7 junio, 2024

Fraction equivalent to 3/5 (solution and explanation)

Some fractions equivalent to 3/5 are:

3/5
6/10
9/15
12/20
15/25
18/30
21/35
24/40
27/45
30/50
33/55
36/60
39/65
42/70
45/75
48/80
51/85
54/90
57/95
60/100

To identify what are equivalent fractions to 3/5 it is necessary to know the definition of equivalent fractions. In mathematics, two equivalent objects are understood to be 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 are the numbers 2 and 2/1, since they both represent the same number.

What fractions are equivalent to 3/5?

The 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 finally obtained 3/5.

For example, the fraction 6/10 satisfies 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 build a fraction equivalent to 3/5 what must be done is the following:

– Choose an integer «m» any, 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 if 12/20 is equivalent to 3/5 or not, we proceed to simplify the fraction 12/20. If you divide both the numerator and denominator by 2, you get the fraction 6/10.

An answer cannot be given yet, since the fraction 6/10 can be simplified a bit more. By again dividing the numerator and denominator 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, since both the numerator and the denominator are divisible by 3.

After simplifying by 3, it is obtained 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 that will 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 indeed equivalent.

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

Applying the same procedure as in 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?

Decomposing both the numerator and denominator into prime factors yields -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?

Although 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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