Complete the following statements by filling in the blanks.

(1) 21 ÷ 7 … ∵ 21 = 7 × 3

(2) 45 ÷ 15 = …. ∵ 45 …… × ……

(3) We continue to carry out division until we get remainder zero or a whole number less than the ………….

(4) Dividend = division × (….) + (….), 0 ≤ remainder < divisor

(5) When we divide 43 by 5, the quotient is ………… and the remainder is ……….

Here, dividend = ………., divisor = ………

∴ 43 = 5 × …… + ……

(6) 2y × ……… = 10y²

(7) 5x × ……… = 15x⁴

(8) m² × ……… = 9m⁴

(9) 3m × ………… = 9m⁴⁺

(1) Here,

21/7

We know that 7 when multiplied by 3, we get 21 as the result.

So when 21 is divided by 7 we get 3 as the quotient.

So the answer is

21÷7 = 3 Q 21 = 7 × 3

(2) Here,

45/15

We know that 15 when multiplied by 3, we get 45 as the result.

So when 45 is divided by 15 we get 3 as the quotient.

So the answer is

45÷15 = 3 Q 45 = 15 × 3

(3) We continue to carry out division until we get remainder zero or a whole number less than the divisor.

(4) The above relation is as follows:

Dividend = Divisor × Quotient + Remainder

The number which we divide is called the dividend and the number by which we divide is called as divisor.

The result obtained is called as quotient and the number leftover is called as the remainder.

(5) For any number to be perfectly divisible by 5, the number should end by 5 or zero.

So 43 is not perfectly divisible by 5.

When we divide 43 by 5, the quotient is 8 and the remainder is 3.

When we divide 43 by 5, the quotient is 8 and the remainder is 3

Here, dividend = 43, divisor = 5

43 = 5 × 8 + 3

(6) For the polynomial 2y,

When 2y is multiplied 5y,

2× 5 = 10 and y × y = y²

So,

2y × 5y = 10 y²

(7) For the polynomial 5x,

When 5x is multiplied 3x³,

3 × 5 = 15 and x³ × x = x⁴

So,

5x × 3x³ = 15 x⁴

(8) For the polynomial m²,

When m² is multiplied 9 m²,

1 × 9 = 9 and m² × m² = m⁴

So,

m² × 9 m² = 9 m⁴

(9) For the polynomial 3m,

When 3m is multiplied 3 m³,

3 × 3 = 9 and m³ × m = m⁴

So,

3m × 3 m³ = 9 m⁴