Selina solutions concise mathematics class 6 icse Solutions for Chapter 19 fundamental operations related to algebraic expressions

Q1) Fill in the blanks :

(i) 5 + 4 = ………… and 5x + 4x = ………….

(ii) 12 + 18 = ………… and 12x2y + 18x2y = ………….

(iii) 7 + 16 = ………….. and 7a + 16b = …………

(iv) 1 + 3 = ………… and x2y + 3xy2 = ………..

(v) 7 – 4 = …………… and 7ab – 4ab = …………..

(vi) 12 – 5 = ………… and 12x – 5y = ……………

(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….

(viii) 28 – 13 = …………. and 28ax2 – 13a2x = ………….

Q1) Fill in the blanks :

(i) 5 + 4 = ………… and 5x + 4x = ………….

(ii) 12 + 18 = ………… and 12x2y + 18x2y = ………….

(iii) 7 + 16 = ………….. and 7a + 16b = …………

(iv) 1 + 3 = ………… and x2y + 3xy2 = ………..

(v) 7 – 4 = …………… and 7ab – 4ab = …………..

(vi) 12 – 5 = ………… and 12x – 5y = ……………

(vii) 35 – 16 = ………….. and 35ab – 16ba = ………….

(viii) 28 – 13 = …………. and 28ax2 – 13a2x = ………….

Q2) Fill in the blanks :

(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….

(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….

(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y = ………………

(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….

(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..

(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………

(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….

Q2) Fill in the blanks :

(i) The sum of – 2 and – 5 = …………. and the sum of – 2x and – 5x = …………….

(ii) The sum of 8 and – 3 = ………….. and the sum of 8ab and – 3ab = ………….

(iii) The sum of – 15 and – 4 = …………….. and the sum of – 15x and -4y = ………………

(iv) 15 + 8 + 3 = ……….. and 15x + 8y + 3x = …………….

(v) 12 – 9 + 15 = …………… and 12ab – 9ab + 15ba = ……………..

(vi) 25 – 7 – 9 = and 25xy – 7xy – 9yx = ……………

(vii) – 4 – 6 – 5 = …………. and – 4ax – 6ax – 5ay = …………….

Q3) Add:

(i) 8xy and 3xy

(ii) 2xyz, xyz and 6xyz

(iii) 2a, 3a and 4b

(iv) 3x and 2y

(v) 5m, 3n and 4p

(vi) 6a, 3a and 9ab

(vii) 3p, 4q and 9q

(viii) 5ab, 4ba and 6b

(ix) 50pq, 30pq and 10pr

(x) – 2y, – y and – 3y

(xi) – 3b and – b

(xii) 5b, – 4b and – 10b

(xiii) – 2c, – c and – 5c

Q3) Add:

(i) 8xy and 3xy

(ii) 2xyz, xyz and 6xyz

(iii) 2a, 3a and 4b

(iv) 3x and 2y

(v) 5m, 3n and 4p

(vi) 6a, 3a and 9ab

(vii) 3p, 4q and 9q

(viii) 5ab, 4ba and 6b

(ix) 50pq, 30pq and 10pr

(x) – 2y, – y and – 3y

(xi) – 3b and – b

(xii) 5b, – 4b and – 10b

(xiii) – 2c, – c and – 5c

Q4) Evaluate:

(i) 6a - a - 5a - 2a

(ii) 2b - 3b - b + 4b

(iii) 3x - 2x - 4x + 7x

(iv) 5ab + 2ab - 6ab + ab

(v) 8x - 5y - 3x + 10y

Q4) Evaluate:

(i) 6a - a - 5a - 2a

(ii) 2b - 3b - b + 4b

(iii) 3x - 2x - 4x + 7x

(iv) 5ab + 2ab - 6ab + ab

(v) 8x - 5y - 3x + 10y

Q5) Evaluate : (i) -7x + 9x + 2x - 2x

(ii) 5ab - 2ab - 8ab + 6ab

(iii) -8a _ 3a + 12a + 13a - 6a

(iv) 19abc - 11abc - 12abc + 14abc

Q5) Evaluate : (i) -7x + 9x + 2x - 2x

(ii) 5ab - 2ab - 8ab + 6ab

(iii) -8a _ 3a + 12a + 13a - 6a

(iv) 19abc - 11abc - 12abc + 14abc

Q6) Subtract the first term from the second : (i) 4ab,6ba

(ii) 4.8b, 6.8b

(iii) 3.5abc, 10.5abc

(iv) 3\frac{1}{2}mn,\ 8\frac{1}{2}nm

Q6) Subtract the first term from the second : (i) 4ab,6ba

(ii) 4.8b, 6.8b

(iii) 3.5abc, 10.5abc

(iv) 3\frac{1}{2}mn,\ 8\frac{1}{2}nm

Q7) Simplify :

(i) 2a^2b^2+5ab^2+8a^2b^2-3ab^2

(ii) 4a+3b-2a-b

(iii) 2xy+4yz+5xy+3yz-6xy

(iv) ab+15ab-11ab-2ab

(v) 6a^2-3b^2+2a^2+5b^2-4a^2

(vi) 8abc+2ab-4abc+ab

(vii) 9xyz+15yxz-10zyx-2zxy

(viii) 13pqr+2p+4q-6pqr+5pqr

(ix) 4ab+0-2ba

(x) 6x^2y-2xy^2+5x^2y-xy^2

(xi) 6.4a+5.3b-2.4a-2.2b

(xii) 2.5a+4.6b+1.2a-3.6b

(xiii) 22m-12\frac{1}{2}n-15p+16n

(xiv) 6p+\frac{2}{3}q-1\frac{1}{2}p+\frac{1}{3}q+2q

(xv) 2\frac{2}{3}xy-3\frac{1}{2}xy+3\frac{1}{3}xy-2\frac{1}{2}xy

Q7) Simplify :

(i) 2a^2b^2+5ab^2+8a^2b^2-3ab^2

(ii) 4a+3b-2a-b

(iii) 2xy+4yz+5xy+3yz-6xy

(iv) ab+15ab-11ab-2ab

(v) 6a^2-3b^2+2a^2+5b^2-4a^2

(vi) 8abc+2ab-4abc+ab

(vii) 9xyz+15yxz-10zyx-2zxy

(viii) 13pqr+2p+4q-6pqr+5pqr

(ix) 4ab+0-2ba

(x) 6x^2y-2xy^2+5x^2y-xy^2

(xi) 6.4a+5.3b-2.4a-2.2b

(xii) 2.5a+4.6b+1.2a-3.6b

(xiii) 22m-12\frac{1}{2}n-15p+16n

(xiv) 6p+\frac{2}{3}q-1\frac{1}{2}p+\frac{1}{3}q+2q

(xv) 2\frac{2}{3}xy-3\frac{1}{2}xy+3\frac{1}{3}xy-2\frac{1}{2}xy

Q1) Find the sum of:

(i) 3a+4b+7c, -5a+3b-6c and 4a-2b-4c

(ii) 2x^2+xv-y^2,\ -x^2+2xy+3y^{2\ }and\ 3x^2-10xy+4y^2

(iii) x^2-x+1,\ -5x^2+2x-2\ and\ 3x^2-3x+1

(iv) a^2-ab+bc,\ 2ab+bc-2a^2\ and\ -3bc+3a^2+ab

(v) 4x^2+7-3x,\ 4x-x^2+8\ and\ -10+5x-2x^2

(vi) 3x+4xy-y^2,\ xy-4x+2y^2\ and\ 3y^2-xy+6x

Q1) Find the sum of:

(i) 3a+4b+7c, -5a+3b-6c and 4a-2b-4c

(ii) 2x^2+xv-y^2,\ -x^2+2xy+3y^{2\ }and\ 3x^2-10xy+4y^2

(iii) x^2-x+1,\ -5x^2+2x-2\ and\ 3x^2-3x+1

(iv) a^2-ab+bc,\ 2ab+bc-2a^2\ and\ -3bc+3a^2+ab

(v) 4x^2+7-3x,\ 4x-x^2+8\ and\ -10+5x-2x^2

(vi) 3x+4xy-y^2,\ xy-4x+2y^2\ and\ 3y^2-xy+6x

Q2) Add the following expressions : (i) -17x^2-2xy+23y^2,-9y^2+15x^2+7xy\ and\ 13x^2+3y^2-4xy

(ii) -x^2-3xy+3y^2+8,\ 3x^2-5y^2-3+4xy\ and\ -6xy+2x^2-2+y^2

(iii) a^3-2b^3+a,\ b^3-5a+4a^3

Q2) Add the following expressions : (i) -17x^2-2xy+23y^2,-9y^2+15x^2+7xy\ and\ 13x^2+3y^2-4xy

(ii) -x^2-3xy+3y^2+8,\ 3x^2-5y^2-3+4xy\ and\ -6xy+2x^2-2+y^2

(iii) a^3-2b^3+a,\ b^3-5a+4a^3

Q3) Evaluate :

(i) 3a-(a+2b)

(ii) (5x-3y) - (x+y)

(iii) (8a+15b) - (3b-7a)

(iv) (8x+7y) - (4y-3x)

(v) 7-(4a-5)

(vi) (6y-13) - (4-7y)

Q3) Evaluate :

(i) 3a-(a+2b)

(ii) (5x-3y) - (x+y)

(iii) (8a+15b) - (3b-7a)

(iv) (8x+7y) - (4y-3x)

(v) 7-(4a-5)

(vi) (6y-13) - (4-7y)

Q4) Subtract :

(i) 5a-3b+2c from a-4b-2c

(ii) 4x-6y+3z from 12x+7y-21z

(iii) 5-a-4b+4c from 5a-7b+2c

(iv) -8x-12y+17z from x-y-z

(v) 2ab+cd-ac-2bd from ab-2cd+2ac+bd

Q4) Subtract :

(i) 5a-3b+2c from a-4b-2c

(ii) 4x-6y+3z from 12x+7y-21z

(iii) 5-a-4b+4c from 5a-7b+2c

(iv) -8x-12y+17z from x-y-z

(v) 2ab+cd-ac-2bd from ab-2cd+2ac+bd

Q5)

(i) Take -ab+bc-ca from bc-ca+ab

(ii) Take 5x+6y-3z from 3x+5y-4z

(iii) Take \frac{-3}{2}p+q-r\ from\ \frac{1}{2}p-\frac{1}{3}q-\frac{3}{2}r

(iv) Take 1-a+a^2\ from\ a^2+a+1

Q5)

(i) Take -ab+bc-ca from bc-ca+ab

(ii) Take 5x+6y-3z from 3x+5y-4z

(iii) Take \frac{-3}{2}p+q-r\ from\ \frac{1}{2}p-\frac{1}{3}q-\frac{3}{2}r

(iv) Take 1-a+a^2\ from\ a^2+a+1

Q6) From the sum of x + y – 2z and 2x – y + z subtract x + y + z.

Q6) From the sum of x + y – 2z and 2x – y + z subtract x + y + z.

Q7) From the sum of 3a – 2b + 4c and 3b – 2c subtract a – b – c.

Q7) From the sum of 3a – 2b + 4c and 3b – 2c subtract a – b – c.

Q8) Subtract x – 2y – z from the sum of 3x – y + z and x + y – 3z.

Q8) Subtract x – 2y – z from the sum of 3x – y + z and x + y – 3z.

Q9) Subtract the sum of x + y and x – z from the sum of x – 2z and x + y + z

Q9) Subtract the sum of x + y and x – z from the sum of x – 2z and x + y + z

Q10) By how much should x + 2y – 3z be increased to get 3x ?

Q10) By how much should x + 2y – 3z be increased to get 3x ?

Q11) The sum of two expressions is . If one of them is , find the other.

Q11) The sum of two expressions is 5x^2-3y^2. If one of them is 3x^2+4xy-y^2, find the other.

Q12) The sum of two expressions is 3a^2+2ab-b^2. If one of them is 2a^2+3b^2, find the other.

Q12) The sum of two expressions is 3a^2+2ab-b^2. If one of them is 2a^2+3b^2, find the other.

Q1) Fill in the blanks : (i) 6 x 3 = .......... and 6x\times3x=.......

(ii) 6 x 3 = ......... and 6x^2\times3x^3=......

(iii) 5 x 4= ........ and 5x\times4y=......

(iv) 4 x 7 = ......... and 4ax\times7x=......

(v) 6 x 2 = ......... and 6xy\times2xy=........

(vi) 12 x 4 = ......... and a^2xy^2\times8a^3x^2y=........

(vii) 15 x 3 = .......... and 15x\times3x^5y^2=.........

Q1) Fill in the blanks : (i) 6 x 3 = .......... and 6x\times3x=.......

(ii) 6 x 3 = ......... and 6x^2\times3x^3=......

(iii) 5 x 4= ........ and 5x\times4y=......

(iv) 4 x 7 = ......... and 4ax\times7x=......

(v) 6 x 2 = ......... and 6xy\times2xy=........

(vi) 12 x 4 = ......... and a^2xy^2\times8a^3x^2y=........

(vii) 15 x 3 = .......... and 15x\times3x^5y^2=.........

Q2) Fill in the blanks : (i) 4x\times6x\times2=.........

(ii) 3ab\times6ax

(iii) x\times2x^2\times3x^3

(iv) 5\times5a^3=.........

(v) 6\times6x^2\times6x^3y^2=........

(vi) -8x\times-3x=-........

(vii) -5\times-3x\times5x^2=.........

(viii) 8\times-4xy^2\times3x^3y^2=.......

(ix) -4x\times5xy\times3z=........

(x) 5x\times2x^2y\times\left(-7y^3\right)\times2x^3y^2=.........

Q2) Fill in the blanks : (i) 4x\times6x\times2=.........

(ii) 3ab\times6ax

(iii) x\times2x^2\times3x^3

(iv) 5\times5a^3=.........

(v) 6\times6x^2\times6x^3y^2=........

(vi) -8x\times-3x=-........

(vii) -5\times-3x\times5x^2=.........

(viii) 8\times-4xy^2\times3x^3y^2=.......

(ix) -4x\times5xy\times3z=........

(x) 5x\times2x^2y\times\left(-7y^3\right)\times2x^3y^2=.........

Q3) Find the value of :

(i) 3x^3\times5x^4

(ii) 5a^2\times7a^7

(iii) 3abc\times6ac^3

(iv) a^2b^2\times5a^3b^4

(v) 2x^2y^3\times5x^3y^4

(vi) abc\times bcd

Q3) Find the value of :

(i) 3x^3\times5x^4

(ii) 5a^2\times7a^7

(iii) 3abc\times6ac^3

(iv) a^2b^2\times5a^3b^4

(v) 2x^2y^3\times5x^3y^4

(vi) abc\times bcd

Q4) Multiply:

(i) a+ b by ab

(ii) 3ab-4b by 3ab

(iii) 2xy-5by by 4bx

(iv) 4x+2y by 3xy

(v) x^2-x by 2x

(vi) 1+4x by x

(vii) 9xy^2+3x^2y\ by 5xy

(viii) 6x-5y by 3axy

Q4) Multiply:

(i) a+ b by ab

(ii) 3ab-4b by 3ab

(iii) 2xy-5by by 4bx

(iv) 4x+2y by 3xy

(v) x^2-x by 2x

(vi) 1+4x by x

(vii) 9xy^2+3x^2y\ by 5xy

(viii) 6x-5y by 3axy

Q5) Multiply:

(i) -x+y-z and -2x

(ii) xy-yz and x^2yz^2

(iii) 2xyz+3xy and -2y^2z

(iv) -3xy^2+4x^2y\ and\ -xy

(v) 4xy and -x^2y-3x^2y^2

Q5) Multiply:

(i) -x+y-z and -2x

(ii) xy-yz and x^2yz^2

(iii) 2xyz+3xy and -2y^2z

(iv) -3xy^2+4x^2y\ and\ -xy

(v) 4xy and -x^2y-3x^2y^2

Q6) Multiply :

(i) 3a+4b-5c and 3a

(ii) -5xy and -xy^2-6x^2y

Q6) Multiply :

(i) 3a+4b-5c and 3a

(ii) -5xy and -xy^2-6x^2y

Q7) Multiply :

(i) x + 2 and x + 10

(ii) x + 5 and x – 3

(iii) x – 5 and x + 3

(iv) x – 5 and x – 3

(v) 2x+ y and x + 3y

(vi) (3x – 5y) and (x + 6y)

(vii) (x + 9y) and (x – 5y)

(viii) (2x + 5y) and (2x + 5y)

Q7) Multiply :

(i) x + 2 and x + 10

(ii) x + 5 and x – 3

(iii) x – 5 and x + 3

(iv) x – 5 and x – 3

(v) 2x+ y and x + 3y

(vi) (3x – 5y) and (x + 6y)

(vii) (x + 9y) and (x – 5y)

(viii) (2x + 5y) and (2x + 5y)

Q8) Multiply :

(i) 3abc\ and\ -5a^2b^2c

(ii) x-y+z\ and\ -2x

(iii) 2x-3y-5z and -2y

(iv) -8xyz+10x^2yz^3\ and\ xyz

(v) xyz\ and\ -13xy^2z+15x^2yz-6xyz^2

(vi) 4abc-5a^2bc-6ab^2c\ and\ -2abc^2

Q8) Multiply :

(i) 3abc\ and\ -5a^2b^2c

(ii) x-y+z\ and\ -2x

(iii) 2x-3y-5z and -2y

(iv) -8xyz+10x^2yz^3\ and\ xyz

(v) xyz\ and\ -13xy^2z+15x^2yz-6xyz^2

(vi) 4abc-5a^2bc-6ab^2c\ and\ -2abc^2

Q9) Find the product of :

(i) xy - ab and xy + ab

(ii) 2abc - 3xy and 2abc + 3xy

(iii) a + b - c and 2a - 3b

(iv) 5x - 6y - 7z and 2x + 3y

(v) 5x - 6y - 7z and 2x + 3y + z

(vi) 2a + 3b - 4c and a- b - c

Q9) Find the product of :

(i) xy - ab and xy + ab

(ii) 2abc - 3xy and 2abc + 3xy

(iii) a + b - c and 2a - 3b

(iv) 5x - 6y - 7z and 2x + 3y

(v) 5x - 6y - 7z and 2x + 3y + z

(vi) 2a + 3b - 4c and a- b - c

Q1) Divide : (i) 3a by a

(ii) 15x by 3x

(iii) 16m by 4

(iv) 20x^{2\ }by\ 5x

(v) 30p^2\ by\ 10p^2

(vi) 14a^3b^3\ by\ 2a^2

(vii) 18pqr^2\ by\ 3pq

(viii) 100 by 50b

Q1) Divide : (i) 3a by a

(ii) 15x by 3x

(iii) 16m by 4

(iv) 20x^{2\ }by\ 5x

(v) 30p^2\ by\ 10p^2

(vi) 14a^3b^3\ by\ 2a^2

(vii) 18pqr^2\ by\ 3pq

(viii) 100 by 50b

Q2) Fill in the blanks

(i) 4x\times6x\times2=.......

(ii) 3ab\times6ax\times2=........

(iii) x\times2x^2\times3x^2=................

(iv) 5\times5a^3=...........

(v) 6\times6x^2\times6x^2y^2=............

(vi) -8x\times-3x=-...........

(vii) -5\times-3x\times5x^2=...........

(viii) 8\times-4xy^2\times3x^3y^2

(ix) -4x\times5xy\times3z=..........

(x) 5x\times2x^2y\times\left(-7y^3\right)\times2x^3y^2=.............

Q2) Simplyfy:

(i) 2x^5\div x^2

(ii) 6a^8\div3a^3

(iii) 20xy\div-5xy

(iv) -24a^2b^2c^2\div6ab

(v) -5x^2y\div xy^2

(vi) 40p^3q^4r^5\div10p^3q

(vii) -64x^4y^3z\div4x^3y^2z

(viii) 35xy^5\div7x^2y^4

Q3) Divide :

(i) -\frac{3}{4}\ by\ 2m

(ii) -15p^6q^8\ by\ -5p^6q^7

(iii) -21m^5n^7\ by\ -5p^6q^7

(iv) 36a^4x^5y^6\ by\ 4x^2a^3y^2

(v) 20x^3a^6\ by\ 5xy

(vi) \frac{28a^2b^3}{c^2}\ by\ 4abc

(vii) \frac{2a^2}{9b^2}\ by\ \frac{3b}{2a}

(viii) \frac{-5.5x^2}{y}\ by\ \frac{11x}{y}

(ix) \frac{64x^2y^2}{z^2}\ by\ \frac{8xy}{z}

Q3) Divide :

(i) -\frac{3}{4}\ by\ 2m

(ii) -15p^6q^8\ by\ -5p^6q^7

(iii) -21m^5n^7\ by\ -5p^6q^7

(iv) 36a^4x^5y^6\ by\ 4x^2a^3y^2

(v) 20x^3a^6\ by\ 5xy

(vi) \frac{28a^2b^3}{c^2}\ by\ 4abc

(vii) \frac{2a^2}{9b^2}\ by\ \frac{3b}{2a}

(viii) \frac{-5.5x^2}{y}\ by\ \frac{11x}{y}

(ix) \frac{64x^2y^2}{z^2}\ by\ \frac{8xy}{z}

Q4) Simplify : (i) \frac{-15m^5n^2}{-3m^5}

(ii) \frac{35x^4y^2}{-15x^2y^2}

(iii) \frac{-24x^6y^2}{6x^6y}

Q4) Simplify : (i) \frac{-15m^5n^2}{-3m^5}

(ii) \frac{35x^4y^2}{-15x^2y^2}

(iii) \frac{-24x^6y^2}{6x^6y}

Q5) Divide:

(i) 9x^3-6x^2\ by\ 3x

(ii) 6m^2-16m^3+10m^4\ by\ -2m

(iii) 15x^3y^2+25x^2y^3-36x^4y^4\ by\ 5x^2y^2

(iv) 36a^3x^5-24a^4x^4+18a^5x^3\ by\ -6a^3x^3

Q5) Divide:

(i) 9x^3-6x^2\ by\ 3x

(ii) 6m^2-16m^3+10m^4\ by\ -2m

(iii) 15x^3y^2+25x^2y^3-36x^4y^4\ by\ 5x^2y^2

(iv) 36a^3x^5-24a^4x^4+18a^5x^3\ by\ -6a^3x^3