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How to do double digit long division step by step?

How to do double digit long division step by step?

More books about long division for kids

How to do Long Division with Remainders?

When we are given a long division to do it will not always work out to a whole number. Sometimes there will be numbers left over. These are known as remainders. Taking an example similar to that on the Long Division page it becomes more clear: 435 ÷ 25. If you feel happy with the process on the Long Division

page you can skip the first bit.
 

	4 ÷ 25 = 0 remainder 4	The first number of the dividend is divided by the divisor.
		The whole number result is placed at the top. Any remainders are ignored at this point.
	25 × 0 = 0	The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into.
	4 – 0 = 4	Now we take away the bottom number from the top number.
		Bring down the next number of the dividend.
	43 ÷ 25 = 1 remainder 18	Divide this number by the divisor.
		The whole number result is placed at the top. Any remainders are ignored at this point.
	25 × 1 = 25	The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into.
	43 – 25 = 18	Now we take away the bottom number from the top number.
		Bring down the next number of the dividend.
	185 ÷ 25 = 7 remainder 10	Divide this number by the divisor.
		The whole number result is placed at the top. Any remainders are ignored at this point.
	25 × 7 = 175	The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into.
	185 – 175 = 10	Now we take away the bottom number from the top number.
		There is still 10 left over but no more numbers to bring down.
		With a long division with remainders the answer is expressed as 17 remainder 10 as shown in the diagram

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.

0 0 0 9  rem 276 579 5 3 1 2 1 9 5 2 1 1

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 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1
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.	9 1  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9
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.	9 1  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9 4 3 2 9
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.	9 1 7  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9 4 3 2 9 4 0 5 3
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	9 1 7  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9 4 3 2 9 4 0 5 3 2 7 6
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

External Link

• How to do long division step by step? (video)
• How to do long division for kids

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• How to do long division step by step?
• How to do long division with remainders?
• How do you do long division with decimals?
• Understanding long division as repeated subtraction
• Teaching Long Division
• Double Division with 3 Digit Divisors
• How to do long division with two digit quotients?
• Long Division of Polynomials Step by Step
• How to do long division with 2 digit divisor?
• How to do long division with two digit quotients?

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Posted in: Long Division

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 

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Posted in: Basic and Anvanced Math

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.

			3	9	4
	×			1	2

Note that the number with the smaller number of digits goes at the bottom.

Step 2: Multiply 394 by 2.

			3	9	4
	×			1	2
			7	8	8

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.

			3	9	4
	×			1	2
			7	8	8
		3	9	4	0

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.

			3	9	4
	×			1	2
			7	8	8
		3	9	4	0
		4	7	2	8

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.

			1	6	4
	×			3	9

Note that the number with the smaller number of digits goes at the bottom.

Step 2: Multiply 164 by 9.

			1	6	4
	×			3	9
		1	4	7	6

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.

			1	6	4
	×			3	9
		1	4	7	6
		4	9	2	0

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.

			1	6	4
	×			3	9
		1	4	7	6
		4	9	2	0
		6	3	9	6

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

3.9 × 0.164 = 0.6396


Multiplication (Flash Kids Flash Cards) 

Multiplication 0-12 Flash Cards 

Multiplication 0-12 Flash Cards 

Multiplication 0 to 12 Flash Cards (Brighter Child Flash Cards) 

Multiplication War (Flash Kids Flash Cards) 

Source: Mark Riedel, mathsonline.org

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Posted in: Basic and Anvanced Math