Multiplication Table can be set to any multipliers between 3 and 20. Just click the + or - button to change the table. Use the mouse pointer or arrow keys to move from square to square and the multipliers in the top row and left column will be highlighted. You can lock and unlock the highlight by clicking the mouse.

  1. 1 2 3 1 3 2 of Example 25 in the cycle notation is written as (23). We can combine two such permutations: (12)(23) which means that we rst permute 2 and 3: 1 2 3 7!1 3 2 and then we permute 1 and 2: 1 3 2 7!2 3 1. Let us look next at the group S 3.
  2. The 3 tens to the tens column. Then multiply the tens, adding the 3 regrouped tens. Write 5 in the tens place and regroup the 1 hundred. Then multiply the hundreds, adding the regrouped hundred. Write 9 in the hundreds place.

This is a complete lesson with explanations and exercises about the standard algorithm of multiplication (multiplying in columns), meant for fourth grade. First, the lesson explains (step-by-step) how to multiply a two-digit number by a single-digit number, then has exercises on that. Next, the lesson shows how to multiply how to multiply a three or four-digit number, and has lots of exercises on that. there are also many word problems to solve.

Multiplication

The standard algorithm of multiplication is based on the principle that you already know: multiplying in parts (partial products): simply multiply ones and tens separately, and add.

However, in the standard way the adding is done at the same time as multiplying. The calculation looks more compact and takes less space than the “easy way to multiply” you have learned.

The standard way to multiply'The easy way'

1
63
× 4
2

1
63
× 4
2 52

4 × 6 + 1 = 25

Write 25 in front of the 2.
Note that 25 tens
means 250!

In the 'easy way,' we multiply in parts, and the adding is done separately.

The standard way to multiply'The easy way'

3
75
× 7
5

3
75
× 7
5 25

Multiply the ones:
7 × 5 = 35
Regroup the 3 tens.

Multiply & add the tens:
7 × 7 + 3 = 52

7 5
× 7
3 5
+ 4 9 0

5 2 5

1. Multiply using both methods: the standard one and the easy one.

a.
b.

2. Multiply using both methods: the standard one and the easy one.

a.
b.

3. Multiply. Be careful with the regrouping.

a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.


4. Solve. Also, write number sentences (additions, subtractions, multiplications) on the empty lines.

a. What is the cost of buying three chairs for $48 each?

_________________________________________________

And the cost for six chairs? ____________________________

b. You earn $77 a day. How many days do you need to work
in order to have $600 or more? Guess and check.

_________________________________________________

_________________________________________________


With a 3- or 4-digit number you have to regroup many times.

13
238
× 4
52

Multiply the ones first.

4 × 8 = 32

Write 2 in the ones
place and regroup
the 3 tens to the
tens column.

Then multiply the tens,
adding the 3 regrouped
tens.

4 × 3 + 3 = 15

Write 5 in the tens place
and regroup the 1 hundred.

4 × 2 + 1 = 9

Write 9 in the hundreds place.

1
 7 6 52
× 5
0

32 1
765 2
× 5
2 6 0

Multiply the ones:

5 × 2 = 10

Write 0 in the ones
place and regroup
the 1 ten.

Then the tens. Add
the regrouped ten:

5 × 5 + 1 = 26

Write 6 in the tens
place and regroup
the 2 hundreds.

Multiply the
hundreds.

5 × 6 + 2 = 32

Write 2 in the
hundreds place,
and regroup the
3 thousands.

Multiply the thousands:

5 × 7 + 3 = 38

Write 38 in front of
the 260.

5. Multiply using both methods: the standard one and the easy one.

a.


b.
c.



6. Multiply using the standard method.

a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.

7. Solve the word problems. Also, write number sentences (additions, subtractions,
multiplications) to show what you calculate.

Permute 3 1 9 Multiplication Tables

a. The school has 304 students. To go to
the museum, they hired buses which can
each seat 43 passengers. How many buses
did they need?
Hint: Guess and check.
b. The school also has 24 teachers. How many
seats were left empty in those buses when all
the students and all the teachers joined the trip?

This old video of mine below also also explains how to teach the multiplication algorithm. At first, the video goes through the partial products algorithm (multiplying in parts), and then explains the standard multiplication algorith (as in the lesson on this page).


This lesson is taken from Maria Miller's book Math Mammoth Multiplication 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

Math Mammoth Multiplication 2

A self-teaching worktext for 4th grade that covers multiplying by whole tens and hundreds, multi-digit multiplication in columns, order of operations, word problems, scales problems, and money problems.

Download ($5.10). Also available as a printed copy.


  • Place Value

Calculator Use

Multiplication of positive or negative whole numbers or decimal numbers as the multiplicand and multiplier to calculate the product using long multiplication. The solution shows the work for the Standard Algorithm.

2
6
2
5
2
6
1
2

How To Do Long Multiplication

Long multiplication means you're doing multiplication by hand. The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. These are the steps to do long multiplication by hand:

  1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.
  2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number
  3. Write the answer below the equals line
  4. If that answer is greater than nine, write the ones place as the answer and carry the tens digit
  5. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.
  6. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.
  7. Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.
  8. When you finish multiplying, draw another answer line below your last row of answer numbers.
  9. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.

Long Multiplication with Decimals

Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow.

  1. Count the total number of decimal places contained in both the multiplicand and the multiplier.
  2. Ignore the decimals and right align the numbers one on top of the other as if they were integers
  3. Multiply the numbers using long multiplication.
  4. Insert a decimal point in the product so it has the same number of decimal places equal to the total from step 1.

Example Long Multiplication with Decimals

Multiply 45.2 by 0.21

There's 3 total decimal places in both numbers.

Ignore the decimal places and complete the multiplication as if operating on two integers.

4
2
1
4
2
0
4
2

Rewrite the product with 3 total decimal places.

Answer = 9.492

Therefore: 45.2 × 0.21 = 9.492

Long Multiplication with Negative Numbers

When performing long multiplication you can ignore the signs until you have completed the standard algorithm for multiplication. Once you complete the multiplication follow these two rules:

  1. If one number is positive and one number is negative make the product negative.
  2. If both numbers are negative or both numbers are positive make the product positive.

Long Multiplication Example: Multiply 234 by 56

Long Multiplication Steps:
Stack the numbers with the larger number on top. Align the numbers by place value columns.

Multiply the ones digit in the bottom number by each digit in the top number
6 × 4 = 24
Put the 4 in Ones place
Carry the 2 to Tens place

2
4
6
4

6 × 3 = 18
Add the 2 that you carried = 20
Put the 0 in the Tens place
Carry the 2 to the Hundreds place

2
2
4
6
4


6 × 2 = 12
Add the 2 that you carried = 14
This is the last number to multiply so write the whole number answer. No need to carry the 1.

2
2
4
6
4
4

Move one place to the left. Multiply the tens digit in the bottom number by each digit in the top number.
5 × 4 = 20
Add a row to your multiplication answer
When you write your answer, shift one column to the left
Put the 0 in Ones place
Carry the 2 to Tens place

2
4
6
4
4

5 × 3 = 15
Add the 2 that you carried = 17
Put the 7 in the Tens place
Carry the 1 to the Hundreds place

1
2
4
6
4
4
7

Permute 3 1 9 Multiplication Tables Worksheets Pdf



5 × 2 = 10
Add the 1 that you carried = 11
This is the last number to multiply so write the whole number answer. No need to carry the 1.

1
2
4
6
4
4
1
7


Add the numbers in the columns using long addition
4 + 0 = 4
0 + 0 = 0
4 + 7 = 11
write the 1 and carry 1
1 + 1 + 1 = 3

Once you add the columns you can see the long multiplication result: 234 × 56 = 13104.

2
4
6
4
4
1
7
1
1
4

Related Calculators

If you need help with long addition see our Long Addition Calculator to add numbers by long addition and see the work.

For long division see the Long Division Calculator to divide numbers by using long division with remainders. This calculator also shows the work.

If you need to multiply fractions visit our Fractions Calculator. You can do fraction multiplication, addition, subtraction and division here.

References

Math is Fun shows examples of Long Multiplication in an animated video.

Long multiplication is an algorithm and you can find examples of multiplication algorithms at Wikipedia.

Goodman, Len. 'Long Multiplication.' From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/LongMultiplication.html

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