Lessons Grade 7

Chapter 1

Chapter 1: Integers

1.1 Introduction to Integers

Integers are the set of whole numbers that include both positive and negative numbers, as well as zero. They can be written as:

Positive integers: 1, 2, 3, 4, ...

Negative integers: -1, -2, -3, -4, ...

Zero: 0

Integers are used to represent real-world situations like temperatures, elevations, and financial transactions. For example, if the temperature is -5°C, it means the temperature is 5 degrees below zero.

1.2 Comparing Integers

When comparing integers, we use the number line. On the number line, numbers to the right are greater, and numbers to the left are smaller.

Examples:

3 is greater than -5 because 3 is to the right of -5 on the number line.

-7 is smaller than 2 because -7 is to the left of 2.1.3 Addition and Subtraction of Integers

Adding and subtracting integers can be understood better by using a number line. Here's how it works:

Addition of Integers:

If both integers are positive, simply add them.

Example: 3 + 2 = 5

If both integers are negative, add their absolute values and give the result a negative sign.

Example: -3 + (-2) = -5

If one integer is positive and the other is negative, subtract the smaller absolute value from the larger one, and the sign will be that of the integer with the larger absolute value.

Example: 5 + (-3) = 2

Example: -5 + 3 = -2

Subtraction of Integers: To subtract an integer, add its opposite:

Example: 5 - (-3) = 5 + 3 = 8

Example: -5 - 3 = -5 + (-3) = -8

1.4 Multiplication and Division of Integers

Multiplication of Integers:

When multiplying two integers with the same sign (both positive or both negative), the result is positive.

Example: 3 × 2 = 6, and -3 × -2 = 6

When multiplying two integers with different signs, the result is negative.

Example: 3 × -2 = -6, and -3 × 2 = -6

Division of Integers:

The division rules are the same as the multiplication rules.

Example: 6 ÷ 2 = 3, and -6 ÷ -2 = 3

Example: 6 ÷ -2 = -3, and -6 ÷ 2 = -3

Exercises

Exercise 1: Compare the following pairs of integers using >,

3 ___ -2

-7 ___ 5

0 ___ -3

-10 ___ 7

-4 ___ -9

Exercise 2: Solve the following additional problems:

18 + (-7) = ?

-5 + 7 = ?

-6 + (-4) = ?

10 + (-12) = ?

5 + (-9) = ?

Exercise 3: Solve the following subtraction problems:

6 - (-3) = ?

-4 - 6 = ?

-8 - (-5) = ?

2 - (-9) = ?

-9 - 4 = ?

Exercise 4: Solve the following multiplication problems:

3 × (-2) = ?

-5 × 4 = ?

(-7) × (-3) = ?

6 × (-2) = ?

-8 × 5 = ?

Exercise 5: Solve the following division problems:

12 ÷ (-4) = ?

-18 ÷ 6 = ?

15 ÷ (-3) = ?

-36 ÷ 9 = ?

-20 ÷ (-4) = ?