Chapter Contents

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1.1 Integers 1.2 Integer Operations 1.3 Rational Numbers 1.4 Fraction Operations 1.5 Factors & Multiples 1.6 GCF & LCM 1.7 Order of Operations Practice Questions

Big Idea

Numbers are like tools. Some numbers help you count, some show values below zero, and some show parts of a whole. In this chapter, you learn how to read numbers, compare numbers, and solve problems using the correct math rules.

Operation means a math action, like adding, subtracting, multiplying, or dividing.

1.1 Integers

An integer means a whole number, zero, or a negative whole number. So integers do not have fractions or decimals.

Examples of integers:

-8, -3, 0, 4, 10, 25

A positive number is bigger than zero. A negative number is smaller than zero. Zero is in the middle.

-5-4-3-2-1012345

On a number line, numbers become bigger as you move right. Numbers become smaller as you move left.

Absolute value means the distance from zero. Distance is never negative.

Example:

|-7| = 7 because -7 is 7 steps away from zero.

|5| = 5 because 5 is 5 steps away from zero.

1.2 Integer Operations

Integer operations are math actions using positive and negative whole numbers.

Addition Rules

If the signs are the same, add the numbers and keep the sign.

(-3) + (-4) = -7

5 + 6 = 11

If the signs are different, subtract the smaller amount from the bigger amount, then keep the sign of the number with the bigger absolute value.

(-8) + 3 = -5

10 + (-4) = 6

Subtraction Rule

Subtracting a negative is like adding.

7 - (-3) = 7 + 3 = 10

Multiplication and Division Rules

Same signs make a positive answer. Different signs make a negative answer.

(-2) × (-5) = 10

(-2) × 5 = -10

12 ÷ (-3) = -4

1.3 Rational Numbers

A rational number is a number that can be written as a fraction. Fractions, many decimals, integers, and mixed numbers can be rational numbers.

Examples:

1/2, -3/4, 0.25, 5, -9

Terminating Decimals

A terminating decimal is a decimal that stops.

0.5, 0.25, 1.75

Repeating Decimals

A repeating decimal is a decimal that keeps repeating the same pattern.

1 ÷ 3 = 0.333...

2 ÷ 3 = 0.666...

Converting Fractions and Decimals

To change a fraction to a decimal, divide the top number by the bottom number.

1/2 = 1 ÷ 2 = 0.5

1/4 = 1 ÷ 4 = 0.25

1.4 Fraction Operations

A fraction shows part of a whole. The top number is called the numerator, and the bottom number is called the denominator.

Adding Fractions

If denominators are the same, add the top numbers only.

2/7 + 3/7 = 5/7

If denominators are different, make the bottom numbers the same first.

1/2 + 1/4 = 2/4 + 1/4 = 3/4

Multiplying Fractions

Multiply top × top and bottom × bottom.

2/3 × 3/4 = 6/12 = 1/2

Dividing Fractions

Keep the first fraction, change division to multiplication, and flip the second fraction.

1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2

1.5 Factors and Multiples

A factor is a number that divides another number exactly with no remainder.

Factors of 12: 1, 2, 3, 4, 6, 12

A multiple is the answer you get when you multiply a number by 1, 2, 3, 4, and so on.

Multiples of 5: 5, 10, 15, 20, 25

Prime Numbers

A prime number has only two factors: 1 and itself.

2, 3, 5, 7, 11

Composite Numbers

A composite number has more than two factors.

4, 6, 8, 9, 10, 12

Prime Factorization

Prime factorization means breaking a number into prime numbers multiplied together.

12 = 2 × 2 × 3

18 = 2 × 3 × 3

1.6 GCF and LCM

GCF

GCF means Greatest Common Factor. It is the biggest factor two numbers share.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 18: 1, 2, 3, 6, 9, 18

GCF = 6

LCM

LCM means Least Common Multiple. It is the smallest multiple two numbers share.

Multiples of 4: 4, 8, 12, 16

Multiples of 6: 6, 12, 18, 24

LCM = 12

1.7 Order of Operations

Order of operations means the correct order to solve a math expression. Without this rule, people could get different answers.

PEMDAS / BEDMAS

Parentheses or Brackets first
Exponents next
Multiplication and Division from left to right
Addition and Subtraction from left to right