The rational number does not exist between 1/3 and and 1/2 is
A 17/48
B 23/48
C 3/8
D 1/8
The correct answer and explanation is:
To find a rational number between 13\frac{1}{3} and 12\frac{1}{2}, we first need to express both fractions with a common denominator.
- Convert the fractions to a common denominator:
The denominators of 13\frac{1}{3} and 12\frac{1}{2} are 3 and 2, respectively. The least common denominator (LCD) of 3 and 2 is 6.
- 13\frac{1}{3} can be rewritten as 26\frac{2}{6} by multiplying both the numerator and denominator by 2.
- 12\frac{1}{2} can be rewritten as 36\frac{3}{6} by multiplying both the numerator and denominator by 3.
So, the fractions are now 26\frac{2}{6} and 36\frac{3}{6}, and we are looking for a rational number between them.
- Find the rational number between them:
Now, we simply need to find a fraction between 26\frac{2}{6} and 36\frac{3}{6}. One possible choice is 512\frac{5}{12}, which lies between the two fractions.
- Check the options:
We now check the options given:
- 1748\frac{17}{48} is approximately 0.354, which is between 26\frac{2}{6} (approximately 0.333) and 36\frac{3}{6} (0.5), so it is a valid candidate.
- 2348\frac{23}{48} is approximately 0.479, which is also between the two.
- 38\frac{3}{8} is exactly 0.375, which fits as well.
- 18\frac{1}{8} is 0.125, which is too small to fit between 13\frac{1}{3} and 12\frac{1}{2}.
Among the choices, C. 38\frac{3}{8} is a valid rational number between 13\frac{1}{3} and 12\frac{1}{2}. Thus, the correct answer is C. 38\frac{3}{8}.
In conclusion, to find a rational number between two given fractions, it’s often helpful to first find a common denominator and then identify a fraction that falls between them. By comparing the values, we can quickly determine the correct answer.