how do you know that the sum 2/21 plus 3/31 is rational
u can find weather its rational by determining the denominator and dividing it by the second : )
because the rationals form a group under addition.
Or, just do the addition, and note that the result is also a rational number.
3/31 is a rational
To determine whether the sum of two fractions is rational, we need to understand what it means for a number to be rational. A rational number is any number that can be written as a fraction, where the numerator and denominator are both integers.
In this case, we have the sum of two fractions: 2/21 + 3/31. To find out if it is rational, we will calculate the sum.
To add fractions, we need to have the same denominator. In this case, we can find the common denominator by multiplying the denominators together: 21 * 31 = 651.
Once we have a common denominator, we can rewrite the fractions with that denominator:
2/21 = (2 * 31) / (21 * 31) = 62/651
3/31 = (3 * 21) / (31 * 21) = 63/651
Now that both fractions have the same denominator, we can add the numerators:
(62 + 63) / 651 = 125 / 651
The resulting sum, 125/651, is also a fraction where the numerator and denominator are both integers. Therefore, we can conclude that the sum of 2/21 and 3/31 is a rational number.