Selina Solutions Concise Mathematics Class 6 Chapter 19: Fundamental Operations Exercise 19(D)

Selina Solutions Concise Mathematics Class 6 Chapter 19 Fundamental Operations Exercise 19(D) contains answers designed by expert faculty, in accordance with the ICSE exam. The solutions are in a stepwise manner, for better understanding of the concepts among students. Subject matter experts prepare 100% accurate solutions, with the aim to improve the academic performance of students. These solutions also enable them to increase their analytical and logical thinking. Selina Solutions Concise Mathematics Class 6 Chapter 19 Fundamental Operations Exercise 19(D), free PDF links are given below.

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Access Selina Solutions Concise Mathematics Class 6 Chapter 19: Fundamental Operations Exercise 19(D)

Exercise 19(D)

1. Divide:

(i) 3a by a

(ii) 15x by 3x

(iii) 16m by 4

(iv) 20x² by 5x

(v) 30p² by 10p²

Solution:

(i) 3a by a

3a ÷ a

This can be written as,

3a / a = (3 × a) / a

= 3

Hence, 3a ÷ a = 3

(ii) 15x by 3x

15x ÷ 3x

15x / 3x = (15 × x) / (3 × x)

This can be written as,

= (3 × 5 × x) / (3 × x)

We get,

= 5

Hence, 15x ÷ 3x = 5

(iii) 16m by 4

16m ÷ 4

16m / 4 = (16 × m) / 4

This can be written as,

= (4 × 4 × m) / 4

We get,

= 4m

Hence, 16m ÷ 4 = 4m

(iv) 20x² by 5x

20x² ÷ 5x

20x² / 5x = (20 × x²) / (5 × x)

This can be written as,

= (4 × 5 × x^2-1) / 5

= 4 × x

= 4x

Hence, 20x² ÷ 5x = 4x

(v) 30p² by 10p²

30p² ÷ 10p² = (30 × p²) / (10 × p²)

This can be written as,

= (3 × 10 × p^2-2) / 10

= 3 × p⁰

= 3 × 1

= 3

Hence, 30p² ÷ 10p² = 3

2. Simplify:

(i) 2x⁵ ÷ x²

(ii) 6a⁸ ÷ 3a³

(iii) 20xy ÷ – 5xy

(iv) – 24a²b²c² ÷ 6ab

(v) – 5x²y ÷ xy²

Solution:

(i) 2x⁵ ÷ x²

= (2 × x⁵) / x²

= 2 × x^5-2

= 2 × x³

We get,

= 2x³

Hence, 2x⁵ ÷ x² = 2x³

(ii) 6a⁸ ÷ 3a³

= (6 × a⁸) / (3 × a³)

This can be written as,

= (2 × 3 × a^8-3) / 3

We get,

= 2 × a⁵

= 2a⁵

Hence, 6a⁸ ÷ 3a³ = 2a⁵

(iii) 20xy ÷ – 5xy

= (20 × x × y) / (- 5 × x × y)

This can be written as,

= (4 × 5) / – 5

We get,

= – 4

Hence, 20xy ÷ – 5xy = – 4

(iv) – 24a²b²c² ÷ 6ab

= (- 24 × a² × b² × c²) / (6 × a × b)

This can be written as,

= (-4 × 6 × a^2-1 × b^2-1 × c²) / 6

We get,

= – 4 × a × b × c²

= – 4abc²

Hence, – 24a²b²c² ÷ 6ab = – 4abc²

(v) – 5x²y ÷ xy²

= (- 5 × x² × y) / (x × y²)

This can be written as,

= (- 5 × x^2-1) / y^2-1

We get,

= (- 5 × x) / y

= – 5x / y

Hence, – 5x²y ÷ xy² = – 5x / y

3. Divide:

(i) (- 3m / 4) by 2m

(ii) – 15p⁶q⁸ by – 5p⁶q⁷

(iii) – 21m⁵n⁷ by 14m²n²

(iv) 36a⁴x⁵y⁶ by 4x²a³y²

(v) 20x³a⁶ by 5xy

Solution:

(i) (- 3m / 4) by 2m

= – 3m / 4 ÷ 2m = – 3m / 4 × 1 / 2m

= – (3 × m) / (4 × 2 × m)

We get,

= – 3 / 8

Hence, (- 3m / 4) ÷ 2m = – 3 / 8

(ii) – 15p⁶q⁸ by – 5p⁶q⁷

– 15p⁶q⁸ ÷ – 5p⁶q⁷ = (- 15 × p⁶ × q⁸) / (- 5 × p⁶ × q⁷)

This can be written as,

= (3 × 5 × q^8-7) / 5

We get,

= 3 × q

= 3q

Hence, – 15p⁶q⁸ ÷ – 5p⁶q⁷ = 3q

(iii) – 21m⁵n⁷ by 14m²n²

– 21m⁵n⁷ ÷ 14m²n² = (- 21 × m⁵ × n⁷) / (14 × m² × n²)

This can be written as,

= (- 3 × 7 × m^5-2 × n^7-2) / (2 × 7)

= (- 3 × m³ × n⁵) / 2

We get,

= – 3m³n⁵ / 2

Hence, – 21m⁵n⁷ ÷ 14m²n² = – 3m³n⁵ / 2

(iv) 36a⁴x⁵y⁶ by 4x²a³y²

36a⁴x⁵y⁶ ÷ 4x²a³y² = (36 × a⁴ × x⁵ × y⁶) / (4 × x² × a³ × y²)

This can be written as,

= (4 × 9 × a^4-3 × x^5-2 × y^6-2) / 4

= 9 × a¹ × x³ × y⁴

We get,

= 9ax³y⁴

Hence, 36a⁴x⁵y⁶ ÷ 4x²a³y² = 9ax³y⁴

(v) 20x³a⁶ by 5xy

20x³a⁶ ÷ 5xy = (20 × x³ × a⁶) / (5 × x × y)

This can be written as,

= (4 × 5 × x^3-1 × a⁶) / (5 × y)

We get,

= (4 × x² × a⁶) / y

= 4x²a⁶ / y

Hence, 20x³a⁶ ÷ 5xy = 4x²a⁶ / y

4. Simplify:

(i) (- 15m⁵n²) / (- 3m⁵)

(ii) 35x⁴y² / – 15x²y²

(iii) (- 24x⁶y²) / (6x⁶y)

Solution:

(i) (-15m⁵n²) / (- 3m⁵) = (-15 × m⁵ × n²) / (- 3 × m⁵)

This can be written as,

= (3 × 5 × m^5-5 × n²) / 3

= 5 × m⁰ × n²

= 5 × 1 × n²

= 5n²

Hence, (-15m⁵n²) / (- 3m⁵) = 5n²

(ii) 35x⁴y² / – 15x²y²

35x⁴y² / – 15x²y² = (35 × x⁴ × y²) / (- 15 × x² × y²)

This can be written as,

= – (5 × 7 × x^4-2 × y^2-2) / (3 × 5)

= – (7 × x² × y⁰) / 3

We get,

= – 7x²y / 3

Hence, 35x⁴y² / – 15x²y² = – 7x²y / 3

(iii) (- 24x⁶y²) / (6x⁶y)

(- 24x⁶y²) / (6x⁶y) = (- 24 × x⁶ × y²) / (6 × x⁶ × y)

This can be written as,

= (- 4 × 6 × x^6-6 × y^2-1) / 6

= – 4 × x⁰ × y¹

= – 4y

Hence, (- 24x⁶y²) / (6x⁶y) = – 4y

5. Divide:

(i) 9x³ – 6x² by 3x

(ii) 6m² – 16m³ + 10m⁴ by – 2m

(iii) 15x³y² + 25x²y³ – 36x⁴y⁴ by 5x²y²

(iv) 36a³x⁵ – 24a⁴x⁴ + 18a⁵x³ by – 6a³x³

Solution:

(i) 9x³ – 6x² by 3x

9x³ – 6x² ÷ 3x = (9 × x³ – 6 × x²) / (3 × x)

Separating the terms, we get

= (9 × x³) / (3 × x) – (6 × x²) / (3 × x)

We get,

= 3 × x^3-1 – 2 × x^2-1

= 3x² – 2x

Hence, 9x³ – 6x² ÷ 3x = 3x² – 2x

(ii) 6m² – 16m³ + 10m⁴ by – 2m

6m² – 16m³ + 10m⁴ ÷ – 2m = (6 × m²– 16 × m³ + 10 × m⁴) / – 2 × m

Separating the terms, we get

= (6 × m² / – 2 × m) – (16 × m³) / (- 2 × m) + (10 × m⁴) / (- 2 × m)

= – 3 × m^2-1 + 8 × m^3-1 – 5 × m^4-1

= – 3 × m + 8 × m² – 5 × m³

We get,

= – 3m + 8m² – 5m³

Hence, 6m² – 16m³ + 10m⁴ ÷ – 2m = – 3m + 8m² – 5m³

(iii) 15x³y² + 25x²y³ – 36x⁴y⁴ by 5x²y²

15x³y² + 25x²y³ – 36x⁴y⁴ ÷ 5x²y² = (15x³y² + 25x²y³ – 36x⁴y⁴) / (5x²y²)

= (15 × x³ × y²) / (5 × x² × y²) + (25 × x² × y³) / (5 × x² × y²) – (36 × x⁴ × y⁴) / (5 × x² × y²)

On further calculation, we get

= 3 × x^3-2 × y^2-2 + 5 × x^2-2 × y^3-2 – (36 × x^4-2 × y^4-2) / 5

We get,

= 3 × x¹ × y⁰ + 5 × x⁰ × y¹ – (36 × x² × y²) / 5

= 3x + 5y – (36x²y²) / 5

Hence, 15x³y² + 25x²y³ – 36x⁴y⁴ ÷ 5x²y² = 3x + 5y – (36x²y²) / 5

(iv) 36a³x⁵ – 24a⁴x⁴ + 18a⁵x³ by – 6a³x³

36a³x⁵ – 24a⁴x⁴ + 18a⁵x³ ÷ (– 6a³x³) = (36a³x⁵ – 24a⁴x⁴ + 18a⁵x³) / – 6a³x³

= (36.a³.x⁵) / (-6.a³.x³) – (24.a⁴.x⁴) / (-6.a³.x³) + (18.a⁵.x³) / (-6.a³.x³)

We get,

= – 6.x^5-3 + 4.a^4-3.x^4-3 – 3.a^5-3

= – 6x² + 4ax – 3a²

Hence, 36a³x⁵ – 24a⁴x⁴ + 18a⁵x³ ÷ (– 6a³x³) = – 6x² + 4ax – 3a²