To identify what are the equivalent fractions to 3/5 it is necessary to know the definition of equivalent fractions. In mathematics we mean two objects equivalent to those that represent the same, abstractly or not.
Therefore, to say that two (or more) fractions are equivalent means that both fractions represent the same number.
A simple example of equivalent numbers are numbers 2 and 2/1, since both represent the same number.
Which 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 that both"p"and"p" q"can be simplified and get at the end 3/5.
For example, the 6/10 fraction complies with 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 exist?
The number of fractions equivalent to 3/5 is infinite. To build a fraction equivalent to 3/5 what should be done is the following:
- Choose a whole number"m"any, different from zero.
- Multiply both the numerator and the denominator by"m".
The result of the previous 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 previous explanation.
1- Will the fraction 12/20 be equivalent to 3/5?
To determine whether 12/20 is equivalent or not to 3/5, the 12/20 fraction is simplified. If both numerator and denominator are divided by 2, fraction 6/10 is obtained.
Still can not give an answer, since the fraction 6/10 can be simplified a little 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 equivalents?
In this example it can be seen that the denominator is not divisible by 2. Therefore, the fraction is simplified by 3, since both the numerator and the denominator are divisible by 3.
After simplifying between 3 we get that 6/15 = 2/5. As 2/5 ≠ 3/5 then it is concluded 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 they 18/30 and 3/5 equivalents?
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 fractions given are equivalent.
5- Will they be 3/5 and 40/24 equivalents?
Applying the same procedure of the previous exercise, you can write the numerator as 2 * 2 * 2 * 5 and 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 fractions given are not equivalent.
6- Is the fraction -36 / -60 equivalent to 3/5?
When decomposing both the numerator and the denominator in 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 fractions given are equivalent.
7- Are 3/5 and -3/5 equivalents?
Although the fraction -3/5 is made up of the same natural numbers, the minus sign makes both fractions different.
Therefore, fractions -3/5 and 3/5 are not equivalent.
References
- Almaguer, G. (2002). Mathematics 1. Editorial Limusa.
- Anderson, J. G. (1983). Technical Shop Mathematics (Illustrated ed.). Industrial Press Inc.
- Avendaño, J. (1884). Complete manual of elementary and higher elementary instruction: for use by aspirants to teachers and especially of students of the Normal Schools of the Province (2 ed., Vol. 1). Printing of D. Dionisio Hidalgo.
- Bussell, L. (2008). Pizza by parts: fractions! Gareth Stevens.
- Coates, G. and. (1833). The Argentine arithmetic: ò Complete treatise of practical arithmetic. For the use of schools. Impr. of the state.
- Cofré, A., & Tapia, L. (1995). How to Develop Mathematical Logical Reasoning University Editorial.
- From sea. (1962). Mathematics for the workshop. Reverte
- DeVore, R. (2004). Practical Problems in Mathematics for Heating and Cooling Technicians (Illustrated ed.). Cengage Learning
- Lira, M. L. (1994). Simon and Mathematics: Mathematics text for the second basic year: student's book. Andres Bello.
- Jariez, J. (1859). Full course of physical and mechanical mathematical sciences applied to the industrial arts (2 ed.). railroad printing.
- Palmer, C. I., & Bibb, S. F. (1979). Practical mathematics: arithmetic, algebra, geometry, trigonometry and slide rule (reprint ed.). Reverte