# The Standard Multiplication Algorithm

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.

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       6  3 ×     4 2
 1       6  3 ×     4 2  5  2
 Multiply the ones: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).
 Then multiply the tens, adding the 1 ten thatregrouped. 4 × 6  +  1 = 25 Write 25 in front of the 2. Note that 25 tensmeans 250!
 6  3 ×     4 1  2 +  2  4  0 2  5  2

 In the "easy way," we multiply in parts, and the adding is done separately.
The standard way to multiply "The easy way"
 3       7  5 ×     7 5
 3       7  5 ×     7 5  2  5
 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.

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 b.

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

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 b.

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.

 3     2  3  8 ×        4 2
 1   3       2  3  8×        4 5  2

 1    3       2  3  8×        4 9  5  2

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,
tens.

4 × 3  +  3 = 15

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

Then multiply the hundreds,
hundred.

4 × 2  +  1 = 9

Write 9 in the hundreds place.

 1      7  6  5  2 ×             5 0
 2   1       7  6  5  2×             5 6  0

 3    2    1       7  6  5  2×             5 2  6  0

 3    2    1       7  6  5  2×             5  3  8  2  6  0

Multiply the ones:

5 × 2 = 10

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

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.
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 c.
 d.

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 my book Math Mammoth Multiplication 2. The lesson addresses the following Common Core standards for 4th grade: 4.OA.1, 4.OA.2, 4.OA.3, and 4.NBT.5

#### 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.