Division, while a fundamental arithmetic operation, can sometimes be challenging, especially when dealing with large numbers or complex equations. However, armed with a few clever tricks and techniques, division can become remarkably easier and more manageable.
In this article, we delve into division hacks designed to simplify calculations and boost your mathematical calculations.
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What is Division?
Division is a mathematical operation used to distribute a quantity into equal parts or to find out how many times one number (the divisor) is contained within another number (the dividend). The result of division is called the quotient.
The formula for division is: Quotient = Divisor/Dividend​
For example: 10/2=5
In this example,
- Dividend = 10
- Divisor = 2
- Quotient = 5
This means that 10 divided by 2 equals 5.
Easy Division Tricks
Here are easy division tricks to fasten your calculation:
Use Divisibility Test
Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
Example: 246 (Last digit is 6, so it's divisible by 2)
Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
Example: 123 (1+2+3 = 6, which is divisible by 3)
Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Example: 548 (Last two digits form 48, which is divisible by 4)
Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5.
Example: 735 (Last digit is 5, so it's divisible by 5)
Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
Example: 210 (Divisible by both 2 and 3)
Divisibility by 7: A number is divisible by 7 if the difference between twice the unit digit and the rest of the number is divisible by 7.
Example: 434 (2·4 = 8, 43 - 8 = 35, which is divisible by 7)
Divisibility by 8: A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Example: 1,024 (Last three digits form 024, which is divisible by 8)
Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Example: 1,341 (1+3+4+1 = 9, which is divisible by 9)
Divisibility by 10: A number is divisible by 10 if its last digit is 0. Example: 560 (Last digit is 0, so it's divisible by 10)
Divisibility by 11: A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is divisible by 11.
Example: 5,027 (Odd places: 5+7=12, Even places: 0+2=2, 12-2=10, which is divisible by 11)
Multiplication Facts as Division Shortcuts
Using multiplication facts as division shortcuts is handy trick. This approach taps into the concept that division is essentially the reverse of multiplication. By mastering your multiplication tables, you can effortlessly apply them to solve division problems.
For example, let's consider the division problem 56 ÷ 8. If you recall that 8 times 7 equals 56, you can promptly deduce that 56 divided by 8 is 7. This demonstrates how familiarity with multiplication facts can serve as effective math division tricks, simplifying division tasks for learners of all ages.
'10s', '100s', and '1000s' Division Trick
When faced with dividing large numbers by 10, 100, or 1000, it might appear daunting at first. However, there's a simple trick that involves shifting the decimal point. This method is incredibly practical, offering a straightforward way to divide large numbers without getting tangled in complex calculations.
For instance, let's say you need to divide 5,000 by 100. Rather than laboriously working through the problem step by step, you can employ the trick of moving the decimal point two places to the left (since you're dividing by 100). Thus, 5,000 becomes 50.00. By discarding the extra zeros, you're left with 50.
Doubling and Halving Division Trick
Here's a simple trick to make division easier, especially with big numbers that might seem hard at first. You just need to double one number and halve the other. Even though the numbers change, the overall answer stays the same.
Example: Let's divide 120 by 6 using this trick.
Here's how to do it:
- Double the number you're dividing by (the divisor). So, double 6 to get 12.
- Halve the number you're dividing into (the dividend). So, halve 120 to get 60.
Now, instead of dividing 120 by 6, you divide 60 by 12.
60/12 = 5
This trick helps make the math easier, especially when the numbers are big. Just remember to double one number and halve the other, and you're good to go!
Reciprocals and Inverse Operations
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Understanding reciprocals and inverse operations can be helpful math division tricks, especially when kids start dealing with fractions and more complicated numbers. The reciprocal of a number is just 1 divided by that number. Using reciprocals can turn division into multiplication, which many students find simpler.
Example: Suppose you need to divide 1 by 3 (written as 1 ÷ 3). Instead of division, you can multiply 1 by the reciprocal of 3. The reciprocal of 3 is 1/3. So, you do 1 × 1/3, which equals 1/3. This method provides an easy way to divide, especially when working with fractions, by changing division problems into multiplication ones.
Solved Questions on Math Division Tricks
Question 1: Determine if 729 is divisible by 9.
Solution:
According to the divisibility rule of 9, a number is divisible by 9 if the sum of its digits is divisible by 9. For 729, 7+2+9=187+2+9=18, which is divisible by 9. Therefore, 729 is divisible by 9.
Question 2: Is 3,240 divisible by 6?
Solution:
A number is divisible by 6 if it's divisible by both 2 and 3. Since 3,240 is even (ends with a 0), it's divisible by 2. To check if it's divisible by 3, we add its digits: 3+2+4+0=93+2+4+0=9. Since 9 is divisible by 3, 3,240 is divisible by 6.
Question 3: Determine if 840 is divisible by 8.
Solution:
For a number to be divisible by 8, the last three digits should form a number divisible by 8. In this case, the last three digits of 840 are 840, which is divisible by 8. Hence, 840 is divisible by 8.
Practice Questions on Math Division Tricks
- Is 5,862 divisible by 9?
- Determine if 2,178 is divisible by 3.
- Check if 4,320 is divisible by 8.
- Is 2,673 divisible by 6