# Ex.12.1 Q1 Algebraic Expressions Solution - NCERT Maths Class 7

## Question

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of \(z\) from \(y.\)

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

(iii) 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.

## Text Solution

**Reasoning:**

Let us first understand the meaning or definition of terms variable, constants and arithmetic operations

Variables are the letters used in an algebraic expression that can take any value. For e.g. \(a, b, c\) or \(z\) etc. and it can take any value which can be either \(2\) or \(5\) or any other number. Constants always have fixed values in the algebraic expressions. They cannot be assumed or changed. Arithmetic Operations are Addition, subtraction, multiplication and division.

**Steps:**

(i) Subtraction of \(z\) from \(y.\)

\[y - z\]

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

\[\frac{1}{2}\left( {x + y} \right)\]

(iii) The number *\(z\)* multiplied by itself.

\[z \times z = {z^2}\]

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

\[\frac{1}{4}pq\]

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

\[\left( {x \times x} \right) + \left( {y \times y} \right) = {x^2} + {y^2}\]

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

\[5 + 3\left( {m \times n} \right) = 5 + 3mn\]

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

\[10 - \left( {y \times z} \right) = 10 - yz\]

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

\[\left( {a \times b} \right)-\left( {a + b} \right) = ab - \left( {a + b} \right)\]