WHAT ARE THE FRACTIONS EQUIVALENT TO 3/5? - MATHS - 2025

To identify which are the fractions equivalent to 3/5, it is necessary to know the definition of equivalent fractions. In mathematics, it is understood by two objects equivalent to those that represent the same thing, abstractly or not.

Therefore, saying that two (or more) fractions are equivalent means that both fractions represent the same number.

A simple example of equivalent numbers is the numbers 2 and 2/1, since they both represent the same number.

Which fractions are equivalent to 3/5?

Fractions equivalent to 3/5 are all those fractions of the form p / q, where «p» and «q» are integers with q ≠ 0, such that p ≠ 3 and q ≠ 5, but both «p» and « q »can be simplified and obtained at the end 3/5.

For example, the fraction 6/10 fulfills that 6 ≠ 3 and 10 ≠ 5. But also, by dividing both the numerator and the denominator by 2, you get 3/5.

Therefore, 6/10 is equivalent to 3/5.

How many fractions equivalent to 3/5 are there?

The number of fractions equivalent to 3/5 is infinite. To construct a fraction equivalent to 3/5, what must be done is the following:

- Choose any integer «m», different from zero.

- Multiply both the numerator and the denominator by «m».

The result of the above operation is 3 * m / 5 * m. This last fraction will always be equivalent to 3/5.

Exercises

Below is a list of exercises that will serve to illustrate the above explanation.

1- Will the fraction 12/20 be equivalent to 3/5?

To determine whether or not 12/20 is equivalent to 3/5, the fraction 12/20 is simplified. If both numerator and denominator are divided by 2, the fraction 6/10 is obtained.

An answer cannot be given yet, since the fraction 6/10 can be simplified a bit more. By dividing the numerator and denominator again by 2, you get 3/5.

In conclusion: 12/20 is equivalent to 3/5.

2- Are 3/5 and 6/15 equivalent?

In this example it can be seen that the denominator is not divisible by 2. Therefore, we proceed to simplify the fraction by 3, because both the numerator and the denominator are divisible by 3.

After simplifying by 3, we obtain that 6/15 = 2/5. Since 2/5 ≠ 3/5 then it follows that the given fractions are not equivalent.

3- Is 300/500 equivalent to 3/5?

In this example you can see that 300/500 = 3 * 100/5 * 100 = 3/5.

Therefore, 300/500 is equivalent to 3/5.

4- Are 18/30 and 3/5 equivalent?

The technique to be used in this exercise is to decompose each number into its prime factors.

Therefore, the numerator can be rewritten as 2 * 3 * 3 and the denominator can be rewritten as 2 * 3 * 5.

Therefore, 18/30 = (2 * 3 * 3) / (2 * 3 * 5) = 3/5. In conclusion, the given fractions are equivalent.

5- Will 3/5 and 40/24 be equivalent?

Applying the same procedure as the previous exercise, the numerator can be written as 2 * 2 * 2 * 5 and the denominator as 2 * 2 * 2 * 3.

Therefore, 40/24 = (2 * 2 * 2 * 5) / (2 * 2 * 2 * 3) = 5/3.

Now, paying attention you can see that 5/3 ≠ 3/5. Therefore, the given fractions are not equivalent.

6- Is the fraction -36 / -60 equivalent to 3/5?

When decomposing both the numerator and the denominator into prime factors, it is obtained that -36 / -60 = - (2 * 2 * 3 * 3) / - (2 * 2 * 3 * 5) = - 3 / -5.

Using the rule of signs, it follows that -3 / -5 = 3/5. Therefore, the given fractions are equivalent.

7- Are 3/5 and -3/5 equivalent?

Even though the fraction -3/5 is made up of the same natural numbers, the minus sign makes the two fractions different.

Therefore, the fractions -3/5 and 3/5 are not equivalent.

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