Multiplying and dividing numbers each have their own methods. The two main methods for multiplication are the grid method and the column method. The easiest method when dividing is short division (or "bus stop" method). These methods can also be applied when multiplying and dividing decimals.
Multiplication
Grid method
procedure
1.
Split up the numbers into their place values. For example: 248=200+40+8
2.
Draw a grid with these place values on the top and left of the grid.
3.
Multiply each number with the others in the grid and put the answers in the corresponding box.
4.
Add up all the numbers in the boxes.
Example 1
What is 248×35?
First, write 248 as 200+40+8, and 35 as 30+5.
Then, as 248 has three digits, and 35 has 2 digits, draw a 3×2 grid, putting the place values around the grid as shown below:
×
200
40
8
30
5
Fill in all the gaps by multiplying the numbers:
×
200
40
8
30
200×30=6000
40×30=1200
8×30=240
5
200×5=1000
40×5=200
8×5=40
Add up all the numbers in the grid:
6000+1200+1000+240+200+40=8680
248×35=8680
Column method
procedure
1.
Arrange the two numbers in a column, similar to the arrangement for column addition and subtraction.
2.
Take the digit in the ones column and multiply it by the other number, writing down the answer below.
3.
Repeat this with every digit of one of the numbers, adding the correct number of zeroes to represent the place value.
4.
Add up all the numbers that have been written as a result of multiplication.
Example 2
What is 17×34?
17×34=578
Note: In the example above, the second line of working has a zero, as you are multiplying the number 17 by 30.
Multiplying decimals
To multiply decimals, follow this procedure:
procedure
1.
Count how many digits past the decimal point both numbers have, and add these together.
2.
Multiply both numbers as if they were whole numbers (using the grid or column method if necessary).
3.
Move the decimal point to the left by the same amount of spaces as the number from the first step.
Example 3
What is 24.8×0.35?
First, 24.8 has 1 number past the decimal point, and 0.35 has 2 numbers past the decimal point. Adding these together gives 2+1=3.
Then, multiply the two numbers together as if they were whole numbers. From the first example:
248×35=8680
Lastly, move the decimal point to the left three times, giving:
24.8×0.35=8.680↶↶↶
24.8×0.35=8.68
Division
The "bus stop" method
The "bus stop" method for division goes as follows:
procedure
1.
Write the dividend (first number) under the "bus stop" and the divisor (second number) as follows: 128÷8→8)128
2.
Starting from the left-hand side of the number being divided, find how many times the divisor goes into the first digit. Write the answer on top of the line in the corresponding position.
3.
If there is a remainder, "carry over" into the column to the right of this digit. If the number cannot be divided into, read the next column as a two digit number, including the undivided digit.
4.
Repeat until the last digit has been divided. The answer is now on the top of the line.
Example 4
What is 128÷8?
128÷8=16
Dividing decimals
To divide two decimals (or a decimal and a whole number), multiply both numbers by the same power of 10 (10, 100, 1000, etc.) until both numbers are whole numbers. Then, proceed with the division as per usual.
Example 5
What is 1.28÷0.08?
Multiplying both numbers by 100 will make them whole numbers. Hence:
1.28÷0.08=(1.28×100)÷(0.08×100)
1.28÷0.08=128÷8, which was completed in the example above.
1.28÷0.08=16
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Learn with Basics
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Length:
Unit 1
Multiplying and dividing decimals by 10, 100 and 1000
Unit 2
Multiplying decimals by whole numbers
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Unit 3
Methods for multiplication and division
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FAQs - Frequently Asked Questions
How do you multiply decimals?
To multiply decimals:
1. Count how many digits are to the right of the decimal point in each number and add to get the total.
2. Remove the decimal and multiply the numbers as if they were whole numbers.
3. Move the decimal point to the left of the units digit of the answer by the same number.
How do I divide using decimals?
To divide using decimals simply multiply the dividend and divisor by the same power of 10 until both are whole numbers and divide as usual.
How do I multiply and divide using decimals?
A decimal can be expressed as a whole number divided by a power of 10. Multiplication and division with decimals can be made simpler by using whole numbers and then applying this same division at the end.
