Multiplication on Number Line
Multiplication on a number line refers to the application of multiplication operation on a given set of numbers via a number line. A number line is a visual representation of numbers on a straight line with numbers placed at equal intervals on an infinite line that extends on both sides, horizontally. The arithmetic operations can be performed on a number line addition, subtraction, division, and multiplication. As we move towards the right side of a number line, the numbers increase; as we move towards the left, the numbers decrease.
In this article, let's learn the multiplication of numbers on a number line.
Introduction to Multiplication on Number Line
Multiplication on a number line is the application of multiplication operation on a given set of numbers on a number line. Multiplication is also known as repeated addition. To perform multiplication on a number line, we start from zero and move towards the right side of the number line for a given number of times. Let us consider an example. Multiply 3 × 5 using a number line.
Starting from zero, three groups of 5 equal intervals need to be formed on the number line. This way we will reach 15 forming 3 individual groups. Observe the following number line that shows 3 × 5 = 15.
Representing Multiplication of Numbers on Number Line
On a number line, integers are marked at equal intervals and are categorized as positive numbers and negative numbers. The origin is 0 (zero), which stands in the middle of the number line. To the right of the origin, there are positive numbers and to the left of the origin, there are negative numbers. Hence, a number line represents integers including positive as well as negative numbers.
Multiplication of Positive Numbers on Number Line
When multiplying two or more positive numbers, there is a simple rule as it just follows simple multiplication. Since this is multiplication, we will move towards the right side of the number line. Let's solve 6 × 4. Starting from zero, six groups of 4 equal intervals need to be formed on the number line. This way we will reach 24 forming 6 individual groups.
Multiplication of Negative Numbers on Number Line
When multiplying more than two negative numbers, use the Even-Odd Rule: Count the number of negative signs. In the case of an even number of negatives, the result is positive, but for an odd number of negatives, the result is negative.
Let's consider an example. Starting from zero, seven groups of 3 equal intervals need to be formed on the number line. This way we will reach 21 forming seven individual groups. But because of the negative sign with 3, the groups will be formed towards the left of the number line.
In the case, both the numbers are negative, the result will be positive only, such as (-5) × (-2) = 10.
Related Topics
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Multiplication on Number Line Examples
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Example 1: Using a number line, determine the product, 4 × 4.
Solution:
Since this is multiplication, we will move towards the right side of the number line.
- Step 1: Start from zero.
- Step 2: Four groups of 4 equal intervals need to be formed on the number line. The first group equals the first jump from 0 to 4.
- Step 3: Similarly, the second group equals the next jump from 4 to 8. Then, the third group from 8 to 12 and then the fourth group from 12 to 16.
This way we will reach 16 forming 4 individual groups.
FAQs on Multiplication on Number Line
What Is Multiplication of Numbers on Number Line?
Multiplication on a number line is the application of multiplication operation on a given set of numbers on a number line. For example, 8 × 2. Starting from zero, eight groups of 2 equal intervals need to be formed on the number line. This way we will reach 16 forming 8 individual groups.
What Are the Rules for the Multiplication of Integers on Number Line?
Given below are the rules for the multiplication of integers on a number line.
- Positive number × Positive number = Positive number
- Negative number × Negative number = Positive number
- Negative number × Positive number = Negative number
- Positive number × Negative number = Negative number
How To Multiply Numbers on a Number Line?
To multiply numbers using a number line we start from zero and move towards the right side of the number line for a given number of times. Let us consider an example. Multiply 4 × 3 using a number line. Since this is multiplication, we will move towards the right side of the number line. Starting from zero, four groups of 3 equal intervals need to be formed on the number line. This way we will reach 12 forming 4 individual groups. Observe the following number line that shows 4 × 3 = 12.
What Is 8 Times 1/2 on a Number Line?
On a number line, start from 0, jump from 0 to midway between 0 and 1 which represents 1/2. Starting from zero, eight groups of 1/2 equal intervals need to be formed on the number line. This way we will reach 4 forming 8 individual groups.