Q: Find two consecutive odd natural numbers, the sum of whose squares is \$202\$.

We have, Let the two odd consecutive numbers \$x\,\text{and}\,x+2\$ So, According to given question, \$ {{x}^{2}}+{{\left( x+2 \right)}^{2}}=202 \$ \$ \Rightarrow {{x}^{2}}+{{x}^{2}}+4+4x=202 \$ \$ \Rightarrow 2{{x}^{2}}+4x=198 \$ \$ \Rightarrow {{x}^{2}}+2x=99 \$ \$ \Rightarrow {{x}^{2}}+2x-99=0 \$ \$ \Rightarrow {{x}^{2}}+\left( 11-9 \right)x-99=0 \$ \$ \Rightarrow {{x}^{2}}+11x-9x-99=0 \$ \$ \Rightarrow x\left( x+11 \right)-9\left( x+11 \right)=0 \$ \$ \Rightarrow \left( x+11 \right)x-9=0 \$ If, \$ x+11=0 \$ \$ \Rightarrow x=-11 \$ If, \$ x-9=0 \$ \$ x=9 \$ So, \$x+2=9+2=11\$ Hence, this is the answer.

Q: Find the reduced form of the ratio of the first quantity to second quantity.\$5\ litre,\ 2500\ ml\$

\$\frac{5litre}{2500ml}=\frac{5\times 1000ml}{2500ml}=\frac{50}{25}=2\$

Q: Is there any natural number that has no predecessor?

\$\textbf{Step 1: Checking for the smallest natural number.}\$ \$\text{The range of natural numbers is from 1 to infinity}\$ \$\therefore\$ \$ \text{The smallest natural number is 1.}\$\$\textbf{Step 2: Checking for the predecessor of 1}\$ \$\text{The predecessor of 1 i.e. } 1 - 1 = 0\$ \$\text{But 0 is a whole number and not a natural number}\$ \$\therefore \text{1 is a Natural number that has no predecessor.}\$\$\textbf{Yes, there is a natural number that has no predecessor, which is 1.}\$

Q: How many whole numbers are there between \$1032\$ and \$1209\$?

Number of whole numbers between two whole numbers \$a\$ and \$b\$ is given by \$b-a-1\$.To find the whole numbers between \$1032\$ and \$1209\$\$=(1209 - 1032) - 1 \\= 177 - 1\$\$ = 176\$Hence \$176\$ whole numbers lie between \$1032\$ and \$1209\$

Q: Given, \$A=\left\{ x:-1<x\le -5,x\in R \right\} \$ and \$B=\left\{ x:-4<x\le 3,x\in R \right\} \$Represent on different number lines:(i) \$A\cap B\$(ii) \$A'\cap B\$(iii) \$A-B\$

\$A=\{x:-1<x\leq 5,x\in R\}\$\$B=\{x:-4<x\leq 3,x\in R\}\$\$(i)\$ \$A\cap B\$=the numbers which are both in A and B\$\implies A\cap B=\{x:-1<x\leq 3,x\in R\}\$\$(ii)\$ \$A'\cap B\$=the numbers which are not in A but are in B\$\implies A'\cap B=\{x:-4<x\leq -1,x\in R\}\$\$(iii)\$ \$A-B=\$ the numbers which is in A but not in B\$\implies A-B\{x:3<x\leq 5,x\in R\}\$

Q: Represent the following numbers on the number line:\$2, 0, 3, 5, 7, 11, 15\$.

\$2, 0, 3, 5, 7, 11, 15\$ are shown on number line, with circles.

Q: How many whole numbers are there between \$32\$ and \$53\$?

Whole numbers between \$32\$ and \$53\$ is \$20\$ \$(53-32-1=20)\$\$(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)\$

Q: Add \$8+(-5)\$ on number line.

REF.Image\$\therefore 8+(-5)=3\$

Question 1

Find two consecutive odd natural numbers, the sum of whose squares is $202$.

Accepted Answer

We have,&#10;&#10;Let the two odd consecutive numbers $x\,\text{and}\,x+2$&#10;&#10;So,&#10;&#10;According to given question,&#10;&#10;$ {{x}^{2}}+{{\left( x+2 \right)}^{2}}=202 $&#10;&#10;$ \Rightarrow {{x}^{2}}+{{x}^{2}}+4+4x=202 $&#10;&#10;$ \Rightarrow 2{{x}^{2}}+4x=198 $&#10;&#10;$ \Rightarrow {{x}^{2}}+2x=99 $&#10;&#10;$ \Rightarrow {{x}^{2}}+2x-99=0 $&#10;&#10;$ \Rightarrow {{x}^{2}}+\left( 11-9 \right)x-99=0 $&#10;&#10;$ \Rightarrow {{x}^{2}}+11x-9x-99=0 $&#10;&#10;$ \Rightarrow x\left( x+11 \right)-9\left( x+11 \right)=0 $&#10;&#10;$ \Rightarrow \left( x+11 \right)x-9=0 $&#10;&#10;If,&#10;&#10;$ x+11=0 $&#10;&#10;$ \Rightarrow x=-11 $&#10;&#10;If,&#10;&#10;$ x-9=0 $&#10;&#10;$ x=9 $&#10;&#10;So,&#10;&#10;$x+2=9+2=11$&#10;&#10;Hence, this is the answer.

Question 2

Find the reduced form of the ratio of the first quantity to second quantity.$5\ litre,\ 2500\ ml$

Accepted Answer

$\frac{5litre}{2500ml}=\frac{5\times 1000ml}{2500ml}=\frac{50}{25}=2$

Question 3

Is there any natural number which has no successor?

Accepted Answer

Every natural number has successor.There are infinite natural numbers & hence there is no last natural number.Hence, every natural number has successor.

Question 4

Is there any natural number that has no predecessor?

Accepted Answer

$\textbf{Step 1: Checking for the smallest natural number.}$                $\text{The range of natural numbers is from 1 to infinity}$                $\therefore$ $ \text{The smallest natural number is 1.}$$\textbf{Step 2: Checking for the predecessor of 1}$                $\text{The predecessor of 1 i.e. } 1 - 1 = 0$                $\text{But 0 is a whole number and not a natural number}$                $\therefore \text{1 is a Natural number that has no predecessor.}$$\textbf{Yes, there is a natural number that has no predecessor, which is 1.}$

Question 5

Find the coordinates of the points $A,B,C,D$ from the following graph.

Accepted Answer

A = (2,4)B = (2,-5)C = (-2,1)D = (-3,-5)

Question 6

How many whole numbers are there between $1032$ and $1209$?

Accepted Answer

Number of whole numbers between two whole numbers $a$ and $b$ is given by $b-a-1$.To find the whole numbers between $1032$ and $1209$$=(1209 - 1032) - 1 \= 177 - 1$$ = 176$Hence $176$ whole numbers lie between $1032$ and $1209$

Question 7

Given, $A=\left\{ x:-1<x\le -5,x\in R \right\} $ and $B=\left\{ x:-4<x\le 3,x\in R \right\} $Represent on different number lines:(i) $A\cap B$(ii) $A'\cap B$(iii) $A-B$

Accepted Answer

$A=\{x:-1<x\leq 5,x\in R\}$$B=\{x:-4<x\leq 3,x\in R\}$$(i)$  $A\cap B$=the numbers which are both in A and B$\implies A\cap B=\{x:-1<x\leq 3,x\in R\}$$(ii)$  $A'\cap B$=the numbers which are not in A but are in B$\implies A'\cap B=\{x:-4<x\leq -1,x\in R\}$$(iii)$   $A-B=$ the numbers which is in A but not in B$\implies A-B\{x:3<x\leq 5,x\in R\}$

Question 8

Represent the following numbers on the number line:$2, 0, 3, 5, 7, 11, 15$.

Accepted Answer

$2, 0, 3, 5, 7, 11, 15$ are shown on number line, with circles.

Question 9

How many whole numbers are there between $32$ and $53$?

Accepted Answer

Whole numbers between $32$ and $53$ is $20$ $(53-32-1=20)$$(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)$

Question 10

Add $8+(-5)$ on number line.

Accepted Answer

REF.Image$\therefore 8+(-5)=3$

Addition and Subtraction of Natural and Whole Numbers

Language

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REVISE WITH CONCEPTS

Whole Number Operations on the Number Line

Estimation of whole number operations.

QUICK SUMMARY WITH STORIES

Draw a Number Line for the Whole Numbers

Addition of Whole Numbers on the Number line

Subtraction of Whole Numbers on the Number line

Multiplication of Whole Numbers on the Number line