What Are The Fractions Equivalent To 3/5?

To identify which fractions are equivalent to 3/5, you need 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 that 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 get 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.

References

  1. Almaguer, G. (2002). Mathematics 1. Editorial Limusa.
  2. Anderson, JG (1983). Technical Shop Mathematics (Illustrated ed.). Industrial Press Inc.
  3. Avendaño, J. (1884). Complete manual of elementary and higher primary instruction: for the use of aspiring teachers and especially of the students of the Normal Schools of the Province (2 ed., Vol. 1). Printing of D. Dionisio Hidalgo.
  4. Bussell, L. (2008). Pizza in parts: fractions! Gareth Stevens.
  5. Coates, G. and. (1833). The Argentine arithmetic: ò Complete treatise on practical arithmetic. For the use of schools. Print of the state.
  6. Cofré, A., & Tapia, L. (1995). How to Develop Mathematical Logical Reasoning. University Publishing House.
  7. From sea. (1962). Mathematics for the workshop. Reverte.
  8. DeVore, R. (2004). Practical Problems in Mathematics for Heating and Cooling Technicians (Illustrated ed.). Cengage Learning.
  9. Lira, ML (1994). Simon and mathematics: text of mathematics for the second basic year: student’s book. Andres Bello.
  10. Jariez, J. (1859). Complete course of physical mathematical sciences I mechanics applied to the industrial arts (2 ed.). railway printing press.
  11. Palmer, CI, & Bibb, SF (1979). Practical math: arithmetic, algebra, geometry, trigonometry, and slide rule (reprint ed.). Reverte.

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