we can use equivalent ratios.
Let's test each ratio:
1. Start Fraction 20 over 30 equals Start Fraction 2 over 3 End Fraction
If we multiply both the numerator and denominator of Start Fraction 2 over 3 by 10, we get Start Fraction 20 over 30, which means this ratio forms a proportion with Start Fraction 20 over 30.
2. Start Fraction 20 over 30 equals Start Fraction 4 over 6 End Fraction
If we simplify Start Fraction 4 over 6, we get Start Fraction 2 over 3, which means this ratio forms a proportion with Start Fraction 20 over 30.
3. Start Fraction 20 over 30 equals Start Fraction 1 over 2 End Fraction
If we multiply both the numerator and the denominator of Start Fraction 1 over 2 by 20, we get Start Fraction 20 over 40, which is not equivalent to Start Fraction 20 over 30. Therefore, this ratio does not form a proportion with Start Fraction 20 over 30.
Thus, the ratios Start Fraction 2 over 3 End Fraction and Start Fraction 4 over 6 End Fraction both form a proportion with Start Fraction 20 over 30.
To find a ratio that forms a proportion with the fraction Start Fraction 20 over 30, we need to find a ratio that has an equivalent value.
Let's start by simplifying the given fraction Start Fraction 20 over 30:
Start Fraction 20 over 30 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 10. This gives us:
Start Fraction 20 over 30 simplifies to Start Fraction 2 over 3.
Now, to find a ratio that forms a proportion with Start Fraction 2 over 3, we can use equivalent ratios. This means we need to multiply or divide both parts of the ratio by the same number.
Let's test some ratios:
1. Ratio: 4:6
Equivalent fraction: Start Fraction 4 over 6 simplifies to Start Fraction 2 over 3.
Since this ratio is equivalent to Start Fraction 2 over 3, it forms a proportion with Start Fraction 20 over 30.
2. Ratio: 5:7
Equivalent fraction: Start Fraction 5 over 7
This ratio is not equivalent to Start Fraction 2 over 3, so it does not form a proportion with Start Fraction 20 over 30.
3. Ratio: 10:14
Equivalent fraction: Start Fraction 10 over 14 simplifies to Start Fraction 5 over 7.
This ratio is not equivalent to Start Fraction 2 over 3, so it does not form a proportion with Start Fraction 20 over 30.
Therefore, the ratio 4:6 forms a proportion with Start Fraction 20 over 30.