# 7th Class Mathematics Integers Simplifying Arithmetic Expressions

Simplifying Arithmetic Expressions

Category : 7th Class

### 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

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

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

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

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

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

• 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

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