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c Arithmetic and Pre-Algebra
Chapter 1: Basic Arithmetic and PreAlgebra
Introduction
Basic arithmetic and pre-algebra lay
the foundation for all future
mathematical learning
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These concepts include working
with numbers, performing basic
operations, understanding properties
of numbers, and solving simple word
problems
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--Section 1: Operations with Numbers
1
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These
operations are used to manipulate
numbers in different ways
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Example:

Subtraction (−): The process of
finding the difference between two
numbers
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Example:

Division (÷): The process of splitting
a number into equal parts
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2 Working with Negative and
Positive Numbers
When dealing with arithmetic
operations, it's essential to
understand the concept of positive
and negative numbers
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Positive numbers: Numbers greater
than zero
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1
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This rule is
often remembered by the acronym
PEMDAS, which stands for:
P: Parentheses (perform operations
inside parentheses first)
E: Exponents (evaluate powers and
square roots next)
MD: Multiplication and Division
(perform from left to right)
AS: Addition and Subtraction
(perform from left to right)

Example:
Simplify the expression:
First, solve the parentheses:

Now perform the addition and
subtraction from left to right:

The final result is 7
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1 Commutative Property
The commutative property states
that the order of numbers does not
affect the result of addition or
multiplication
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2 Associative Property
The associative property tells us
that when adding or multiplying
numbers, the grouping of numbers
does not affect the result
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3 Distributive Property
The distributive property connects
multiplication with addition and
subtraction
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Distributive property:

Example:
--Section 3: Fractions, Decimals, and
Percentages
3
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Simplifying Fractions: Divide both
the numerator and denominator by
their greatest common divisor
(GCD)
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Example:
Example of Simplification:
Simplify
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Divide both the numerator and
denominator by 3:

3
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The decimal
point separates the whole number
from the fractional part
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Example:
Example:
Convert to a decimal:

3
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Converting a Decimal to a
Percentage: Multiply the decimal by
100 and add the percent sign
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Example:

Example:
Convert 40% to a fraction:
--Section 4: Solving Simple Word
Problems
4
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Steps to Solve Word Problems:
1
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2
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3
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4
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Example:
A store sells apples for $2 each
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--Section 5: Review and Practice
5
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Properties of Numbers:
Commutative, associative, and
distributive properties
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Word Problems: Translating realworld situations into mathematical
equations
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2 Practice Problems
1
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Simplify the fraction
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Convert to a decimal
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Solve the word problem: A group
of friends buys 4 tickets to a movie
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How much do
they spend in total?

5
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2
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4
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The
concepts learned in this chapter
serve as the building blocks for
understanding more advanced
topics such as algebra, geometry,
and beyond
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