7th Class Mathematics Integers Simplifying Arithmetic Expressions

       Simplifying Arithmetic Expressions

To simplify arithmetic expression follow BODMAS RULE  

The value of \[~24-52\left\{ 5-\overline{\left( 13-8 \right)} \right\}\div \left[ 8\text{ }\{5+\left( -7 \right)\times \left( -9 \right)\} \right]\] is ......

(a) 124                                                 

(b) \[-24\]

(c) \[-529\]                          

(d) \[-\left( -24 \right)\]

(e) None of these  

Answer: (d)

Explanation

We have: \[24-52\left\{ 5-\left( 13-8 \right) \right\}\div \left[ 8\text{ }\{5\text{ }+\left( -7 \right)\times \left( -9 \right)\} \right]\]

\[=24-52\left\{ 5-5 \right\}\div \left[ 8\{5+63\} \right]\]                

\[=24-52\times 0\div \left[ 8\text{ }x\text{ }68 \right]\]

\[=24-52\times 0\div 544\]

\[=24-52\times 0\]

\[=24\]

we can write 24 as \[-\left( -24 \right)\] also.  

Pamela tries to use bracket for a mathematical expression "twenty four multiplied by twelve more than the difference of twenty three and five". The correct representation is.

(a) \[24\times \left\{ \left( 23-5 \right)+12 \right\}\]                       

(b) \[24\times \left\{ \left( 23-5 \right) \right\}+12\]

(c) \[24\times \left( 23-5+12 \right)\]                     

(d) \[24\times 23-5+12\]                

(e) None of these  

Answer: (a)

Explanation

The correct representation is \[24\times \left\{ \left( 23-5 \right)+12 \right\}\]    

The value of \[29-2\left\{ 6-\left( 7-3 \right) \right\}+\left[ 3\times \{5+\left( -3 \right)\times \left( -2 \right)\} \right]\]is____.             

(a) 58                                                       

(b) -59

(c) 57                                                    

(d) 59             

(e) None of these  

Answer: (a)    

  If \[P=45-\left[ 5+\{60-\left( 39-8 \right)\} \right]\]and \[Q=-12+\left[ 25-2\{16-9\} \right]\] than then \[\left| P \right|+\left| Q \right|=?\]\[\left| P \right|+\left| Q \right|=?\]

(a) 10                                                    

(b) \[-10\]

(c) 20                                                    

(d) 12

(e) None of these  

Answer: (d)

Explanation

\[p=45-[5+\{60-(39-8)\}]=45-[5+\{60-31\}]\]

\[=45-\left( 5+29 \right]=45-34=11\]and \[Q=-12+\left[ 25-\{2\left( 16-9 \right)\} \right]\]                

\[=-12+\left[ 25-\{2\times 7\} \right]=-12+\left[ 25-14 \right]=-12+11=-1\]

Hence \[\left| P \right|+\left| Q \right|=\left| 11 \right|+\left| -1 \right|=11+1=12\]  

  There are two integers X and Y such that 5 and T are their additive inverse respectively then \[\left| X \right|+\left| Y \right|+\left| S \right|+\left| T \right|\] is equal to

(a)\[\left| X \right|\]                                                    

(b) \[\left| Y \right|+\left| S \right|\]

(c)\[2\left( \left| X \right|+|Y| \right)\]              

(d) \[\left| X \right|+\left| Y \right|\]

(e) None of these  

Answer: (c)

Explanation

Here, \[\left| S \right|=\left| X \right|\]and \[\left| T \right|=\left| Y \right|\]hence,

\[\left| X \right|+\left| Y \right|+\left| S \right|+\left| T \right|\]\[=\left| X \right|+\left| Y \right|+\left| X \right|+\left| Y \right|=2\left( \left| X \right|+|Y| \right)\]  

  If\[P=\left[ 29-\left( -2 \right)\{6-\left( 7-3 \right)\} \right]\]and \[Q=\left[ 3\times \{5+\left( -3 \right)\times \left( -2 \right)\} \right]\]then P - Q is equal to

(a) 10                                                    

(b) 1

(c) -1                                                     

(d) 2

(e) None of these

Answer: (b)      

• The set of integers are Z \[=\left\{ ....,-3,-2,-1,0,\text{ }1,2,\text{ }3,\text{ }......\text{ } \right\}\]
• "0" is neither negative nor positive integers.
• 0 is always greater than negative integers and less than positive integers
• Absolute value of an integer defined as follows
• The product of two negative or two positive integers is always positive.
• The product of one negative and one positive integer is always negative.]
• If a and b are integers so a < b then -a > - b.
  
• \[-x\]and x are additive integers of each other.
• The quotient of two negative or two positive integers is always positive.
• The quotietit of one negative and one positive integer is always negative.

• The number of spatial dimensions we live in is 3
• The smallest number of colors sufficient to color all planar maps is four.
• The only number of the form \[{{x}^{y}}={{y}^{x}}\]with x and y different integers is SIXTEEN
• The only number (other than 0) that is twice the sum of its digits is EIGHTEEN