ExErcisE 18(A) 1. Express each of the following statements ...

Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts

Exercise 18(A)

1. Express each of the following statements in algebraic form: (i) The sum of 8 and x is equal to y. (ii) x decreased by 5 is equal to y. (iii) The sum of 2 and x is greater than y. (iv) The sum of x and y is less than 24. (v) 15 multiplied by m gives 3n. (vi) Product of 8 and y is equal to 3x. (vii) 30 divided by b is equal to p. (viii) z decreased by 3x is equal to y. (ix) 12 times of x is equal to 5z. (x) 12 times of x is greater than 5z. (xi) 12 times of x is less than 5z. (xii) 3z subtracted from 45 is equal to y. (xiii) 8x divided by y is equal to 2z. (xiv) 7y subtracted from 5x gives 8z. (xv) 7y decreased by 5x gives 8z. Solution: (i) The sum of 8 and x is equal to y in algebraic form is written as, 8 + x = y (ii) x decreased by 5 is equal to y in algebraic form is written as, x ? 5 = y (iii) The sum of 2 and x is greater than y in algebraic form is written as, 2 + x > y (iv) The sum of x and y is less than 24 in algebraic form is written as, x + y < 24 (v) 15 multiplied by m gives 3n in algebraic form is written as, 15 ? m = 3n (vi) Product of 8 and y is equal to 3x in algebraic form is written as, 8 ? y = 3x (vii) 30 divided by b is equal to p in algebraic form is written as, 30 ? b = p (viii) z decreased by 3x is equal to y in algebraic form is written as, z ? 3x = y (ix) 12 times of x is equal to 5z in algebraic form is written as, 12 ? x = 5z (x) 12 times of x is greater than 5z in algebraic form is written as, 12 ? x > 5z (xi) 12 times of x is less than 5z in algebraic form is written as,

Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts

12 ? x < 5z (xii) 3z subtracted from 45 is equal to y in algebraic form is written as, 45 ? 3z = y (xiii) 8x divided by y is equal to 2z in algebraic form is written as, 8x ? y = 2z (xiv) 7y subtracted from 5x gives 8z in algebraic form is written as, 5x ? 7y = 8z (xv) 7y decreased by 5x gives 8z in algebraic form is written as, 7y ? 5x = 8z

2. For each of the following algebraic expressions, write a suitable statement in words: (i) 3x + 8 = 15 (ii) 7 ? y > x (iii) 2y ? x < 12 (iv) 5 ? z = 5 (v) a + 2b > 18 (vi) 2x ? 3y = 16 (vii) 3a ? 4b > 14 (viii) b + 7a < 21 (ix) (16 + 2a) ? x > 25 (x) (3x + 12) ? y < 3a Solution: (i) The algebraic expression 3x + 8 = 15 in words is expressed as, 3x plus 8 is equal to 15 (ii) The algebraic expression 7 ? y > x in words is expressed as, 7 decreased by y is greater than x (iii) The algebraic expression 2y ? x < 12 in words is expressed as, 2y decreased by x is less than 12 (iv) The algebraic expression 5 ? z = 5 in words is expressed as, 5 divided by z is equal to 5 (v) The algebraic expression a + 2b > 18 in words is expressed as, a increased by 2b is greater than 18 (vi) The algebraic expression 2x ? 3y = 16 in words is written as, 2x decreased by 3y is equal to 16 (vii) The algebraic expression 3a ? 4b > 14 in words is written as, 3a decreased by 4b is greater than 14 (viii) The algebraic expression b + 7a < 21 in words is written as, b increased by 7a is less than 21

Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts

(ix) The algebraic expression (16 + 2a) ? x > 25 in words is written as, The sum of 16 and 2a decreased by x is greater than 25 (x) The algebraic expression (3x + 12) ? y < 3a in words is written as, The sum of 3x and 12 decreased by y is less than 3a

Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts

Exercise 18(B)

1. Separate the constants and the variables from each of the following: 6, 4y, -3x, 5 / 4, (4 / 5)xy, az, 7p, 0, 9x / y, 3 / 4x, - xz / 3y Solution: 6, 5 / 4and 0 are the constants 4y, -3x, (4 / 5)xy, az, 7p, 9x / y, 3 / 4x and ? xz / 3y are the variables

2. Group the like terms together: (i) 4x, -3y, -x, (2 / 3)x, (4 / 5)y and y. (ii) (2 / 3) xy, -4yx, 2yz, (-2 / 3)yz, zy / 3 and yx. (iii) ?ab2, b2a2, 7b2a, -3a2b2 and 2ab2 (iv) 5ax, -5by, by / 7, 7xa and 2ax / 3 Solution: (i) 4x, -3y, -x, (2 / 3)x, (4 / 5)y and y. Here, the like term are as follows 4x, -x, (2 / 3)x and -3y, (4 / 5)y, y (ii) (2 / 3) xy, -4yx, 2yz, (-2 / 3)yz, zy / 3 and yx. Here, the like terms are as follows (2 / 3) xy, -4yx, yx and 2yz, (-2 / 3)yz, zy / 3 (iii) ?ab2, b2a2, 7b2a, -3a2b2 and 2ab2 Here, the like terms are as follows -ab2, 7b2a, 2ab2 and b2a2, -3a2b2 (iv) 5ax, -5by, by / 7, 7xa and 2ax / 3 Here, the like terms are as follows 5ax, 7xa, 2ax / 3 and ? 5by, by / 7

3.State whether true or false: (i) 16 is a constant and y is a variable but 16y is variable (ii) 5x has two terms 5 and x (iii) The expression 5 + x has two terms 5 and x (iv) The expression 2x2 + x is a trinomial (v) ax2 + bx + c is a trinomial (vi) 8 ? ab is a binomial (vii) 8 + ab is a binomial (viii) x3 ? 5xy + 6x + 7 is a polynomial (ix) x3 ? 5xy + 6x + 7 is a multinomial (x) The coefficient of x in 5x is 5x (xi) The coefficient of ab in ?ab is -1

Selina Solutions Concise Mathematics Class 6 Chapter 18 Fundamental Concepts

(xii) The coefficient of y in -3xy is -3 Solution: (i) 16 is a constant and y is a variable but 16y is variable The given statement is true (ii) 5x has two terms 5 and x The given statement is false (iii) The expression 5 + x has two terms 5 and x The given statement is true (iv) The expression 2x2 + x is a trinomial The given statement is false (v) ax2 + bx + c is a trinomial The given statement is true (vi) 8 ? ab is a binomial The given statement is false (vii) 8 + ab is a binomial The given statement is true (viii) x3 ? 5xy + 6x + 7 is a polynomial The given statement is true (ix) x3 ? 5xy + 6x + 7 is a multinomial The given statement is true (x) The coefficient of x in 5x is 5x The given statement is false (xi) The coefficient of ab in ?ab is -1 The given statement is true (xii) The coefficient of y in -3xy is -3 The given statement is false

4. State the number of terms in each of the following expressions: (i) 2a ? b (ii) 3 ? x + a / 2 (iii) 3x ? x / p (iv) a ? x ? b + c (v) 3x ? 2 + y + 4 (vi) xy ? 2 (vii) x + y ? a (viii) 2x + y + 8 ? y (ix) 2 ? a + 3 ? b + 4 Solution: (i) 2a ? b

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