Maths:Number System Concepts:

1.

43/7

7 =>divisor

43 =>dividend

6 =>Quotient

1 =>Remainder

2.

Factors

42 = 7*2*3

Here 7,2 and 3 are factors of 42.

42 is a multiple of 6.

42 is a multiple of 7.

If a, b are integers(b is not 0)and a/b is an integer.

=> b is a factor of a.

=>a is divisible by b.

=>a is a mulitple of b.

E.g. Positive factors of 12 = 1,2,3,4,6,12.

E.g. Multiples of 12 = 12,24,36,0, -12,-36.......

3.

To find total number of factors.

180= 2^2 *3^2 *5

=>(2+1)*(2+1)*(1+1)=18

=>18*2= 36 ;to include negative factors

4.

Always consider intensive counting unless mentioned otherwise.

5.

Never forget to check negative numbers.

6.

Numbers with exactly three divisors:

Squares of prime numbers.

E.g. => 49,121

They have exactly three factors : 1,7,49 & 1,11,121.

7.

Numbers with exactly 4 divisors:

product of two prime numbers.

E.g.=>21

They have exactly four factors : 1,3,7,21.

8.

Zero is neither positive nor negative.

9.

All integers except zero are factors of zero and zero is multiple of every integer.

10.

Divisibility rules for:

Last digit must be divisible by 2.

Sum of digits must be divisible by 3.

Number formed by last two digits must be divisible by 4.

Last digit must be 0 or 5.

Number must be divisible by both 2 and 3.

11.

In the number 456.789

4 is the Hundred's digit

5 is the Ten's digit

6 is the Unit's digit

7 is the Tenth's digit

8 is the Hundredth's digit

3444.782 rounded to nearest tenth's will be 3444.8

3444.749 rounded to nearest tenth's will be 3444.7

12.

Comparison of fractions:

By Cross multiplication:

compare 6/11 OR 5/9

compare 6*9 OR 11*5

compare 54 OR 55

R.H.S is greater so, 5/9 > 6/11.

General rules for fraction comparison.

If numerator increases, and denomitor remains same, then ratio increases.

=> 6/21 > 3/21

If denominator increases, and numerator remains same, then ratio decreases.

=> 6/21 > 6/22

If a constant is multiplied to both numerator and denominator, then ratio remains same.

=> 2/5 = 6/30 = 12/60

1.

43/7

7 =>divisor

43 =>dividend

6 =>Quotient

1 =>Remainder

2.

Factors

42 = 7*2*3

Here 7,2 and 3 are factors of 42.

42 is a multiple of 6.

42 is a multiple of 7.

If a, b are integers(b is not 0)and a/b is an integer.

=> b is a factor of a.

=>a is divisible by b.

=>a is a mulitple of b.

E.g. Positive factors of 12 = 1,2,3,4,6,12.

E.g. Multiples of 12 = 12,24,36,0, -12,-36.......

3.

To find total number of factors.

180= 2^2 *3^2 *5

=>(2+1)*(2+1)*(1+1)=18

=>18*2= 36 ;to include negative factors

4.

Always consider intensive counting unless mentioned otherwise.

5.

Never forget to check negative numbers.

6.

Numbers with exactly three divisors:

Squares of prime numbers.

E.g. => 49,121

They have exactly three factors : 1,7,49 & 1,11,121.

7.

Numbers with exactly 4 divisors:

product of two prime numbers.

E.g.=>21

They have exactly four factors : 1,3,7,21.

8.

Zero is neither positive nor negative.

9.

All integers except zero are factors of zero and zero is multiple of every integer.

10.

Divisibility rules for:

Last digit must be divisible by 2.

Sum of digits must be divisible by 3.

Number formed by last two digits must be divisible by 4.

Last digit must be 0 or 5.

Number must be divisible by both 2 and 3.

11.

In the number 456.789

4 is the Hundred's digit

5 is the Ten's digit

6 is the Unit's digit

7 is the Tenth's digit

8 is the Hundredth's digit

3444.782 rounded to nearest tenth's will be 3444.8

3444.749 rounded to nearest tenth's will be 3444.7

12.

Comparison of fractions:

By Cross multiplication:

compare 6/11 OR 5/9

compare 6*9 OR 11*5

compare 54 OR 55

R.H.S is greater so, 5/9 > 6/11.

General rules for fraction comparison.

If numerator increases, and denomitor remains same, then ratio increases.

=> 6/21 > 3/21

If denominator increases, and numerator remains same, then ratio decreases.

=> 6/21 > 6/22

If a constant is multiplied to both numerator and denominator, then ratio remains same.

=> 2/5 = 6/30 = 12/60