# 6th Class Mathematics Number System and its Operations Bodmas Rule

## Bodmas Rule

Category : 6th Class

### Bodmas Rule

When a single expression contains many mathematical operations then BODMAS rules are used for the simplification of the expression. The word BODMAS has been arranged according to the priority of the operations.

The letters of BODMAS express the following operations:

B  Stands for Bracket

O Stands for of

D  Stands for Division

M Stands for Multiplication

S   Stands for Subtraction

Brackets

There are three types of Brackets, small, middle or medium and big.

Small Bracket is denoted by ()

Middle Bracket is denoted by {}

Big Bracket is denoted by [ ]

Brackets are used according to the placement of operations. First we use small bracket then middle Bracket and Big bracket is used at last in an expression. i.e. $\left[ \left\{ \left( 4+5 \right)\times 6 \right\}+7 \right].$

Elimination of Brackets

The solution of the expression is obtained by eliminating the brackets. The first priority of eliminating the bracket is small bracket then middle bracket and finally big bracket.

The following steps are used to simplify the expression, $\left[ \left\{ (4+5)\times 6 \right\}+7 \right]:$

I st: Eliminate the small bracket by adding 4 and 5, in small bracket, $[\{(4+5)\times 6\}+7][\{9\times 6\}+7].$

$\text{I}{{\text{I}}^{\text{nd}}}$ : Eliminate the middle bracket by multiplying 9 and 6, in middle bracket, $[\{9\times 6\}+7]=[54+7].$

$\text{II}{{\text{I}}^{\text{rd}}}$: Add 54 and 7 to eliminate big bracket [54 + 7] = 61. The solution of the above given expression is 61.

Simplify: $[\{(34+17)-20\}+21]-20$?

(a) 31

(b) 32

(c) 36

(d) Both (a) and (c)

(e) None of these

Explanation

$[\{(34+17)-20\}+21]-20$ $=[\{51-20\}+21]-20=[31+21]-20=52-20=32.$

How many different three digit numbers can be obtained by using the digits 0,1,3 without repeating any digit in the number?

(a) 4

(b) 5

(c) 3

(d) 2

(e) None of these

Which one of the following is the smallest seven digit number having four different digits?

(a) 1230000

(b) 0000123

(c) 1000023

(d) 1000032

(e) None of these

Simplify:$~45+3\times 2$of $5-\text{(}16+4\text{)}-8\div 4.$

(a) 55

(b) 43

(c) 53

(d) Both (a) and (c)

(e) None of these

Explanation

$45+3\times 2$of $5-(6+4)-8\div 4$ $=~45+3\times 2$of$5-20-8\div 4$ [Bracket removed] $=~~45+3\times 2$of 5 ?20 ? 2 [Operation of division $8\div 4=2]$ =   45 + 30 - 20  - 2 [Operation of multiplication $3\times 2\times 5=30]$ =  75 - 20 - 2 [Operation of addition 45 + 30 = 75] =   75 - 22 = 53 [Operation of subtraction]

Find the value of 6 + 2 [3 + 5{28 ? 12 (12 ? 10)}].

(a) 56

(b) 52

(c) 53

(d) Both (a) and (c)

(e) None of these

Explanation

$6+2[3+5\{28-12(12-10)\}]$$=6+2[3+5\{28-12\times 2\}]$ $=~6+2[3+5\{28-24\}]=6+2[3+5\times 4]=6+2[3+20]$ $=6+2\times 23=6+46=52$

A man gets pass for 1 year for Rs 1500. If the man has been paid 11 payments then find the amount paid by him.

(a) Rs16500

(b) Rs 17000

(c) Rs 17500

(d) Both (a) and (c)

(e) None of these

Explanation

Man paid the amount for one year. Hence, the total money paid by him = 1500 x 11 = Rs 16,500

As per International number system, what comes after ten thousand?

(a) Lakh

(b) Ten Lakh

(c) Hundred Thousand

(d) Million

(e) None of these

Explanation

As per International number system hundred thousandcomes after ten thousand.

Alien gives Mike 123 millions and after a month, Mike returns him 67,735. How much more money Mike should return him to equal the amount?

(a) 122 millions + 932 thousands + 265

(b) 12 lakhs + 93 thousands + 265

(c) 12 crores + 29 lakhs + 32 thousands + 265

(d) Both (a) and (c)

(e) None of these

Explanation

123 millions - 67,735 = 122 millions + 932 thousands +265 = 12 crores + 29 lakhs + 32 thousands + 265.

Ten millions represent which one of the following Indian numbers?

(a) One lakh

(b) Ten lakhs

(c) 1 crore

(d) Both (a) and (b)

(e) None of these

Explanation

Ten millions = 1 crore

The base of Indian number system is:

(a) Ten

(b) Two

(c) Eight

(d) Both (a) and (c)

(e) None of these

Explanation

The base of Indian number system is 10.

How many rows are required to plant 507 rose plants if a man plants minimum possible number of plants which is other than 1 plant in each row?

(a) 170 rows

(b) 169 rows

(c) 180 rows

(d) Both (a) and (c)

(e) None of these

Explanation

$507=3\times 13\times 13.$ Hence, the required number of rows $=13\times 13=169.$

The product of a positive and a negative integer is?

(a) Negative

(b) Positive

(c) Cannot be defined

(d) All of these

(e) None of these

Explanation

Product of a positive and a negative integer is negative.

Fill in the blanks by choosing the number from the given options. 1254 + 200 =____+ 200

(a) 200

(b) 300

(c) 1254

(d) All of these

(e) None of these

Find the difference between largest and smallest 5 digit numbers.

(a) 89900

(b) 89999

(c) 89998

(d) All of these

(e) None of these

Explanation

The difference of largest and smallest 5 digit number is 89999.

If the subtraction of 6540 ? 232* = 4220 then find the value of * from the following options.

(a) 4

(b) 0

(c) 1

(d) None of these

(d) All of these

Explanation

$6540-232*=4220\Rightarrow 6540-4220=2320.$

Hence, the symbol * will be replaced by 0.

Which one of the following options represent the additive identity property of $x$ ?

(a)  $x-0$

(b) $x\times 0$ (c)$x+0$

(d) AII of these

(e) None of these

Explanation

$x+0=x$ represents the additive identity property.

The following numbers 0, 2, 7, 9,17, are to be represented on the number line. Which one of the following options satisfies the position of give numbers on the number line?

(a) These numbers should be on the left hand side from 0

(b) These numbers should be on the right hand side from 0

(c) These numbers cannot be represented on the number line

(d) All of these

(e) None of these

The following numbers 0,-2, 7, - 9, 17, represented on the number line. Which one of the following options is correct about the position of the give numbers on number line?

(a) ?  2, ? 9 will come on the left hand side from 0 and the position of numbers7 and 17 on right hand side from 0.

(b) These numbers will come on the right hand side from 0

(c) These numbers cannot be represented on the number line

(d) All of these

(e) None of these

Explanation

Negative numbers come left from 0 and positive numberscome right from 0.

The following options are the representation of the given numbers on number line, 4, 6, - 8, 7 ,7, - 9. Find the correct option.

(a)

(b)

(c)

(d) All of these

(e) None of these

Explanation

Option (a) correctly represent the given numbers on thenumber line.

Represent the addition of 5 and 6 on the number line and choose which one of the following options is representing their addition?

(a)

(b)

(c)

5 + 6 = 11

(d) All of these

(e) None of these

Explanation

The number line in the option (a) correctly represents the addition of 5 + 6 = 11.

Consider the following statements,

Statement 1: Whole numbers and fractional numbers both can be represented on the number line.

Statement 2: Only whole numbers can be represented on the number line.

Which one of the following options is correct about the above statements?

(a) Statement 1 is true and 2 is false

(b) Statement 1 is false and 2 is true

(c) Both statements are false

(d) Both statements are true

(e) None of these

Explanation

Fractions can also be represented on the number line.

Every natural number is a whole number but every whole number is not a natural number. If natural and whole numbers are represented by N and W respectively then which one of the following options is correct?

(a) {N}={W}

(b) {W}>{N}

(c) {W}<{N}

(d) All of these

(e) None of these

Explanation

The set of all whole numbers is always greater than the set of all natural numbers.

How many prime numbers are there between 100 and 125?

(a) 5

(b) 6

(c) 3

(d) All of these

(e) None of these

Explanation

The numbers which have only two factors, land number itself are called prime number. The prime numbers between 100 and 125are, 101, 103, 107, 109,113.

Counting numbers are called natural numbers. The smallest natural number is ____.

(a) 0

(b) 2

(c) 1

(d) All of these

(e) None of these

Explanation

Counting number 1 is the smallest natural number.

Choose the correct option of predecessor and successor of 100 from the following options:

(a) 98 and 102

(b) 99 and 101

(c) 97 and 103

(d) All of these

(d) None of these

Explanation

The predecessor of a number is just before the number and successor of a number is just after the number.

• Aryabhatta gave the base of Indian number system.
• Binary numbers are used in computers.
• Western world uses base ten or Indian number system.
• Zero was introduced by Brahmgupta.
• Roman numerals are also known as Chinese numerals.

• The numbers with decimal are called decimal numbers or decimal.
• The value of number does not change on adding zero to extreme right of the fractional or decimal part of the number.
• BODMAS rule express the priority of algebraic operations.
• The fractions those have 10, 100 etc. as a denominator can be changed into decimal by placing decimal point among the digits of numerator in this way that the number of digits of fractional part should be equal to the number of zeroes.
• The product of zero with a number is always zero.

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