Tag: order operations and algebra

Questions Related to order operations and algebra

$24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$ using BODMAS rule to reduce the expression.

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $x^2+23x+46$

  2. $-x^2+23x+46$

  3. $-x^2-23x+46$

  4. $-x^2+23x-46$

Show answer
Correct Option: B
Explanation:

$24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $24[x+1]-[x^2-24+x]-[2x^2]\div [x^2]$
$=$ $24x+24-x^2+24-x-2$
$=$ $-x^2+46+23x$
$=$ $-x^2+23x+46$

Solve the expression using BODMAS rule: $3x(x-2)+x(x^2\times 2x)-12x$

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $2x^5-3x^2-18x$

  2. $2x^5+3x^2-18x$

  3. $2x^5+3x^2+18x$

  4. $-2x^5-3x^2-18x$

Show answer
Correct Option: B
Explanation:

$3x(x-2)+x(x^2\times 2x)-12x$
We need to follow BODMAS rule.
=> Brackets (parts of a calculation inside brackets always come first).
=> Orders (numbers involving powers or square roots).
=> Division.
=> Multiplication.
=> Addition.
=> Subtraction.
$=$ $3x(x-2)+x(x^2\times 2x)-12x$
$=$ $3x^2-6x+x^3\times2x^2-12x$
$=$ $3x^2-6x+2x^5-12x$
$=$ $2x^5+3x^2-18x$

If $1\le a\le 2$, then $\sqrt { a-2\sqrt { a-1 }  } -\sqrt { a+2\sqrt { a-1 }  } =$.......

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $2$

  2. $2\sqrt{a-1}$

  3. $-2$

  4. $1$

Show answer
Correct Option: C
Explanation:

$\sqrt{a - 2 \sqrt{a - 1}} - \sqrt{a + 2 \sqrt{a - 1}}$

$\Rightarrow \sqrt{(\sqrt{a - 1})^2 - 2 (1) \sqrt{a - 1} + 1^2} - \sqrt{(\sqrt{(a - 1)})^2 + 2 \sqrt{a - 1} + 1^2}$
$\Rightarrow \sqrt{(\sqrt{a - 1} - 1)^2} - \sqrt{(\sqrt{a - 1} + 1)^2}$
$\Rightarrow (\sqrt{a - 1} - 1) - ( \sqrt{a - 1} + 1)$
$= -2$

A number x is decreased by m% and some other number y is increased by m%. If both the results are equal, find m in terms of x and y. Also, find m if $\displaystyle 2x=3y$.


maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=10$

  2. $\displaystyle m=\frac{100\left ( x-y \right )}{x-y};m=20$

  3. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=30$

  4. $\displaystyle m=\frac{100\left ( x-y \right )}{x+y};m=20$

Show answer
Correct Option: D
Explanation:

Given $ \frac {100 - m}{100} \times x = \frac {100 + m}{100} \times y $
$ => 100x - mx = 100y + my $
$ => 100x - 100y = mx + my $
$ => 100 (x-y) = m (x + y) $
$ => m = \frac {100(x-y)}{x+y} $

When , $ 2x = 3y => x = \frac {3y}{2} $
We have, $ m = \frac {100(\frac {3y}{2} -y)}{\frac {3y}{2} +y} $
$ => m =\frac {100(\frac {y}{2})}{\frac {5y}{2}} $
$ => m =\frac {100}{5} = 20 $

 Make b the subject of formula : $\displaystyle a=\frac{1+b^2}{1-b^2}$. 

maths brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $\displaystyle b=\sqrt{\frac{a+1}{a-1}}$

  2. $\displaystyle b=\sqrt{\frac{a-1}{a+1}}$

  3. $\displaystyle b=2\sqrt{\frac{a-1}{a+1}}$

  4. $\displaystyle b=2\sqrt{\frac{a+1}{a-1}}$

Show answer
Correct Option: B
Explanation:

Given, $ a = \frac {1 +{b}^{2}}{1 - {b}^{2}} $
$ => a -a{b}^{2} = 1 +{b}^{2} $
$ => a- 1 = {b}^{2} (1 + a) $
$ =>{b}^{2} = \frac {a-1}{1+a} $


$ x + y -(z - x -[y + z - (x + y - \left { z + x - (y + z + x) \right})])$ is equal to

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. 3x

  2. 2y

  3. x

  4. 0

Show answer
Correct Option: C
Explanation:

On simplifying, we get
$x + y -(z - x -[y + z - (x + y - \left { z + x - (y + z + x) \right})])\$ 
$=  x + y -(z - x -[y + z - (x + y - \left { z + x - y - z - x \right})])\$ 
$=  x + y -(z - x -[y + z - (x + y - \left { - y \right})])\$ 
$=  x + y -(z - x -[y + z - (x + y + y)])\$ 
$= x + y -(z - x -[y + z - x - y - y)])\$ 
$= x + y -(z - x -[ z - x - y])\$ 
$= x + y -(z - x - z + x + y)\$ 
$= x + y -(y)\$ 
$= x.$

$\frac{1}{3}(-2p+6q-9r)-\frac{1}{6}(-4p -18q +24r) = $

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $-\frac{4}{3}p$

  2. 5q

  3. -7r

  4. 5q-7r

Show answer
Correct Option: D
Explanation:

$\frac{1}{3}(-2p+6q-9r)-\frac{1}{6}(-4p -18q +24r) = \frac{1}{3}(-2p+6q-9r)-\frac{1}{3}(-2p -9q +12r) $
$=\frac{1}{3} [\left (-2p+6q-9r)-(-2p -9q +12r) \right]$
$=\frac{1}{3} (-2p + 6q - 9r + 2p + 9q -12r)$
$=\frac{1}{3} (15q - 21r)$
$=(5q - 7r)$

$ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left ( y + a -\frac{1}{4}(a+y) \right )\right ]$

maths use of brackets order operations and algebra using brackets in algebraic expressions order of operations

  1. $(a+y)^{2}$

  2. $\frac{3a}{16}$

  3. $\frac{9}{16}(a+y)^{2}$

  4. 1

Show answer
Correct Option: C
Explanation:

$ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left ( y + a -\frac{1}{4}(a+y) \right )\right ]$
= $ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{3} \left (\frac{3}{4}(a+y) \right) \right ]$
= $ \frac{3}{4}(a+y) \left [ y + a - \frac{1}{4}(a+y)\right ]$
= $ \frac{3}{4}(a+y) \left [ \frac{3}{4}(a+y)\right ]$
= $ \frac{9}{16}(a+y)^2$

$-84\times 29+365=$?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. $2436$

  2. $2801$

  3. $-2801$

  4. $-2071$

  5. None of these

Show answer
Correct Option: D
Explanation:

Given Exp. $=-84\times (30-1)+365$
$=-(84\times 30)+84+365$
$=-2520+449$
$=-2071$

In a class, there are 18 boys who are over 160 em tall. If these constitute three-fourths of the boys and the total number of boys is two-third of the total number of students in the class, what is the number of girls in the class?

maths place value, ordering and rounding order operations and algebra using brackets in algebraic expressions order of operations

  1. 6

  2. 12

  3. 18

  4. 24

Show answer
Correct Option: B
Explanation:

Total number of boys $\displaystyle=18\div\frac{3}{4}=24$

Total number of students $\displaystyle=24\times\frac{3}{2}=36$

$\therefore$ Number of girls $=36-24=12$