Stuck on division in math class? Try these 5 "mathemagic" tricks!

Has division got you divided?

Division simply means splitting things into fair shares or equal groups, but it's easy to feel like division is a door you can't unlock.

Welcome to Mathemagics!

The good news: beyond that door is another dimension — a dimension not only of numbers and equations, but of strategies, shortcuts, and mind-bending maneuvers. It's a journey into a land where impossible calculations become simple, and numbers reveal their hidden secrets.

You can open this door with a powerful key! A few math tricks and connections will make division easier to understand.

Did you know that multiplication is like repeating addition?

In the same way, you can think of division as repeating subtraction, since it is the opposite of multiplication. So, you can just repeat subtraction to solve division problems.

Multiplying = repeating addition:

5 x 5 = 25

That's:

• 5 + 5 + 5 + 5 + 5
  OR

• 5 added five times

Dividing = repeating subtraction:

25 ÷ 5 = 5

That's:

• 25 - 5 - 5 - 5 - 5 - 5

  OR

• 5 subtracted from 25 five times

This method works well when you're dividing small numbers

When the numbers are larger, this method can become too much.For example, 272 ÷ 8:

• You'd have to subtract 8 from 272 34 times.

• That's 272 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8 - 8!

You can use multiplication to solve division problems!

Think about 2432 ÷ 8:

Let's review some key parts of a division equation:

• Dividend: the number you're dividing (2432)

• Divisor: the equal parts you're dividing it into (8)

• Quotient: the answer (?)

First,look at the first two digits of the dividend (24). We know that 8 × 3 = 24, so the first digit in the quotient is going to be 3.

Next, move to the leftover digits (32). Since 8 × 4 = 32, the next digit in the answer becomes 4.

Because there are no tens left over between 24 and 32, place a 0 in the tens place of the quotient. So:

2432 (dividend) ÷ 8 (divisor) = 304 (quotient)

You can check your answer by multiplying: 304 × 8 = 2432

This strategy shows how division is the opposite of multiplication. If you recognize multiplication facts in the dividend, you can figure out the digits of the quotient.

You can even use it for more difficult equations

Think about 200 ÷ 60:

• You can think "60 x ? = 200" (What number, when multiplied by 60, equals 200?)

• You know that 60 x 3 = 180, and 60 x 4 = 240.

• So, you know the answer lies somewhere between 60 x 3 and 60 x 4.
  

The answer is actually a decimal (3.333), but you can get close to the answer with this method.

3. Connect the Dots

Watch this video to learn how to connect the dots to solve a division problem:

As shown in the video:

• Draw the same number of dots under each number in the dividend.

• Connect the dots using the numbers in the divisor.

• Count the number of times you started a group in each column. This becomes your quotient.

4. Draw Lines and Group Them

If you don't like dots, try drawing lines!

As shown in the video:

1. Draw a chart. Each digit in the dividend gets its own row. For example, if the dividend is 9426, it has 4 digits. So, draw 4 rows in the chart, and put each digit to the left of its row, in order.

2. Next, draw some lines! Draw a line for each number in the digit for that row (draw 9 lines for the first row, 4 in the next row, etc.).

3. Group the lines according to the divisor. If the divisor is 3, draw circles around every group of 3 in each row.

4. Count the number of groups of 3 you have — this becomes your quotient.

5. Repeat 1 & 2 above for the next number. If you have leftovers, add them to the next number in the row.

6. Repeat 1 - 5 for each number in the dividend.

5. Or...Do Both with the Japanese Method!

As shown in the video:

• Draw the same number of horizontal lines as the divisor.

• Draw vertical lines, then a dot where they connect, until you have the first number in the dividend.

• Count the number of groups of vertical/horizontal lines with dots for the quotient.

Now it's your turn to try out these tips to solve division problems!

For more tips on how to solve division problems, check out these Bytes!