Divisibility Rule of 2

If a number is even or a number whose last digit is an even number i.e.  2,4,6,8 including 0, it is always completely divisible by 2.

Example: 508 is an even number and is divisible by 2 but 509 is not an even number, hence it is not divisible by 2. Procedure to check whether 508 is divisible by 2 or not is as follows:

• Consider the number 508
• Just take the last digit 8 and divide it by 2
• If the last digit 8 is divisible by 2 then the number 508 is also divisible by 2.

Divisibility Rules for 3

Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

Consider a number, 308. To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3, then the original number is also divisible by 3. Here, since 11 is not divisible by 3, 308 is also not divisible by 3.

Similarly, 516 is divisible by 3 completely as the sum of its digits i.e. 5+1+6=12, is a multiple of 3.
Divisibility Rule of 4

If the last two digits of a number are divisible by 4, then that number is a multiple of 4 and is divisible by 4 completely.

Example: Take the number 2308. Consider the last two digits i.e.  08. As 08 is divisible by 4, the original number 2308 is also divisible by 4.

Divisibility Rule of 5

Numbers, which last with digits, 0 or 5 are always divisible by 5.
Example: 10, 10000, 10000005, 595, 396524850, etc.

1) 5437 × 1001

=5437 × (1000+1)

= 5437× 1000 + 5437× 1

=5437000 + 5437

=5442437

2)

824× 25

= 824 × (20+5)

= 824× 20 + 824 × 5

=16480+4120

=20600

Medicines are packed in boxes. One box weighs 4kg 500g.

We need to find many the number of boxes that can be loaded in a can that cannot carry beyond 800kg.

Solution:

The weight of one box = 4 kg 500 g = 4 × 1000 g + 500 g = 4500 g   { As we know that 1kg = 1000g}

Maximum load can be loaded in can = 800 kg = 800 × 1000 g = 800000 g

Hence total weight=Maximum load can be loaded in can =800000 g

Number of boxes = Total weight / Weight of each box

Number of boxes = 800000/4500 = 177

Number of boxes = 177
Therefore, 177 boxes can be loaded in a can that cannot carry beyond 800kg.

Developed countries want developing countries to liberalise their trade and investment because then the MNCs belonging to the developed countries can set up factories in less-expensive developing nations, and thereby increase profits, with lower manufacturing costs and the same sale price.

In my opinion, the developing countries should demand, in return, for some manner of protection of domestic producers against competition from imports. Also, charges should be levied on MNCs looking to set base in developing nations.

84-2n-2n²

= 2(42-n-n²) /* Taking 2 common */

= 2( 42 - 7n + 6n - n²) /* splitting the middle term */

= 2[7(6-n)+n(6-n)]

= 2(6-n)(7+n)

Therefore,.

2, (6-n) and (7+n) are factors of given quadratic expression.

1) 12,904 +2,888 

Rounding off 12,904 to the nearest thousands we get, 13,000

And rounding off 2,888 to the nearest thousands we get, 3000

Therefore, 13,000 + 3,000 = 16, 000

Therefore, estimate of 12, 904 + 2,888 is equal to 16,000 according to the general rule.

2)28,292 – 21,496

Rounding off 28,292 to the nearest thousands we get, 28,000

And rounding off 21,496 to the nearest thousands we get, 21,000

Therefore, 28,000 - 21,000 = 7,000

Therefore, estimate of 28,292 - 21,496  is equal to 7,000 according to the general rule.

3)9250 × 29

Rounding off 9250 to the nearest thousands, we get 9000

And, rounding off 29 to the nearest tens, we get 30

Therefore, 9000 x 30 = 2,70,000

It means that estimate of 9250 × 29 is equal to 2,70,000 using general rule.

The child decide to write letters to his friends.

x²+8x+16

=x²+2(4)(x)+4²
=(x+4)²                  ...[∵(a−b)²=a²−2ab+b²]
=(x−4)(x−4)

Number of votes secured by successful candidate = 5,77, 500 votes
Number of secured by his nearest rival = 3,48,700
Margin between them = (5, 77,500 – 3, 48,700) = 2, 28,800

Therefore, the successful candidate won by a margin of 2, 28, 800 votes.

Σ This symbol (called Sigma) means "sum up"

Express 17/7 as mixed fraction

. 17/7 = 2 3/7

Express 73/4 as improper fraction.

73/4 = 18 1/4

The elimination method is used to solve linear equations in two variables, where one of the variables is removed or eliminated. This method is sometimes more comfortable and convenient than the substitution method. Here are the notes provided with the complete steps to solve such linear equations where two variables are used.

In another classification, there are three different algebraic methods to solve simultaneous linear equations. These methods are namely:

1. Substitution method
2. Elimination method
3. Cross-multiplication method

There are many situations which can be mathematically described by two equations that are not in the linear form. But we alter them so that they are reduced to a pair of linear equations. In this article, you will learn how to solve linear equations using the elimination method.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equation gets transformed into one linear equation with only one variable, which can then easily be solved. Before moving to solve the linear equations using the substitution method, get an idea on what the algebraic method and graphical method is.

We know that 1 day is equal to 24 hours

1 hour = 1/24 day

So 8 hours = (1/24) × 8

8 hours = 8/24 day

8 hours = 1/3 day

Hence 1/3 of a day is 8 hours.

(1) – 3 lies to the right on the number line (- 3 > – 8)

2. ) 6 lies to the right on the number line (6 > -6)

3. 

 a)In this figure two lines contain point E, one of them is AE.
b) in this figure 1 line is passing through A i.e AE..
c) In this figure, two pairs of intersecting lines are CO, AE & AE ,EF.

 (1) Factors of 27 = 3 x 3 x 3
Factors of 60 = 2 x 2 x 3 x 5 Factors of 63 = 3 x 3 x 7
H.C.F. (18, 60) = 2 x 3 = 6 H.C.F. (27, 63) = 3 x 3 = 9

 (2 Factors of 91 = 7 x 13
Factors of 105 = 3 x 5 x 7 Factors of 112 = 2 x 2 x 2 x 2 x 7
Factors of 175 = 5 x 5 x 7 Factors of 49 = 7 x 7
H.C.F. = 5 x 7 = 35 H.C.F. = 1 x 7 = 7

Yes,economics in a very basic sense is optimization given the constraints. Scarcity is the biggest and real constraint of our lives.Lets understand with an example,suppose everybody has a lot of money,a lot to buy anything.What would the world look like?Nobody's going to work,no production,no costs,no profits,no exchange rates,no trade,simply there would be no need of any of the economic agents,economic concepts.So,no economics would exist.

Factors of 65: 1, 5, 13, 65

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

9

 predecessor: 8

successor: 10

549

 predecessor: 548

successor: 550

1399

 predecessor : 1398

successor : 1400

(a) Four multiplied by the sum of nine and two.

Answer:  4 (9+2)

b) Divide the difference of eighteen and six by four.

The difference of 18 and 6 is written as 18-6 and it is then divided by four. Hence, the answer will be 

Answer:  

(c) Forty five divided by three times the sum of three and two.

The numerator is explicitly given as 45 while the denominator had some expressions

Denominator = three times the sum of three and two = 3 (sum of three and two) = 3 (3+2).

Hence, the answer will be 

Answer: 

73 - LXXIII

92 - XCII

450 = CDL

655 = DCLV

 8027 = 8000 + 20 + 7

55704   = 50000 + 5000 + 700 + 4

1971, 25751, 847, 7861

Ascending order : 847, 1971, 7861, 25751

Descending order :  25751 , 7861, 1971, 847