Calcula la fracción generatriz de los siguientes decimales:
[tex]$1,05 ; 1,5 ; 0,15$[/tex]
Answer (2)
Convert 1.05 to a fraction: 100 105 = 20 21 .
Convert 1.5 to a fraction: 10 15 = 2 3 .
Convert 0.15 to a fraction: 100 15 = 20 3 .
The generating fractions are: 20 21 , 2 3 , 20 3 .
Explanation
Understanding the Problem We are asked to find the generating fractions (fracciones generatrices) for the decimals 1.05, 1.5, and 0.15. This means we need to convert each decimal into a simplified fraction.
Converting 1.05 to a Fraction For the decimal 1.05, we can write it as a fraction with a denominator of 100: 100 105 To simplify this fraction, we find the greatest common divisor (GCD) of 105 and 100. The GCD is 5. Dividing both the numerator and the denominator by 5, we get: 100 ÷ 5 105 ÷ 5 = 20 21
Converting 1.5 to a Fraction For the decimal 1.5, we can write it as a fraction with a denominator of 10: 10 15 To simplify this fraction, we find the greatest common divisor (GCD) of 15 and 10. The GCD is 5. Dividing both the numerator and the denominator by 5, we get: 10 ÷ 5 15 ÷ 5 = 2 3
Converting 0.15 to a Fraction For the decimal 0.15, we can write it as a fraction with a denominator of 100: 100 15 To simplify this fraction, we find the greatest common divisor (GCD) of 15 and 100. The GCD is 5. Dividing both the numerator and the denominator by 5, we get: 100 ÷ 5 15 ÷ 5 = 20 3
Final Answer Therefore, the generating fractions for the decimals 1.05, 1.5, and 0.15 are 20 21 , 2 3 , and 20 3 respectively.
Examples
Understanding how to convert decimals to fractions is useful in many real-life situations. For example, if you are calculating discounts at a store and a product is 15% off, converting 0.15 to the fraction 20 3 can help you quickly determine the amount of the discount. Similarly, if you need to divide a recipe in half and the recipe calls for 1.5 cups of flour, knowing that 1.5 is 2 3 can make the calculation easier. These conversions are also essential in fields like finance and engineering, where precise calculations are necessary.
Las fracciones generatrices de los decimales 1.05, 1.5 y 0.15 son respectivamente 20 21 , 2 3 , 20 3 . Se calcularon simplificando fracciones relacionadas con un denominador de 100 o 10. Es importante entender cómo convertir y simplificar decimales en fracciones para diversos usos matemáticos.
;
