Grade 7 Integers: A Practical Approach

Understanding Integers ➕➖

Integers are whole numbers that can be positive, negative, or zero. Think of them as points on a number line extending infinitely in both directions. Positive integers are greater than zero (1, 2, 3,...), negative integers are less than zero (-1, -2, -3,...), and zero is neither positive nor negative.

Real-World Examples 🌍

* Temperature: Temperatures can be above zero (positive) or below zero (negative). For example, 25°C is a positive integer, while -5°C is a negative integer. * Sea Level: Heights above sea level are positive integers, and depths below sea level are negative integers. A mountain 1000 meters above sea level is +1000, while a submarine 200 meters below sea level is -200. * Money: Having money is a positive integer, while owing money (debt) is a negative integer. If you have $50, that's +50. If you owe $20, that's -20.

Operations with Integers ➗✖️

1. Addition ➕

* Adding two positive integers: The result is always positive. Example: 3 + 5 = 8 * Adding two negative integers: The result is always negative. Example: (-3) + (-5) = -8 * Adding a positive and a negative integer: Subtract the smaller absolute value from the larger absolute value. The result has the sign of the number with the larger absolute value. Example: (-7) + 4 = -3 (because |-7| > |4| and -7 is negative).

2. Subtraction ➖

Subtracting an integer is the same as adding its opposite. Example: $a - b = a + (-b)$. * Example 1: 5 - 3 = 5 + (-3) = 2 * Example 2: 2 - 5 = 2 + (-5) = -3 * Example 3: 5 - (-3) = 5 + 3 = 8

3. Multiplication ✖️

* Positive x Positive: The result is positive. Example: 3 x 4 = 12 * Negative x Negative: The result is positive. Example: (-3) x (-4) = 12 * Positive x Negative: The result is negative. Example: 3 x (-4) = -12 * Negative x Positive: The result is negative. Example: (-3) x 4 = -12

4. Division ➗

The rules for division are similar to multiplication. * Positive ÷ Positive: The result is positive. Example: 12 ÷ 3 = 4 * Negative ÷ Negative: The result is positive. Example: (-12) ÷ (-3) = 4 * Positive ÷ Negative: The result is negative. Example: 12 ÷ (-3) = -4 * Negative ÷ Positive: The result is negative. Example: (-12) ÷ 3 = -4

Practice Problems ✍️

1. A submarine is 300 feet below sea level. It then rises 120 feet. What is its new depth? 2. The temperature is -8°C. It rises by 15°C. What is the new temperature? 3. You have $25, but you owe your friend $32. What is your net worth?

Code Representation 💻

Here's how you might represent integer operations in Python:

# Addition
positive_sum = 5 + 3  # Output: 8
negative_sum = -5 + (-3)  # Output: -8
mixed_sum = -7 + 4  # Output: -3

# Subtraction
subtraction1 = 5 - 3  # Output: 2
subtraction2 = 2 - 5  # Output: -3
subtraction3 = 5 - (-3)  # Output: 8

# Multiplication
positive_product = 3 * 4  # Output: 12
negative_product = -3 * -4  # Output: 12
mixed_product1 = 3 * -4  # Output: -12
mixed_product2 = -3 * 4  # Output: -12

# Division
positive_division = 12 / 3  # Output: 4.0 (Note: returns a float)
negative_division = -12 / -3  # Output: 4.0
mixed_division1 = 12 / -3  # Output: -4.0
mixed_division2 = -12 / 3  # Output: -4.0

print(positive_sum)
print(negative_sum)
print(mixed_sum)
print(subtraction1)
print(subtraction2)
print(subtraction3)
print(positive_product)
print(negative_product)
print(mixed_product1)
print(mixed_product2)
print(positive_division)
print(negative_division)
print(mixed_division1)
print(mixed_division2)

Understanding integers is crucial for more advanced math concepts. Keep practicing, and you'll master them in no time! 🎉