Tag: order of operations

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Questions Related to order of operations

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

If ${a}^{2}+{b}^{2}+{c}^{2}-ab-bc-ca=0$, then

  1. $a+b=c$
  2. $b+c=a$
  3. $c+a=b$
  4. $a=b=c$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given,

$a^2+b^2+c^2-ab-bc-ca=0$

$\Rightarrow 2(a^2+b^2+c^2-ab-bc-ca)=2(0)$

$\Rightarrow 2a^2+2b^2+2c^2-2ab-2bc-2ca=0$

$\Rightarrow (a^2-2ab+b^2)+(b^2-2bc+c^2)+(c^2-2ca+a^2)=0$

$(a-b)^2+(b-c)^2+(c-a)^2=0$

$\Rightarrow a-b=b-c=c-a=0$

$\therefore a=b=c$
Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

If $\displaystyle b=6-\left [ \frac{4b+3}{2a-5} \right ]$, express a in terms of b.

  1. $\displaystyle a=\frac{33-b}{2\left ( 6-b \right )}$
  2. $\displaystyle a=\frac{b-33}{2\left ( 6-b \right )}$
  3. $\displaystyle a=\frac{33-b}{2\left ( b-6 \right )}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,
$ b = 6 - \left[ \frac { 4b+3 }{ 2a-5 }  \right]  $
$ => \left[ \frac { 4b+3 }{ 2a-5 }  \right] = 6 - b $
$ => 4b + 3 = (6-b)(2a-5) $
$ => 4b + 3 = 12a - 30 - 2ab +5b $
$ => 12a - 33  -2ab + b = 0 $
$ =>  a(12 -2b) = 33 - b $
$ => 2a(6-b) = 33-b $
$ => a = \frac {33-b}{2(6-b)} $

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

Given $\displaystyle b=\frac{2a}{a-2}$ and $\displaystyle c=\frac{3b-4}{4b+3}$, express c in terms of a.

  1. $\displaystyle c=\frac{2a+8}{11a+6}$
  2. $\displaystyle c=\frac{2a-8}{11a-6}$
  3. $\displaystyle c=\frac{2a+8}{11a-6}$

  4. none of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $ c = \frac {3b-4}{4b + 3} $

But, $ b = \frac {2a}{a-2} $
Hence, $ c = \frac {3(\frac {2a}{a-2} )-4}{4(\frac {2a}{a-2} ) + 3} $
$ => c = \frac {6a-4a + 8}{8a +3a - 6} $
$ => c = \frac {2a+8}{11a -6} $

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

The value of $100 - { ( 7 $of $8 + 4 ) \div 5 } $ is

  1. $92$
  2. $78$
  3. $96$
  4. $88$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We apply BODMAS rule to find the value of the given expression. According to BODMAS rule, if an expression contains brackets we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.


Since 'of' stands for multiplication, therefore the given expression becomes 
$100-[(7\times 8+4)\div 5]$ and apply BODMAS rule as shown below:
$ \Rightarrow 100-[(56+4)\div 5]\ \Rightarrow 100-(60\div 5)\ \Rightarrow 100-12\ \Rightarrow 88$
Hence, the value of $100-[(7\times 8+4)\div 5]$ is $88$.

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

Find the value of $\displaystyle \frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times\frac{3}{\frac{5}{6}of\frac{3}{2}\div 1\frac{1}{4}}$.

  1. 4

  2. 3

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given exp.$\displaystyle \frac{2}{1+\frac{1}{\frac{1}{2}}}\times\frac{3}{\frac{15}{12}\div \frac{5}{4}}=\frac{2}{1+2}\times\frac{3}{\frac{15}{12}\times\frac{4}{5}}=\frac{2}{3}\times\frac{3}{1}=2$

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

If $a$ and $ b $ are any two real numbers with opposite signs, which of the following is the greatest?

  1. $\displaystyle (a-b)^{2}$
  2. $\displaystyle (|a|-|b|)^{2}$
  3. $\displaystyle |a^{2}-b^{2}|$
  4. $\displaystyle a^{2}+b^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$(a-b)^2=a^2+b^2-2ab$

as a and b are of oppsite sign ab<0 and -2ab>0,it means $(a-b)^2>a^2+b^2-2|a||b|=(|a|-|b|)^2>(|a2+b^2|)>(|a^2-b^2|)$

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

What is the value of $((x^3-2)\div2^2)\times 4+16$?

  1. $x^3+14$
  2. $x^3-14$
  3. $-x^3+14$
  4. $x^3+16$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$((x^3-2)\div2^2)\times 4+16$
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.
$=$ $((x^3-2)\div2^2)\times 4+16$
$=$ $\dfrac{x^3-2}{4}\times 4+16$
$=$ $x^3+14$

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

Simplify: $3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$

  1. $x^3-3x^2+x+1$
  2. $x^3-3x^2+5x-1$
  3. $x^3+x^2-5x+1$
  4. $x^3+3x^2+5x-1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$
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.
$3x[x^2+1]-[2x(x^2+x-1)+1]-x^2$
$=$ $3x.x^2+3x.1-[2x.x^2+2x.x-2x.1+1]-x^2$
$=$ $3x^3+3x-2x^3-2x^2+2x-1-x^2$
$=$ $x^3-3x^2+5x-1$