Q: The sum of two numbers is \$11\$ and the sum of their reciprocals is \$\dfrac{{11}}{{28}}\$ Find the numbers.

Given sum of two numbers is \$11\$\$x+y=11\$ _____ (1)sum of their reciprocals is \$\dfrac{11}{28}\$.\$\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{11}{48}\$\$\dfrac{y+x}{xy}=\dfrac{11}{48}\$\$28(x+y)= 11xy\$ _______ (2)\$28(11)= 11.xy\$\$xy=28\$Now\$(x-y)^{2}=x^{2}+y^{2}-2xy\\\$\$(x-y)^{2}=(x+y)^{2}-4xy\\\$\$(x-y)^{2}=(11)^{2}-4\times28\\\$\$(x-y)^{2}=121-112\\\$\$(x-y)^{2}=9\\\$\$x-y=\sqrt{9}\\\$\$x-y=3\$ _______ (3)On adding (1) & (3)\$x+y=1\$\$x-y=3\$_________\$2x=14\\\$\$x=\dfrac{14}{2}\\\$\$x=7\\\$putting \$x=7\$ in equation _____ (1)\$x+y=11\\\$\$7 +y=11\\\$\$y=11-7\\\$\$y=4\\\$\$\therefore \$ The two numbers are \$(x,y)=(7,4)\$

Q: Which of the following is an improper fraction?

Since numerator > denominator only in option \$A.\$ Therefore, it is correct.

Q: Jaidev takes \$2\dfrac { 1 }{ 5 } \$ minutes to walk across the school ground. Rahul takes \$\dfrac { 7 }{ 4 } \$ minutes to do the same. who takes less time and by what fraction?

Time taken by Jaidev to walk \$= 2 \dfrac{1}{5}\$ minutes \$=\dfrac{11}{5}\$ minutesTime taken by Rahul to walk across the ground \$=\dfrac{7}{4}\$ minutesNow, compare the fractions\$\dfrac{11}{5}\$\$=\dfrac{11\times4}{5\times4}\$\$=\dfrac{44}{20}\$\$\dfrac{7}{4}\$\$=\dfrac{7\times5}{4\times5}\$\$=\dfrac{35}{20}\$\$\dfrac{44}{20}>\dfrac{35}{20}\$\$⇒\dfrac{7}{4}<\dfrac{11}{5}\$So, Rahul takes lesser time than Jaidev.Difference \$=\dfrac{11}{5}−\dfrac{7}{4}\$\$=\dfrac{11\times4}{5\times4}−\dfrac{7\times5}{4\times5}\$\$=\dfrac{44}{20}−\dfrac{35}{20}\$\$=\dfrac{9}{20}\$So, Rahul takes lesser time than Jaidev, by \$\dfrac{9}{20}\$ minutes.

Q: Which of the following is/are proper fraction?

Proper fraction is a fraction that is less than one, with the numerator less than the denominator.In figure A,Shaded parts \$= 3\$Total parts \$= 8\$Fraction \$=\dfrac{3}{8}\$In figure B,Shaded parts \$= 1\$Total parts \$= 1\$Fraction \$=\dfrac{1}{1}\$In figure C,Shaded parts \$= 1\$Total parts \$= 4\$Fraction \$=\dfrac{1}{4}\$In figure D,Shaded parts \$= 3\$Total parts \$= 7\$Fraction \$=\dfrac{3}{7}\$\$\therefore\$ Figures A, C and D are examples of proper fraction.

Q: A fraction whose numerator is greater than its denominator is fraction.

That will be an improper fractionEx \$\dfrac{6}{5}\$

Q: Which of the following are proper fractions?\$1/2,3/5,10/7,7/4,2,15 /8,16/16,10/11,23/ 10\$

A fraction whose numerator is less than its denominator is called a proper fraction.Here, \$1 / 2, 3/5\$ and \$10 / 11\$ are proper fractions.

Q: State whether the following statements are true \$\left(T\right)\$ or false \$\left(F\right)\$: A fraction in which the numerator is greater than is denominator is called an improper fraction

TrueA fraction in which the numerator is greater than the denominator is called an improper fraction .

Q: Which of the following is not a proper fraction?

Fractions that are greater than \$0\$ but less than \$1\$ are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, then the fraction is an improper fraction. An improper fraction is always \$1\$ or greater than \$1\$.Now looking at options \$\dfrac{2}{3}=.666 1\$So \$\dfrac{6}{5}\$ is Not a Proper fraction.So option \$D\$ is correct.

Q: Convert \$ 2435\ m \$ to \$ km \$ and express the result as a mixed fraction.

We know that\$ 1\ km = 1000\ m \$\$\Rightarrow 1\ m = \dfrac {1}{1000}\ km \$\$\Rightarrow 2435\ m = \dfrac {1}{1000} \times 2435\ km \$\$\Rightarrow 2435\ m = \dfrac {2435}{1000}\ km = \dfrac{487}{200}\ km \$\$ \therefore 2435\ m=2 \dfrac {87}{200} \ km\$

Question 1

The sum of two numbers is $11$ and the sum of their reciprocals is $\dfrac{{11}}{{28}}$ Find the numbers.

Accepted Answer

Given sum of two numbers is $11$$x+y=11$ _____ (1)sum of their reciprocals is $\dfrac{11}{28}$.$\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{11}{48}$$\dfrac{y+x}{xy}=\dfrac{11}{48}$$28(x+y)= 11xy$ _______ (2)$28(11)= 11.xy$$xy=28$Now$(x-y)^{2}=x^{2}+y^{2}-2xy\$$(x-y)^{2}=(x+y)^{2}-4xy\$$(x-y)^{2}=(11)^{2}-4\times28\$$(x-y)^{2}=121-112\$$(x-y)^{2}=9\$$x-y=\sqrt{9}\$$x-y=3$ _______ (3)On adding (1) & (3)$x+y=1$$x-y=3$_________$2x=14\$$x=\dfrac{14}{2}\$$x=7\$putting $x=7$ in equation _____ (1)$x+y=11\$$7 +y=11\$$y=11-7\$$y=4\$$\therefore $ The two numbers are $(x,y)=(7,4)$

Question 2

Which of the following is an improper fraction?

Accepted Answer

Since numerator > denominator only in option $A.$ Therefore, it is correct.

Question 3

Jaidev takes $2\dfrac { 1 }{ 5 } $ minutes to walk across the school ground. Rahul takes $\dfrac { 7 }{ 4 } $ minutes to do the same. who takes less time and by what fraction?

Accepted Answer

Time taken by Jaidev to walk $= 2 \dfrac{1}{5}$ minutes $=\dfrac{11}{5}$ minutesTime taken by Rahul to walk across the ground $=\dfrac{7}{4}$ minutesNow, compare the fractions$\dfrac{11}{5}$$=\dfrac{11\times4}{5\times4}$$=\dfrac{44}{20}$$\dfrac{7}{4}$$=\dfrac{7\times5}{4\times5}$$=\dfrac{35}{20}$$\dfrac{44}{20}>\dfrac{35}{20}$$&#8658;\dfrac{7}{4}<\dfrac{11}{5}$So, Rahul takes lesser time than Jaidev.Difference $=\dfrac{11}{5}&#8722;\dfrac{7}{4}$$=\dfrac{11\times4}{5\times4}&#8722;\dfrac{7\times5}{4\times5}$$=\dfrac{44}{20}&#8722;\dfrac{35}{20}$$=\dfrac{9}{20}$So, Rahul takes lesser time than Jaidev, by $\dfrac{9}{20}$ minutes.

Question 4

Which of the following is/are proper fraction?

Accepted Answer

Proper fraction is a fraction that is less than one, with the numerator less than the denominator.In figure A,Shaded parts $= 3$Total parts $= 8$Fraction $=\dfrac{3}{8}$In figure B,Shaded parts $= 1$Total parts $= 1$Fraction $=\dfrac{1}{1}$In figure C,Shaded parts $= 1$Total parts $= 4$Fraction $=\dfrac{1}{4}$In figure D,Shaded parts $= 3$Total parts $= 7$Fraction $=\dfrac{3}{7}$$\therefore$ Figures A, C and D are examples of proper fraction.

Question 5

A fraction whose numerator is greater than its denominator is           fraction.

Accepted Answer

That will be an improper fractionEx $\dfrac{6}{5}$

Question 6

Which of the following are proper fractions?$1/2,3/5,10/7,7/4,2,15 /8,16/16,10/11,23/ 10$

Accepted Answer

A fraction whose numerator is less than its denominator is called a proper fraction.Here, $1 / 2, 3/5$  and $10 / 11$ are proper fractions.

Question 7

State whether the following statements are true $\left(T\right)$ or false $\left(F\right)$: A fraction in which the numerator is greater than is denominator is called an improper fraction

Accepted Answer

TrueA fraction in which the numerator is greater than the denominator is called an improper fraction .

Question 8

Which of the following is not a proper fraction?

Accepted Answer

Fractions that are greater than $0$ but less than $1$ are called proper fractions.In proper fractions, the numerator is less than the denominator.When a fraction has a numerator that is greater than or equal to the denominator, then the fraction is an improper fraction. An improper fraction is always $1$ or greater than $1$.Now looking at options $\dfrac{2}{3}=.666  < 1$$\dfrac{3}{4}= .75 < 1$$\dfrac{5}{7}= .71  <1$$\dfrac{6}{5}=1.2  > 1$So  $\dfrac{6}{5}$  is Not a Proper fraction.So option $D$ is correct.

Question 9

Express $32.12\bar{35}$ in the form of $\dfrac{p}{q}$ where $p$ and $q$ are integers.

Accepted Answer

Toppr Ask Answer

Question 10

Convert $ 2435\ m $ to $ km $ and express the result as a mixed fraction.

Accepted Answer

We know that$ 1\  km  = 1000\ m $$\Rightarrow 1\ m = \dfrac {1}{1000}\ km $$\Rightarrow  2435\ m = \dfrac  {1}{1000} \times 2435\ km $$\Rightarrow  2435\ m  = \dfrac {2435}{1000}\ km = \dfrac{487}{200}\ km $$ \therefore  2435\ m=2 \dfrac {87}{200} \ km$

Revise with Concepts

Types of Fractions and thier Conversions

Learn with Videos

Quick Summary With Stories

Proper, Improper and Mixed fractions

Adding and subtracting mixed fractions

Word Problems on Adding and Subtracting Mixed Fractions

The sum of two numbers is $11$ and the sum of their reciprocals is $\frac{1 1}{2 8}$ Find the numbers.

Which of the following is an improper fraction?

Jaidev takes $2 \frac{1}{5}$ minutes to walk across the school ground. Rahul takes $\frac{7}{4}$ minutes to do the same. who takes less time and by what fraction?

Which of the following is/are proper fraction?

A fraction whose numerator is greater than its denominator is fraction.

Which of the following are proper fractions?
$1 / 2, 3 / 5, 10 / 7, 7 / 4, 2, 15 / 8, 16 / 16, 10 / 11, 23 / 10$

State whether the following statements are true $(T)$ or false $(F)$ :
A fraction in which the numerator is greater than is denominator is called an improper fraction

Which of the following is not a proper fraction?

Express $32.12 \overset{ˉ}{35}$ in the form of $\frac{p}{q}$ where $p$ and $q$ are integers.

Convert $2435 m$ to $k m$ and express the result as a mixed fraction.

Revise with Concepts

Types of Fractions and thier Conversions

Learn with Videos

Quick Summary With Stories

Proper, Improper and Mixed fractions

Adding and subtracting mixed fractions

Word Problems on Adding and Subtracting Mixed Fractions

The sum of two numbers is 11 and the sum of their reciprocals is 2811​ Find the numbers.

Which of the following is an improper fraction?

Jaidev takes 251​ minutes to walk across the school ground. Rahul takes 47​ minutes to do the same. who takes less time and by what fraction?

Which of the following is/are proper fraction?

A fraction whose numerator is greater than its denominator is fraction.

Which of the following are proper fractions? 1/2,3/5,10/7,7/4,2,15/8,16/16,10/11,23/10

State whether the following statements are true (T) or false (F): A fraction in which the numerator is greater than is denominator is called an improper fraction

Which of the following is not a proper fraction?

Express 32.1235ˉ in the form of qp​ where p and q are integers.

Convert 2435 m to km and express the result as a mixed fraction.

The sum of two numbers is $11$ and the sum of their reciprocals is $\frac{1 1}{2 8}$ Find the numbers.

Jaidev takes $2 \frac{1}{5}$ minutes to walk across the school ground. Rahul takes $\frac{7}{4}$ minutes to do the same. who takes less time and by what fraction?

Which of the following are proper fractions?
$1 / 2, 3 / 5, 10 / 7, 7 / 4, 2, 15 / 8, 16 / 16, 10 / 11, 23 / 10$

State whether the following statements are true $(T)$ or false $(F)$ :
A fraction in which the numerator is greater than is denominator is called an improper fraction

Express $32.12 \overset{ˉ}{35}$ in the form of $\frac{p}{q}$ where $p$ and $q$ are integers.

Convert $2435 m$ to $k m$ and express the result as a mixed fraction.