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Expressions using Letter-Numbers - The Notion of Letter-Numbers

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A 'Letter-Number' or a Literal is a letter of the alphabet used to represent a number whose value is not yet known. Usually, lowercase letters like x,y,z,a,b,cx, y, z, a, b, c are used.

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A Constant is a symbol that has a fixed numerical value, such as 5,−10,125, -10, \frac{1}{2}, or 00.

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A Variable is a symbol (usually a literal) that can be assigned different numerical values depending on the context.

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Operations on Literals: Literals follow the same rules of addition, subtraction, multiplication, and division as regular numbers.

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Addition: The sum of xx and yy is written as x+yx + y.

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Subtraction: yy subtracted from xx is written as x−yx - y.

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Multiplication: xx multiplied by yy is written as xyxy or x⋅yx \cdot y. Note that 3×x3 \times x is written as 3x3x.

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Division: xx divided by yy is written as xy\frac{x}{y} (where y≠0y \neq 0).

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Power of a Literal: If a literal is multiplied by itself multiple times, it is written in exponential form. For example, x×x=x2x \times x = x^2 and y×y×y=y3y \times y \times y = y^3.

📐Formulae

a+b=b+a (Commutative Law of Addition)a + b = b + a \text{ (Commutative Law of Addition)}

a×b=b×a (Commutative Law of Multiplication)a \times b = b \times a \text{ (Commutative Law of Multiplication)}

a(b+c)=ab+ac (Distributive Law)a(b + c) = ab + ac \text{ (Distributive Law)}

a+0=a (Additive Identity)a + 0 = a \text{ (Additive Identity)}

a×1=a (Multiplicative Identity)a \times 1 = a \text{ (Multiplicative Identity)}

x×x×... (n times)=xnx \times x \times ... \text{ (n times)} = x^n

💡Examples

Problem 1:

Write the algebraic expression for: '7 more than the product of xx and yy'.

Solution:

xy+7xy + 7

Explanation:

First, find the product of xx and yy, which is xyxy. Then, add 77 to this product to get xy+7xy + 7.

Problem 2:

The length of a rectangle is 33 units more than twice its breadth bb. Express the length in terms of bb.

Solution:

l=2b+3l = 2b + 3

Explanation:

Twice the breadth is 2×b=2b2 \times b = 2b. Adding 33 units to this gives 2b+32b + 3.

Problem 3:

If x=5x = 5, find the value of the expression 3x−43x - 4.

Solution:

1111

Explanation:

Substitute x=5x = 5 into the expression: 3(5)−4=15−4=113(5) - 4 = 15 - 4 = 11

Problem 4:

Show the sum of 4545 and 3232 using vertical addition format, then express the sum of two literals aa and bb.

Solution:

45+3277\begin{array}{r} 45 \\ + 32 \\ \hline 77 \end{array} Sum of literals: a+ba + b

Explanation:

Numbers are added vertically to find a specific sum, while literals represent a general sum a+ba + b until values are assigned.

The Notion of Letter-Numbers Class 7 Notes & Examples