Multiplication Using Number Lines (Step-by-Step with Examples)

What Does Multiplication on a Number Line Mean?

Multiplication on a number line means showing multiplication as repeated addition using equal jumps on a number line.

When we multiply two numbers, we make equal jumps on the number line. The total distance covered after all the jumps gives the product.

The number line can be used for multiplication.

Let us multiply 1-digit number using a number line.

For multiplying on the number line, we do skip counting.

For example, if we start from 0 and skip count in 2s, we will get 2, 4, 6, 8, 10 and so on, as shown on the number line below.

Now, let us multiply 6 by 3 on the number line.

Multiplying 6 by 3 means '6 times 3'. So we need to skip count six times in 3s.

So, we see that 6 x 3 = 18.

Solved Examples of Multiplication Using Number Lines:

1. (a) Let us multiply 2 by 5 using a number line.

Take 5 jumps of 2 steps each. Where do we reach?

Start from 0. Take 5 jumps of 2 steps each. We reach 10.

2 + 2 + 2 + 2 + 2 = 10

or, 5 × 2 = 10

Now, take 2 jumps of 5 steps each. Where do we reach?

Start from 0. Take 2 jumps of 5 steps each. We again reach 10.

5 + 5 = 10

or, 2 × 5 = 10

The answer in multiplication is called the product.

So, 10 is the product of 2 and 5.

(b) Let us now multiply 2 and 10 on a number line.

Start from 0. Take 10 jumps of 2 steps each. You reach 20.

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 20

or, 10 × 2 = 20

Start from 0. Take 2 jumps of 10 steps each. You again reach 20.

10 + 10 = 20

or, 2 × 10 = 20

10 × 2 = 20 and 2 × 10 = 20

or, 10 × 2 = 2 × 10 = 20

So, 20 is the product of 2 and 10.

2. Flippy wants to reach the pond. He jumps 3 steps each time.

4 jumps of 3 equal to 12

So, 4 × 3 = 12

3. Let us multiply 2 by 6.

Start from 0 and mark 6 groups of 2's to the right of 0. Then make 6 moves of 2 each as shown above. We reach at 12.

So, 2 × 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

4. 

How many jumps are made by the frog?

How big is each jump?

We can write 2 + 2 + 2 = 6 or 3 × 2 = 6.

5. Now, observe the following.

Start at 0.

Hop 3, two times.

Stop at 6.

3 + 3 = 6

2 threes equal 6

2 times 3 equals 6

2 × 3 = 6

5. Look at the multiplication on a line:

Start at 0.

Hop 2, eight times.

Stop at 6.

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 6.

8 times 2 equals 6.

8 × 2 = 6.

6. What Is Multiplication on a Number Line?

Start at 0.

Hop 5, four times.

Stop at 20.

5 + 5 + 5 + 5 = 20.

4 fives equal 20.

4 times 5 equals 20.

4 × 5 = 20.

Remember: Changing the order of numbers being multiplied does not change the product. This means that the product remains the same even if the order of the numbers is changed.

More Example:

(i) If 2 × 10 = 20, then 10 × 2 = 20

(ii) If 5 × 2 = 10, then 2 × 5 = 10

(iii) If 2 × 4 = 8, then 4 × 2 = 8

(iv) If 3 × 10 = 30, then 10 × 3 = 30

(v) If 5 × 3 = 15, then 3 × 5 = 15

(vi) If 3 × 4 = 12, then 4 × 3 = 12

Note:

Multiplication on a number line is repeated addition shown by equal jumps.

Number of jumps = First factor

Size of each jump = Second factor

Landing point = Product

For example:

(a) 3 × 4 = 12 → 3 jumps of 4

(b) 6 × 2 = 12 → 6 jumps of 2

(c) 4 × 5 = 20 → 4 jumps of 5

This visual method makes multiplication easy and fun for every learners.

Why Use a Number Line for Multiplication?

A number line helps students:

• Understand multiplication as repeated addition.
• Visualize equal groups.
• Learn multiplication facts more easily.
• Build a strong foundation before learning larger multiplication problems.

Multiplication of Whole Numbers on Number Line

4. Using the number line, write the whole number which is a product of 2 and 3. Since multiplication is repeated addition, therefore, to evaluate 2 × 3, first start from 0, move 2 units at a time to the right making 3 such moves to obtain 6, as shown in the following figure.

Hence, 2 × 3 = 6.

🎯 Multiplication Using Number Lines Quiz Game:

Practice Worksheet on Multiplication on the Number Line:

1. Multiplication using Number Lines.

(i)

2 × 4 = __________

(ii)

4 × 2 = __________

2. Multiply on the number line. One has been done for you.

(i) 

4 × 5 = 20

(ii)

3 × 2 = _____

(iii)

7 × 1 = _____

(iv)

5 × 3 = _____

3. Multiplication on the Number Lines

(i) Show 2 × 4 on a number line.

(ii) Show 3 × 5 on a number line.

(iii) Show 4 × 6 on a number line.

(iv) Show 5 × 3 on a number line.

(v) Show 7 × 2 on a number line.

Answer Key:

(i) 8

(ii) 15

(iii) 24

(iv) 15

(v) 14

Multiplication Using Number Lines Worksheet

Frequently Asked Questions on Multiplication Using a Number Line:

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Related Pages:

• Concept of Multiplication
• Facts about Multiplication
• Multiplication of Whole Numbers
• Number Line

2nd Grade Math Practice

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