4 × 3 = 12
Place 2 in the ones place,
but write the tens digit (1)
above the tens column as
a little memory note.
You are regrouping
(or carrying).
4 × 6 + 1 = 25 Write 25 in front of the 2. |
In the 'easy way,' we multiply in parts, and the adding is done separately. |
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1. Multiply using both methods: the standard one and the easy one.
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2. Multiply using both methods: the standard one and the easy one.
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3. Multiply. Be careful with the regrouping.
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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. | ||||||||
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5. Multiply using both methods: the standard one and the easy one.
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6. Multiply using the standard method.
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7. Solve the word problems. Also, write number sentences (additions, subtractions,
multiplications) to show what you calculate.
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.
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.
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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.
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:
Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow.
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.
Rewrite the product with 3 total decimal places.
Answer = 9.492
Therefore: 45.2 × 0.21 = 9.492
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:
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
6 × 3 = 18
Add the 2 that you carried = 20
Put the 0 in the Tens place
Carry the 2 to the Hundreds place
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.
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
5 × 3 = 15
Add the 2 that you carried = 17
Put the 7 in the Tens place
Carry the 1 to the Hundreds place
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.
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.
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.
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