Control Racionales

1. Los racionales están compuestos por fracciones positivas y negativas y decimales finitos, periódicos y semiperiódicos.

True

False

Racionales are a set of numbers that include positive and negative fractions, as well as finite, periodic, and semi-periodic decimals. This statement is true because it accurately describes the composition of racionales.

Explanation

Racionales are a set of numbers that include positive and negative fractions, as well as finite, periodic, and semi-periodic decimals. This statement is true because it accurately describes the composition of racionales.

2. La raíz cuadrada de todo número impar es racional

True

False

The statement "La raíz cuadrada de todo número impar es racional" translates to "The square root of every odd number is rational." This statement is false. In fact, the square root of an odd number is irrational. The square root of any prime number is always irrational, and since all odd numbers have at least one prime factor, their square roots are also irrational. Therefore, the correct answer is false.

Explanation

The statement "La raíz cuadrada de todo número impar es racional" translates to "The square root of every odd number is rational." This statement is false. In fact, the square root of an odd number is irrational. The square root of any prime number is always irrational, and since all odd numbers have at least one prime factor, their square roots are also irrational. Therefore, the correct answer is false.

3. El decimal 5,242424242424... corresponde a:

Decimal finito

Decimal periódico

Decimal semiperiódico

Número entero

Número cardinal

The decimal 5,242424242424... corresponds to a decimal periódico because it has a repeating pattern of the digits "24". This indicates that the decimal representation of the number continues indefinitely with this repeating pattern.

Explanation

The decimal 5,242424242424... corresponds to a decimal periódico because it has a repeating pattern of the digits "24". This indicates that the decimal representation of the number continues indefinitely with this repeating pattern.

4. Todos los decimales son números racionales

True

False

The statement "Todos los decimales son números racionales" translates to "All decimals are rational numbers." This statement is false because not all decimals are rational numbers. Rational numbers are numbers that can be expressed as a fraction of two integers, while decimals can be either rational or irrational. Examples of irrational decimals include pi (3.14159...) and the square root of 2 (1.41421...). Therefore, the correct answer is false.

Explanation

The statement "Todos los decimales son números racionales" translates to "All decimals are rational numbers." This statement is false because not all decimals are rational numbers. Rational numbers are numbers that can be expressed as a fraction of two integers, while decimals can be either rational or irrational. Examples of irrational decimals include pi (3.14159...) and the square root of 2 (1.41421...). Therefore, the correct answer is false.

5. 1,3 expresado en fracción corresponde a:

1/3

13/9

13/10

12/10

12/9

The correct answer is 13/10 because when we express 1,3 as a fraction, we can write it as 13/10. This is because the decimal 1.3 can be written as the fraction 13/10, where the numerator is 13 and the denominator is 10.

Explanation

The correct answer is 13/10 because when we express 1,3 as a fraction, we can write it as 13/10. This is because the decimal 1.3 can be written as the fraction 13/10, where the numerator is 13 and the denominator is 10.

6. 0,25 se representa en fracción como:

2/5

25/10

25/99

5/2

1/4

The fraction 1/4 represents the decimal 0.25.

Explanation

The fraction 1/4 represents the decimal 0.25.

7. La fracción 5/8 en porcentaje corresponde a:

58%

16%

62.5%

0.625%

5.8%

The correct answer is 62.5%. To convert a fraction to a percentage, we divide the numerator (5) by the denominator (8) and multiply by 100. In this case, (5/8) * 100 = 62.5%.

Explanation

The correct answer is 62.5%. To convert a fraction to a percentage, we divide the numerator (5) by the denominator (8) and multiply by 100. In this case, (5/8) * 100 = 62.5%.

8. Mariela es la encargada de repartir en igual cantidad 750 caramelos idénticos entre 27 niños que asisten a un paseo escolar, sin que sobre ni falte ningún caramelo. ¿En cuál de las siguientes condiciones Mariela NO puede cumplir su objetivo?

Dos niños no asisten al paseo.

Tres niños más asisten al paseo.

Se quitan 21 caramelos de la cantidad total.

Se agregan 6 caramelos a la cantidad total.

Se quitan 27 caramelos a la cantidad total.

If Mariela wants to distribute 750 candies equally among 27 children, then the total number of candies should be divisible by 27. Since 750 is divisible by 27, she can distribute the candies without any leftovers. However, if 27 candies are removed from the total quantity, the remaining number of candies (750 - 27 = 723) will not be divisible by 27. Therefore, Mariela will not be able to achieve her goal if 27 candies are removed from the total quantity.

Explanation

If Mariela wants to distribute 750 candies equally among 27 children, then the total number of candies should be divisible by 27. Since 750 is divisible by 27, she can distribute the candies without any leftovers. However, if 27 candies are removed from the total quantity, the remaining number of candies (750 - 27 = 723) will not be divisible by 27. Therefore, Mariela will not be able to achieve her goal if 27 candies are removed from the total quantity.

9. Relaciona cada fracción con su representación decimal

1/2

3/4

9/8

8/9

9/5

16/90

Submit

10. 5,242424242424... representado como fracción es equivalente a:

5/100000

5/24

524/90

524/99

173/33

The given repeating decimal 5.2424242424... can be represented as a fraction by considering it as a geometric series. The repeating part is 24, which can be written as 24/99. Since there is a non-repeating part of 5 before the repeating part, the fraction can be written as 5 + 24/99. Simplifying this fraction gives us 173/33.

Explanation

The given repeating decimal 5.2424242424... can be represented as a fraction by considering it as a geometric series. The repeating part is 24, which can be written as 24/99. Since there is a non-repeating part of 5 before the repeating part, the fraction can be written as 5 + 24/99. Simplifying this fraction gives us 173/33.