To do:We have to fill in the given blanks.Solution:(i) Zero has no reciprocal.Any number divided by zero is not defined. Therefore, zero has no reciprocal.(ii) The numbers $1$ and $-1$ are their own reciprocals.Reciprocal of $a$ is $\frac{1}{a}$.This implies, Reciprocal of $1$ is $\frac{1}{1}=1$.Reciprocal of $-1$ is $\frac{1}{-1}=-1$.(iii) The reciprocal ... Read More

Given :(i) \( \frac{7}{4} \) (ii) \( \frac{-5}{6} \).To do :We have to represent the given numbers on the number line.Solution :(i)1) Draw a number line.2) As the number $\frac{7}{4}$ is a positive number so it will be on the right of zero. $\frac{7}{4}$ can be written in mixed fraction as $1\frac{3}{4}$. ... Read More

To do :We have to represent \( \frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11} \) on the number line.Solution :1) Draw a number line.2) The numbers \( \frac{-2}{11}, \frac{-5}{11}, \frac{-9}{11} \) are negative numbers so they will be on the left of zero. The number lies between $0$ and $-1$.3) Divide the line segment between ... Read More

Given:Given rational number is $2$.To do:We have to find  five rational numbers which are smaller than 2.Solution:Numbers to the left of a given number on the number line are less than it and the numbers to the right of it are greater than it.Therefore, Five rational numbers smaller than $2$ ... Read More

To find: We need to find five rational numbers between.(i) \( \frac{2}{3} \) and \( \frac{4}{5} \)(ii) \( \frac{-3}{2} \) and \( \frac{5}{3} \)(iii) \( \frac{1}{4} \) and \( \frac{1}{2} \).Solution: To solve this question, first, we need to convert them into like fractions.(i) LCM of denominators (3 and 5) is 15. ... Read More

Given:The base of an isosceles triangle $=\frac{4}{3}\ cm$The perimeter of the triangle $=4 \frac{2}{15}\ cm = \frac{(4\times 15+2)}{15}\ cm = \frac{(60+2)}{15}\ cm = \frac{62}{15}\ cm$.To do:We have to find the length of either of the remaining equal sides.Solution :Let the length of the equal sides be $y\ cm$ each.We know that, ... Read More

Given:Two numbers are in the ratio of $5 : 3$.They differ by 18.To do:We have to find the numbers.Solution:Let the numbers be $5x$ and $3x$.Given that the difference of the numbers is $18$.Therefore, $5x - 3x = 18$$2x = 18$$x=\frac{18}{2}$$x = 9$$\Rightarrow 5x=5(9)=45$$3x=3(9)=27$Therefore, the numbers are $45$ and $27$. Read More

Given:Three consecutive integers add up to 51.To do:We have to find the integers.Solution:Let the smallest integer be $x$.This implies, The three consecutive integers are $x, x+1, x+2$.According to the question, $x + x + 1 + x + 2 = 51$$3x + 3 = 51$$3x = 51-3$$3x = 48$$x = ... Read More

Given: Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74.To do:We have to find the numbers.Solution:Let the three consecutive integers be $x, x+1$ and $x+2$According to the given question, $2\times x+ 3\times(x+1) + 4\times(x+2) ... Read More

Given:The number of boys and girls are in the ratio of $7:5$.The number of boys is 8 more than the number of girls.To do:We have to find the total strength of the class.Solution:Let the number of boys be $7x$ and the number of girls be $5x$.According to the question, $7x ... Read More