Represent the following 4 7 , 1 1 7 , 3 4 7 and 5 1 7 on a number line.

Given, 4 1 7 , 1 1 7 , 3 4 7 and 5 1 7 Here, we have one proper fraction and three mixed fractions. We know that proper fractions have values less than 1 . So, 4 7 can be located between the whole numbers 0 and 1 . In the number line already there is 7 equal segments in between each number. Since, the denominator of 4 7 is 7 , mark a point after 4 th segment from 0 . A whole number and a fraction combine will give a mixed fraction. We know that, 1 1 7 > 1 . So, it can be plotted between 1 and 2 . Since the denominator is 7 , mark a point after 1 st segment from 1 to the right side. We know that, 3 4 7 > 3 . So, it can be plotted between 3 and 4 . Since the denominator is 7 , mark a point after 4 th segment from 3 to the right side. We know that, 5 1 7 > 5 . So, it can be plotted between 5 and 6 . Since the denominator is 7 , mark a point after 1 st segment from 5 to the right side. Hence, the required answer is given below

Determine if the rational number 2 5 is an integer.

Given rational number is 2 5 . We know that, an integer is a number which can be positive, negative or zero, but it can not be a decimal or fraction. A rational number p q q ≠ 0 can be an integer only if: Condition 1 : q = 1 and p is any integer, for example 0 1 , - 16 1 , or Condition 2 : both p and q are integers, and p is a multiple of q , for example 4 2 , - 6 3 . Here, the rational number 2 5 does not satisfy any of the above two conditions. Hence, the rational number 2 5 is not an integer.

Determine whether rational number 17 2 is an integer.

Given rational number is 17 2 An integer is a number which can be positive, negative or zero number, but it can not be a decimal or fraction. A rational number p q q ≠ 0 can be an integer only if, q = 1 and p is any whole number Clearly, we can see that the given rational number is in fraction form. Therefore, it is not an integer. Hence, 17 2 is not an integer.

Determine whether rational number 16 2 is an integer.

An integer is a whole number which can be positive or negative number including zero, but it can not be a decimal or fraction. Given rational number is 16 2 Dividing numerator by denominator, we get 16 2 = 8 Here, 8 is a positive whole number. Hence, 16 2 is an integer.