Tag: maths

Questions Related to maths

Convert the following into a fraction:

$0.2\times 0.02\times 0.002$

converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

  1. $\dfrac {1}{125}$

  2. $\dfrac {1}{1250}$

  3. $\dfrac {1}{125000}$

  4. None of these

Show answer
Correct Option: C
Explanation:

$\dfrac {2}{10}\times \dfrac {2}{100} \times \dfrac {2}{1000}$

$= \dfrac {8}{10\times 100\times 1000}$
$= \dfrac {4}{5\times 100\times 1000}$
$= \dfrac {1}{125000}$

So, option $C$ is correct.

$2.\overline{8768}$  expressed as a rational number is 

converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

  1. $\displaystyle 2\frac{878}{999}$

  2. $\displaystyle 2 _{10}^{9}$

  3. $\displaystyle 2\frac{292}{333}$

  4. $\displaystyle 2\frac{4394}{4995}$

Show answer
Correct Option: C
Explanation:

$\displaystyle 2.\overline{8768}=2+0.\overline{8768}$
= $\displaystyle 2+\frac{8768-8}{9990}=2+\frac{8760}{9990}$
= $\displaystyle 2+\frac{292}{333}=2\frac{292}{333}$

Express the following as a fraction and simplify:

$2.45$

converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

  1. $\cfrac {49}{20}$

  2. $\cfrac {20}{49}$

  3. $\cfrac {19}{20}$

  4. $\cfrac {20}{19}$

Show answer
Correct Option: A
Explanation:

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify:
$2.45 = 2\cfrac{45}{100} = 2\cfrac{9}{20}$    ...Mixed fraction

$=\cfrac{49}{20}$     ....Improper fraction

The decimal number $53.234$ is a rational number whose denominator is ............

converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

  1. $100000$

  2. $10000$

  3. $1000$

  4. $100$

Show answer
Correct Option: C
Explanation:

$53.234 = \dfrac {53234}{1000} = \dfrac {53234}{10^{3}}$
Denominator is $1000$.
Therefore, $C$ is the correct answer.

Express the infinite decimal .212121 as a common fraction.

converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

  1. $\frac{21}{100}$

  2. $\frac{23}{99}$

  3. $\frac{7}{100}$

  4. $\frac{7}{99}$

  5. $\frac{7}{33}$

Show answer
Correct Option: E
Explanation:

$Let\quad x=0.212121...\ 100x=21.212121....\ 100x-x=21\ 99x=21\ x=\frac { 21 }{ 99 } =\frac { 7 }{ 33 } $

So correct answer will be option E

The area of a rectangle of length (x + 2) units and breadth (x -8) units is

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $x^2-16$

  2. $x^2-6x-16$

  3. $x^2-10x+16$

  4. $x^2-10$

Show answer
Correct Option: B
Explanation:

$l\times b=(x+2)(x-8)$
$=x^2+[(2)+(-8)]x+(2)(-8)$
$=x^2-6x-16$

A closed box made of steel of uniform thickness has length breadth and height 12 dm, 10 sm and 8 dm respectively If the thickness of the steel sheet is 1 dm then the inner surface area is

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $ \displaystyle 456$ $\displaystyle dm^{2}$

  2. $ \displaystyle 376$ $\displaystyle dm^{2}$

  3. $ \displaystyle 264$ $\displaystyle dm^{2}$

  4. $ \displaystyle 696$ $\displaystyle dm^{2}$

Show answer
Correct Option: B
Explanation:

A closed box made by steel with uniform thickness length 12 dm ,breath  10 dm and 8 dm and thickness  of steel is 1 dm

Then inner length =12-2=10 dm ,breadth=10-2=8 dm and height=8-2=6 dm 
So surface area of box=$2(lw+wh+lh)=2(10\times 8)+(8\times 6)+(10\times 6)=2(80+48+60)=2\times 188=376 dm ^{2}$

The side of a square is 2 cm Semicircles are constructed on two sides of the square then the area of the whole figure is

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $ \displaystyle (4+\pi )cm^{2} $

  2. $ \displaystyle (4+4\pi )cm^{2} $

  3. $ \displaystyle 4\pi cm^{2} $

  4. $ \displaystyle 8\pi cm^{2} $

Show answer
Correct Option: A
Explanation:

The side of square is 2 cm 

Then area of square =$(2)^{2}=4 cm^{2}$
The Semicircle constructed on two side diameter 2 cm then radius =1 cm
Then area of one semicircle =$\frac{\pi r^{2}}{2}=\frac{\pi (1)^{2}}{2}=\frac{\pi }{2}$
Then  area of two semicircle=$2\times \frac{\pi }{2}=\pi $
So total area of whole figure=$(4+\pi )cm^{2}$

A square of side x is taken A rectangle is cut out from this square such that one side of the rectangle is half that of the square and the other is $\displaystyle \frac{1}{3}$ of the first side of the rectangle
What is the area of the remaining portion?

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $\displaystyle \left ( \frac{3}{4} \right )x^{2}$

  2. $\displaystyle \left ( \frac{7}{8} \right )x^{2}$

  3. $\displaystyle \left ( \frac{11}{12} \right )x^{2}$

  4. $\displaystyle \left ( \frac{15}{16} \right )x^{2}$

Show answer
Correct Option: C
Explanation:

Let the side of square is x 

Then area of square=$x^{2}$
Given one side of rectangle is half of square=$\frac{x}{2}$
And second side is $\frac{1}{3}$ of other side=$\frac{1}{3}\times \frac{x}{2}=\frac{x}{6}$
Then area of rectangle =$\frac{x}{2}\times \frac{x}{6}=\frac{(x)^{2}}{12}$
So remaining area of square =$x^{2}-\frac{(x)^{2}}{12}=\frac{11x^{2}}{12}$

Find the area of a triangle whose sides are 9 cm, 12 cm, and 15 cm.

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $34cm^2$

  2. $44cm^2$

  3. $54cm^2$

  4. $55cm^2$

Show answer
Correct Option: C
Explanation:
Given sides of the triangle
$a=9$cm
$b=12$cm
$c=15$cm
The given triangle is a right angle triangle
because $9^2+12^2=15^2$
$\therefore$Area $=\dfrac{1}{2}\times 9\times 12=54$ sq cm
Area $=54$ sq cm.