Sunday, December 19, 2010

How do you teach long multiplication?

How to do long multiplication with decimals?


Decimal values are used to symbolize fraction numbers. In the multiplication with decimals are writing exclusive of a fraction having denominator and denominator. Decimal values are might be greater than 1 or less than 1. For the model, the fraction 4/10 might be written as the decimal value as 0.4 and marked as four tenths or zero point four. The decimal of 45/10 is 4.5 which can be marked as four and five tenths. In this article we shall discuss about multiplication with decimals.

Sample Problem for Multiplication with Decimals:

To multiply decimals, we require the following steps.
         • Multiplying the two values with null decimal point.
         • Once we obtain the final answer, make sure to design the decimal point.
         • Number of digits at the back the decimal point in the outcome will be equivalent to the total number of digits after the decimal point in the two numbers being multiplied.
Pro 1:  Solving the decimal multiply for the given values 0.04 by 1.6     
Sol :    Start with: 0.04 x 1.6
            Multiply without decimal points: 4x 16 = 72
            0.04 has 2 decimal places, and 1.6 has 1 decimal place.
            So the answer has 3 decimal places: 0.072
Pro 2:  Solving the decimals multiply for the given values 0.08 by 3.2    
Sol :    Start with: 0.08 x 3.2
            Multiply without decimal points: 8 x 32 = 256
            0.08 has 2 decimal places, and 3.2 have 1 decimal place.
            So the answer has 3 decimal places: 0.256
Pro 3:  Solving the decimals multiply for the given values 0.03 by 2.8    
Sol :    Start with: 0.03 x 2.8
            Multiply without decimal points: 3 x 28 = 84
            0.03 has 2 decimal places, and 2.8 have the 1 decimal place.
            So the answer has 3 decimal places: 0.084
Pro 4 :  Solving the decimals multiply for the given values 0.06 by 4.8    
Sol :   Start with: 0.06 x 4.8
            Multiply without decimal points: 4 x 48 = 288
            0.06 has 2 decimal places, and 4.8 have the 1 decimal place.
            So the answer has 3 decimal places: 0.288

Practice Problem for Multiplication with Decimals:

Solving the decimals multiply for the given values 0.12 by 5.3
Ans : 0.636
Solving the decimals multiply for the given values 0.16 by 7.8
Ans : 1.248
 Marvelous Multiplication: Games and Activities that Make Math Easy and Fun
Marvelous Multiplication: Games and Activities that Make Math Easy and Fun 


Long multiplycation: 27 multiply 43?









Teaching long multiplication to children

How to do long multiplication step by step?

Long multiplication extends tables work so that numbers bigger than 10 can be multiplied without using a calculator. There are a number of ways to do this.

The traditional method is demonstrated in the example below. This method is very versatile and can handle decimals as well as whole numbers. In the box on the right you can enter your own multiplications. Watch as the solution unfolds step by step.

Let's look at doing the sum 12 × 394, which was randomly generated when you loaded the page.
Of course, we could simply keep adding 394s together until we have 12 lots of 394, but that could take a very long time. Instead, we use the following method:

Step 1: Set the multiplication out as follows.


394
×

12

Note that the number with the smaller number of digits goes at the bottom.
Step 2: Multiply 394 by 2.


394
×

12



788
The result of 2 × 394 is shown in bold.
Step 3: Next, multiply 394 by 10. This is the same as multiplying 394 by 1 and by 10. We place a zero to the right and then write down the result of 1 × 394.


394
×

12



788

3940

The result of 1 × 394 is shown in bold and the additional zero has been shown in blue.
Step 4: Finally, add these two rows together to give the final answer.


394
×

12



788

3940


4728

The final answer for 12 × 394 is 4728.

These techniques can be extended to numbers with any number of digits and to numbers involving decimals. For example, if the sum were 1.2 × 3.94, notice that there are 3 digits after the decimal point in total in the sum.
The answer would also have three digits after the decimal point, so instead of 4728,
1.2 × 3.94 = 4.728
Using the same rules for numbers with decimal points:
1.2 × 39.4 = 47.28
12 × 3.94 = 47.28
1.2 × 0.394 = 0.4728

If you refresh this page or press F5, a different long multiplication will be generated. We suggest you try this a number of times and then enter your own in the box on the right until you are familiar with the method.
Let's look at doing the sum 39 × 164, which was randomly generated when you loaded the page.
Of course, we could simply keep adding 164s together until we have 39 lots of 164, but that could take a very long time. Instead, we use the following method:
Step 1: Set the multiplication out as follows.


164
×

39

Note that the number with the smaller number of digits goes at the bottom.
Step 2: Multiply 164 by 9.


164
×

39


1476
The result of 9 × 164 is shown in bold.
Step 3: Next, multiply 164 by 30. This is the same as multiplying 164 by 3 and by 10. We place a zero to the right and then write down the result of 3 × 164.


164
×

39


1476

4920

The result of 3 × 164 is shown in bold and the additional zero has been shown in blue.
Step 4: Finally, add these two rows together to give the final answer.


164
×

39


1476

4920


6396

The final answer for 39 × 164 is 6396.

These techniques can be extended to numbers with any number of digits and to numbers involving decimals. For example, if the sum were 3.9 × 1.64, notice that there are 3 digits after the decimal point in total in the sum.
The answer would also have three digits after the decimal point, so instead of 6396,
3.9 × 1.64 = 6.396
Using the same rules for numbers with decimal points:
3.9 × 16.4 = 63.96
39 × 1.64 = 63.96


Source: Mark Riedel, mathsonline.org

Teaching long division with 2 digit quotient

How to do Long division tricks for kids?

"In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving arbitrarily large numbers to be performed by following a series of simple steps"


Solution for 742 ÷ 31 - with remainder

Step 1

Long division works from left to right. Since 31 will not go into 7, a grey 0 has been placed over the 7 and we combine the first two digits to make 74. Note the other digits in the original number have been turned grey to emphasise this.
The closest we can get to 74 without exceeding it is 62 which is 2 × 31. These values have been added to the division, highlighted in red.

02
 rem 29

31742

62

31 × table
1 × 31 =31
2 × 31 =62
3 × 31 =93
4 × 31 =124
5 × 31 =155
6 × 31 =186
7 × 31 =217
8 × 31 =248
9 × 31 =279

Step 2

Next, work out the remainder by subtracting 62 from 74. This gives us 12. Bring down the 2 to make a new target of 122.

2
 rem 29

31742

62

122

31 × table
1 × 31 =31
2 × 31 =62
3 × 31 =93
4 × 31 =124
5 × 31 =155
6 × 31 =186
7 × 31 =217
8 × 31 =248
9 × 31 =279

Step 3

With a target of 122, the closest we can get is 93 by multiplying 31 by 3. Write the 93 below the 122 as shown.

23 rem 29

31742

62

122

93

31 × table
1 × 31 =31
2 × 31 =62
3 × 31 =93
4 × 31 =124
5 × 31 =155
6 × 31 =186
7 × 31 =217
8 × 31 =248
9 × 31 =279

Step 4

Finally, subtract 93 from 122 giving 29. Since there are no other digits to bring down, 29 is therefore also the remainder for the whole sum.
So 742 ÷ 31 = 23 rem 29

23 rem 29

31742

62

122

93

29

31 × table
1 × 31 =31
2 × 31 =62
3 × 31 =93
4 × 31 =124
5 × 31 =155
6 × 31 =186
7 × 31 =217
8 × 31 =248
9 × 31 =279

Long division traditional method

Step by step long division for kids

How to explain long division to children?

Solution for 531219 ÷ 579 - with remainder

Step 1

Long division works from left to right. Since 579 will not go into 5, a grey 0 has been placed over the 5 and we combine the first two digits to make 53. In this case, 53 is still too small. A further 0 is added above 3 and a third digit is added to make 531. Note the other digits in the original number have been turned grey to emphasise this.
The closest we can get to 531 without exceeding it is 5211 which is 9 × 579. These values have been added to the division, highlighted in red.

0009

 rem 276

579531219

5211

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211



Step 2

Next, work out the remainder by subtracting 5211 from 5312. This gives us 101. Bring down the 1 to make a new target of 1011.

9

 rem 276

579531219

5211

1011

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211






Step 3

With a target of 1011, the closest we can get is 579 by multiplying 579 by 1. Write the 579 below the 1011 as shown.

91
 rem 276

579531219

5211

1011

579

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211




Step 4

Next, work out the remainder by subtracting 579 from 1011. This gives us 432. Bring down the 9 to make a new target of 4329.

91
 rem 276

579531219

5211

1011

579

4329

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211



Step 5

With a target of 4329, the closest we can get is 4053 by multiplying 579 by 7. Write the 4053 below the 4329 as shown.

917 rem 276

579531219

5211

1011

579

4329

4053

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211


Step 6

Finally, subtract 4053 from 4329 giving 276. Since there are no other digits to bring down, 276 is therefore also the remainder for the whole sum.
So 531219 ÷ 579 = 917 rem 276

917 rem 276

579531219

5211

1011

579

4329

4053

276

579 × table
1 × 579 =579
2 × 579 =1158
3 × 579 =1737
4 × 579 =2316
5 × 579 =2895
6 × 579 =3474
7 × 579 =4053
8 × 579 =4632
9 × 579 =5211

Long Division Books

Fun Math Games for Kids