Multiplication and Division of Integers

When working with integers, some simple rules are required for multiplication and division. It is important for class 6 maths learners to understand these rules and concepts, as they lay the foundation for more complex mathematical operations later. Let us look at these operations in detail.

Understanding integers

Integers are a set of numbers that includes all whole numbers and their negative counterparts. This means that integers can be positive, negative, or zero. For example:

• Positive integers: 1, 2, 3, 4, 5, ...
• Negative integers: -1, -2, -3, -4, -5, ...
• Zero: 0

Multiplication of integers

Basic rules

When multiplying integers, the rules depend on the signs (positive or negative) of the numbers being multiplied. Here are some main rules you should remember:

• positive × positive = positive
• negative × negative = positive
• positive × negative = negative
• negative × positive = negative

If the signs of both the integers are the same then the product will be positive and if the signs of the integers are different then the product will be negative.

Visual example of multiplication

Text example

Let's look at some examples:

• -4 × 5 = -20 (negative × positive gives a negative result)
• 3 × -7 = -21 (positive × negative will give negative result)
• -6 × -2 = 12 (negative × negative gives a positive result)
• 8 × 0 = 0 (Any number × zero gives 0)

The above examples illustrate the application of the rules. When the signs are different, the product is negative. When the signs are the same, the product is positive.

Division of integers

Basic rules

Like multiplication, division follows a set of rules based on the signs of the integers:

• positive ÷ positive = positive
• negative ÷ negative = positive
• positive ÷ negative = negative
• negative ÷ positive = negative

When the signs of both the integers are same then the quotient is positive and when the signs of the integers are different then the quotient is negative.

Visual example of partitioning

Text example

We can also see examples of segmentation in the text:

• 15 ÷ 3 = 5 (positive ÷ positive equals positive)
• -18 ÷ -6 = 3 (negative ÷ negative = positive)
• 20 ÷ -4 = -5 (positive ÷ negative = negative)
• -25 ÷ 5 = -5 (negative ÷ positive = negative)

It is important to remember that division by zero is undefined in mathematics, because zero cannot be a divisor.

Practical tips

When dealing with multiplication and division of integers, keep in mind the signs of the numbers. A simple way to remember the rules is this:

• If the signs are the same, the answer is positive.
• If the signs are different then the answer will be negative.

Practicing these rules with different numbers will strengthen your understanding. You can create your own examples to test these rules.

Problem-solving scenarios

Word problems

Applying integer multiplication and division to real-world scenarios can make these operations more relevant and understandable:

• Expense Management: If you spend $5 every day, the total expense over 10 days can be represented by 5 × -10 = -50. This negative result represents the expense as lost money.
• Change in temperature: If the temperature drops 2°C every hour, the decrease in 4 hours can be calculated as -2 × 4 = -8 degrees.
• Calculation of Profit: The profit earned of -3 units in 7 days will be given as -3 × 7 = -21 in total.

Custom question

Try solving these additional problems to further improve your skills:

1. Calculate 7 × (-5).
2. Determine the result of -9 ÷ 3.
3. Find the result for -12 × -4.
4. What is -16 ÷ -2 equal to?

By working through each example, check if your answers match the solutions. Practising these methods helps develop confidence and proficiency in handling integers.

Comments