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Ten is the first two-digit even number that comes after 9 and before 11. Having tenfingers and ten toes may have probably led our early mathematicians to consider ten as the base value in our decimal number system.
For some, 10 is considered as the end of a cycle and perfection. Pythagoras and hisfollowers considered 10 to be the most sacred number of all.
This is because adding numbers from 1 to 4 will be equivalent to 10 – which for them signifies existence (1), creation (2), life (3), and the elements of earth, air, fire, and water.
10 is indeed an important number in our number system – and knowing more numbers that are connected to this number can also be of great help to our lives.
Are you ready to board another journey of finding multiples of 10? Say no more as we start our flight towards this exciting expedition!
Multiples of 10 are 10, 20, 30, 40, 50, 60, 70 …
When an integer is multiplied by ten, the products are multiples of ten. A multiple of 10 is a sequence in which the difference between its consecutive numbers is 10.
Multiples of 10 can also mean that every time a number is divided by 10, it will always result to a zero remainder. We can acquire a positive multiple of 10 by simply multiplying 10 to any positive number.
Similarly, multiplying 10 to any negative integer yields a negative multiple of 10. Remember that fractions cannot be utilized to generate a multiple of 10 because a whole number is required.
There is an endless number of multiples of ten. However, its factor will always be finite. There are only four exact factors of 10, which are 1, 2, 5, and 10. On the other hand, the multiples of 10 are 10, 20, 30, 40, 50… and so on.
Now, let’s take a look at this table.
All multiples of 10 are also multiples of 2 and 5, such as 10, 20, 30, 40, 50, etc.
2, 4, 8, 14, 16, and so on are all multiples of two but not multiples of ten.
Some of the multiples of 5 that are not multiples of 10 are 5, 15, 25, 35, 45… and so on.
The table above shows that even though all multiples of 10 are also a multiple of 2 and 5, it does not mean that every multiple of 2 and 5 are also multiples of 10.
Now, let’s journey further in determining the multiples of 10.
Multiples of 10 are as easy as counting 123s – and so as finding its nth multiple. We can do this by using the two previously learned methods – skip counting and multiplication!
To find the consecutive multiples of 10 through skip counting, we will start with 10. Then, to find the next multiple, we will simply add 10.
Hence, 10 + 10 = 20.
Skip counting is also referred toas repeated addition – which means, to get any multiple of 10, we will repeat adding 10 until we get to the nth we want to get.
Now, since we now know that adding two 10s will result to 20, adding another 10 will give us the result of 30.
Now, let’s look try another method in finding multiples of 10.
Multiplication is the faster way we can solve to get any multiples of a number. When we say that a number can be expressed as 10n, we are certain that it is a multiple of 10.
For example, to find the 45th multiple of 10, we will simply multiply 10 by 45. Hence, 10 x 45 = 450. This is a more convenient way than adding 10 repeatedly for 45 times.
1st multiple
10
10 x 1 = 10
2nd multiple
10 + 10 = 20
10 x 2 = 20
3rd multiple
10 + 10 + 10 = 30
10 x 3 = 30
4th multiple
10 + 10 + 10 + 10 = 40
10 x 4 = 40
5th multiple
10 + 10 + 10 + 10 + 10 = 50
10 x 5 = 50
Notice how the outcome of skip-counting and multiplication will always give the same result? This is due to the fact that both are methods in finding any multiples of 10.However, for some, they see multiplication as a quicker method.
Did you know that…Multiplying any number by multiples of ten is much easier than conventionalmultiplication? This can be done by simply copying the nth multiple we are looking for and adding the trailing 0 at the end of the number!
Multiplying any number by multiples of ten is much easier than conventionalmultiplication? This can be done by simply copying the nth multiple we are looking for and adding the trailing 0 at the end of the number!
Say, we are looking for the 9th multiple of 10. Using this method, we simply copy 9, and add 0 after 9. Thus, we have 90!
Let’s try another one! Suppose we are looking for the 25th multiple of 10. Using this technique, we have 25 – and adding 0 to it will result to 250!
It is very simple and remarkable, isn’t it?
The table displays the first 30 positive multiples of 10 as well as how it is formed. We can readily see that multiplying any number by 10 produces various multiples of 10.
Did you notice something?
If we get any multiples of 10, we will always have a result that ends with 0! This observation will help us easily determine that a number is a multiple of 10.
Now, let’s try solving real-life problems that involve multiples of 10.
Sandara decided to count all the ten-dollar bills she had. She found out that she had 20 ten-dollar bills in her wallet, 2 ten-dollar bills in her pocket, and 5 ten-dollar bills she found in her room. How much money does Sandara have?
To solve this problem, we need to find the total number of ten-dollar bills Sandara has. We can do this by adding all the ten-dollar bills she found in her wallet, pocket, and room. Thus, 20 + 2 + 5 = 27.
Then, to find the total money Sandara has, we are simply going to multiply 27 by ten dollars.
Hence, 27 x $10 = $270.
Therefore, Sandara’s total money is $270.
Now, let’s try to work on another problem.
Rexford joined a team building in their school fair. On one of the tasks, they were given a clue that they needed to answer to proceed to the next station. The clue says:
Determine the number that is being described.
What is my number?
Can you help Rexford solve their task?
To help Rexford with their task, the first thing we need to do is find the common multiple of 10 and 7. Hence, by listing all the common multiples of 7 and 10, we will have the numbers 70, 140, 210, 280, 350… and so on.
The next condition says that the number should be between 100 and 200. Thus, from the list, the only number that satisfies the given condition is 140.
Therefore, the number Rexford’s team is looking for is 140.
See… finding any multiples of ten is not as complicated as you think it was – and so is solving problems involving multiples of 10.
Are you now ready to challenge yourself more?
Which of the following is a multiple of 10?
What is the 89th multiple of 10?
890
Jeremiah is working as a freelance artist. He targets to work 10 hours a day. On his first week, Jeremiah worked for five days. The following week, he worked for six days straight. How many hours did Jeremiah work for two consecutive weeks?
110 hours
The first five multiples of 10 are 10, 20, 30, 40, and 50.
Yes, all multiples of 10 will always have a units digit of 0.
To find any multiples of 10, we simply need to multiply 10 to any integers – positive and negative integers such as 1, 2, 3, 4… and -1, -2, -3, -4…
The fifth multiple of 10 is 50.
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