Given 5/3, we want to know which of 20/12,15/9, or 10/6 are equivalent fractions:
Each of these is equivalent to 5/3.
Fractions are equivalent if they have the same decimal expansion. In each case the decimal for the fraction is `1.bar(6) `
Also note that in each case we can multiply 5/3 by some form of 1 to get the other fraction:
`5/3 * 4/4=20/12 `
Since 1 is the multiplicative identity (multiplying by 1 does not change the value) each of these represent the same real number.
5/3 is equal to all three choices. If you reduce each fraction you will see that they all simplify to 5/3.
To answer this question, set 5/3 equal to each possible answer and cross multiply. If the result of the cross multiplication is a number equal to the same number then the two fractions are equal as well. This a a test of proportionality.
5/3 = 20/12?
Cross multiplying results in 5x12 = 3x20
thus 60 = 60 and this is true.
5/3 = 15/9?
5x9 = 3x15
45 = 45 and this is true
30 = 30 and this is true.
Therefore 5/3 = 20/12 and 15/9 and 10/6.
The other method is to divide all into decimals and compare the result.
5/3 = 1.6666..
20/12 = 1.6666...
15/9 = 1.6666...
10/6 = 1.6666...
Therefore they are all equal to each other.
You can see which fractions are equivalent to the other fractions by seeing if both the numerator and denominator of the fraction is a multiple of the original fraction's corresponding numerator and denominator. The catch is, when you find how many times the original numerator is divisible into the new numerator, it needs to be divisible the same with the corresponding denominators.
Here's an example:
Is `5/3` divisible to `10/6` ?
In this example, you can see that with the numerators, 5 goes into 10 TWO times. Next, we can check the denominators. 3 goes into 6 TWO times, as well. Since both the numerators and denominators go TWICE into the corresponding numerators and denominators, those fractions are EQUIVALENT.
Let's check an example of a fraction that DOES NOT work:
Is `5/3` divisible to `10/9` ?
In this example, you can clearly see that these two fractions are not divisible. Why? Because 5 goes into 10 TWO times, BUT with the denominators, 3 goes into 9 THREE times. Since the numerators and denominators do not go into the corresponding numerators and denominators the same amount of times, these fractions are not equivalent.
You can try these with your question and find out that all of the fractions are equivalent to the original.
Hope I helped!
The simple answer is that all of these are equivalent fractions.
it just depends on what number you multiplied the numerator and denominator by.