Multiplication of Numbers Using the Number Line
There are three friends: Sam, Rob, and Zoe. They start counting their total number of fingers. Sam counted 1, 2, 3,…10 fingers in total on two hands.
Rob and Zoe also counted their fingers. There were 10 fingers for each friend.
So, how many fingers are there in total?
Sam’s fingers + Rob’s fingers + Zoe’s fingers
This implies, 10 + 10 + 10 = 30
So, the three friends have a total of 30 fingers.
This is one way of calculating the number of fingers, but you may wonder if there is an easier method. Well, there is. It is known as multiplication.
Using multiplication, we can easily find the total number of fingers without counting every finger.
What is Multiplication?
Multiplication is an easy operation that gives the total number of objects when we combine equal groups. In addition, multiplication is the repeated summation of the same things. If you take a number and add it repeatedly for some time, then the answer of the summation gives the product, also called the multiplication product. For example, we can add 6 four times repeatedly.
6 + 6 + 6 + 6 = 6 × 4 = 24
Here, ‘x’ is the symbol of multiplication.
Certain terms are used to multiply two numbers using a number line:
Counters: Counters are the number of single objects in a group. For example, if there are 8 balls in each group, it would imply that there are 8 counters in a group.
Equal groups: Equal groups are the ones having the same number of counters.
Skip count:
If a monkey starts from 0 and jumps 5 numbers each time, he will reach 5, 10, 15,… This is called skip counting. In other words, if we count numbers while skipping certain numbers, we are skipping counting.
Multiplication on a number line:
Steps for multiplying two numbers on a number line:
Step 1: Make a number line starting with 0.
Step 2: Look for the number of counters and groups.
Step 3: Start with jumping from 0, and the size of the jump should be equal to the number of counters.
Step 4: Jump according to the number of groups.
For example:
We can find 3 × 5 on number line:
3 × 5 means 3 groups of 5. This means the size of each jump is 5. The total number of jumps is 3.
Now, make a number line starting with 0. Start with jumping from 0. Skip count by 5 three times.
Therefore, 3 × 5 = 15
Find: 4 × 6
4 × 6 means 4 groups of 6.
Number of jumps: 4
The size of each jump: 6
Therefore, 4 × 6 = 24.
Solved Number Line Multiplication Examples
Example 1: Find: 3 × 7 using the number line.
Solution:
3 × 7 means 3 groups of 7.
Number of jumps: 3
Size of each jump: 7
Therefore, 3 × 7 = 21
Example 2: After the multiplication of two numbers on the number line, the result will be:
Find the number of groups and the size of each jump. Also, find the product of the multiplication.
Solution:
The total number of jumps is 5. And the size of each jump is 4.
Therefore,
5 × 4 = 20
Therefore, the multiplication product is 20.
Example 3: John practices math problems for 2 hours every day. How many hours does he practice in 4 days? Draw jumps and label the number line.
Solution:
John practices for 2 hours every day.
Number of days he practice = 4
Therefore, we multiply practice hours per day by the number of days to find the total practice hours.
Total practice hours = 2 × 4
Therefore, 2 × 4 = 8
John practices math problems for 8 hours over four days.
Example 4: Smith has a photo album. There are 6 pages in it. Find the total number of images if each page has 3 pictures.
Solution:
To find the total number of pictures, we multiply the number of pages by the number of pictures per page. There are 6 pages, which means there are 6 groups. And each page has 3 pictures.
So, the number of groups = 6
The size of each jump = 3
Therefore, 6 × 3 = 18
There are 18 pictures in Smith’s album.
Yes, we can multiply two numbers using number lines. To multiply numbers on the number line, start with jumping from 0. The size of the jump should be equal to the number of counters and the total jumps should be equal to the number of groups.
Draw a number line and then make jumps of equal size each time. Take note of the numbers. The obtained number will show a skip count equal to the size of the jump.
For example, if we start from 0, jump 4 numbers each time, we get the following series:
4, 8, 12, 16,…etc.
So, we obtained a skip count of the number equal to the jump size.
If we draw equal jumps on a number line, it shows a bunch of counts every time. Each bunch represents a group. For example, if there are 4 jumps of 5 counts each, it implies 4 equal groups having 5 counts each.
4 groups of 5