Question

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1. Get the algebraic expressions in the following cases using variables, constants and
arithmetic operations.
(1) Subtraction of z from y.
(ii) One-half of the sum of numbers x and y.
The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of numbers m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.
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Answer 1

Answer

• Subtraction of z from y.

Sol : y - z

• One-half of the sum of numbers x and y

Sol : x + y / 2

• The number z multiplied by itself.

Sol : z × z or z²

• One-fourth of the product of numbers p and q

Sol : pq / 4

• Numbers x and y both squared and added.

Sol : x² + y²

• Number 5 added to three times the product of numbers m and n.

Sol : 3mn + 5

• Product of numbers y and z subtracted from 10.

Sol : 10 - yz

• Sum of numbers a and b subtracted from their product.

Sol : ab - (a+b)

More to know :

A linear equation is a mathematical statement that has both sides equal that is LHS is equal to RHS and gives a straight line when plotted in a graph .Constants are numbers that have a fixed value . Variables are the terms whose value is unknown . Their value is not fixed while solving linear equations often will at their value as alphabets . Generally they are x , y and z .When the number of equations is the same as the number of variables there is likely to be a solution for that . Well not guaranteed in all cases .When an equation has no solution it is called inconsistent .When an equation has a solution it is called consistent .When each equation gives new information it is called independent equation whereas generally there are dependent equations .

Answer 2

Answer:

(i) Subtraction of z from y.

Solution:-

= Y – z

(ii) One-half of the sum of numbers x and y.

Solution:-

= ½ (x + y)

= (x + y)/2

(iii) The number z multiplied by itself.

Solution:-

= z × z

= z2

(iv) One-fourth of the product of numbers p and q.

Solution:-

= ¼ (p × q)

= pq/4

(v) Numbers x and y both squared and added.

Solution:-

= x2 + y2

(vi) Number 5 added to three times the product of numbers m and n.

Solution:-

= 3mn + 5

(vii) Product of numbers y and z subtracted from 10.

Solution:-

= 10 – (y × z)

= 10 – yz

(viii) Sum of numbers a and b subtracted from their product.

Solution:-

= (a × b) – (a + b)

= ab – (a + b)

Step-by-step explanation:

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