Represent 5 2 on a number line.

We need to represent 5 2 on the number line. In a rational number, the numeral below the bar (denominator), tells the number of equal parts into which the first unit has been divided. The numeral above the bar (numerator) tells about the number of parts that has to be considered to denote the given point on the number line. Let us represent point O to represent 0 , point B to the right of O to represent 1 . Here the denominator is 2 , the line segment OB between 0 and 1 is divided into two equal parts. Now since the numerator is 5 so five parts are taken to get the point that represents the rational number 5 2 denoted by the point A . Therefore, the number line is shown below:

Represent 5 2 on a number line.

We need to represent 5 2 on the number line. In a rational number, the numeral below the bar (denominator), tells the number of equal parts into which the first unit has been divided. The numeral above the bar (numerator) tells about the number of parts that has to be considered to denote the given point on the number line. Let us represent point O to represent 0 , point B to the right of O to represent 1 . Here the denominator is 2 , the line segment OB between 0 and 1 is divided into two equal parts. Now since the numerator is 5 so five parts are taken to get the point that represents the rational number 5 2 denoted by the point A . Therefore, the number line is shown below:

Verify and name the following property: 4 7 + 2 3 + 3 5 = 4 7 + 2 3 + 3 5

We know the associative property for the addition of rational numbers say that if a , b and c are three rational numbers, then a + b + c = a + b + c is true. In the given mathematical statement 4 7 + 2 3 + 3 5 = 4 7 + 2 3 + 3 5 , the associative property for the addition of rational numbers is used. Now, we shall verify the property. We shall convert all the three given rational numbers into equivalent rational numbers with denominators equal to their LCM, which is 105 . Thus, we have, 4 7 = 4 × 15 7 × 15 = 60 105 2 3 = 2 × 35 3 × 35 = 70 105 3 5 = 3 × 21 5 × 21 = 63 105 LHS = 4 7 + 2 3 + 3 5 = 60 105 + 70 105 + 63 105 = 60 + 70 105 + 63 105 = 130 105 + 63 105 = 130 + 63 105 = 193 105 RHS = 4 7 + 2 3 + 3 5 = 60 105 + 70 105 + 63 105 = 60 105 + 70 + 63 105 = 60 105 + 133 105 = 60 + 133 105 = 193 105 So, LHS = RHS. Hence, proved.

Verify x = - ( - x ) for x = - 8 11 .

We are given to verify x = - ( - x ) for x = - 8 11 . LHS = x = - 8 11 . RHS = - - x = - - - 8 11 = - 1 × 8 11 = - 1 1 × 8 11 = - 1 × 8 1 × 11 [For multiplying two rational numbers, we multiply the numerator by the numerator and the denominator by the denominator] = - 8 11 So, we have, LHS = RHS. Hence, verified.

Find the smaller rational number out of - 4 7 and - 5 8 .

We are given to find the smaller rational number out of - 4 7 and - 5 8 . For this, we shall make the denominators of both the given rational numbers equal their LCM and compare their numerators. The rational number with the smaller numerator is smaller. The LCM of 7 and 8 is 56 . So, - 4 7 = - 4 × 8 7 × 8 = - 28 56 and - 5 8 = - 5 × 7 8 × 7 = - 35 56 . We have, - 35 < - 28 . So, - 35 56 < - 28 56 . Therefore, - 5 8 < - 4 7 .

Is it true to say that 7 6 is same as - 1 1 6 ?

7 6 is a positive rational number. But, - 1 1 6 = - 7 6 is a negative rational number. We know that a positive rational number is always greater than a negative rational number. So, 7 6 is greater than - 1 1 6 . Therefore, it is not true to say that 7 6 is same as - 1 1 6 .