Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
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 are used.
A Constant is a symbol that has a fixed numerical value, such as , or .
A Variable is a symbol (usually a literal) that can be assigned different numerical values depending on the context.
Operations on Literals: Literals follow the same rules of addition, subtraction, multiplication, and division as regular numbers.
Addition: The sum of and is written as .
Subtraction: subtracted from is written as .
Multiplication: multiplied by is written as or . Note that is written as .
Division: divided by is written as (where ).
Power of a Literal: If a literal is multiplied by itself multiple times, it is written in exponential form. For example, and .
📐Formulae
💡Examples
Problem 1:
Write the algebraic expression for: '7 more than the product of and '.
Solution:
Explanation:
First, find the product of and , which is . Then, add to this product to get .
Problem 2:
The length of a rectangle is units more than twice its breadth . Express the length in terms of .
Solution:
Explanation:
Twice the breadth is . Adding units to this gives .
Problem 3:
If , find the value of the expression .
Solution:
Explanation:
Substitute into the expression:
Problem 4:
Show the sum of and using vertical addition format, then express the sum of two literals and .
Solution:
Sum of literals:
Explanation:
Numbers are added vertically to find a specific sum, while literals represent a general sum until values are assigned.