# The Standard Multiplication Algorithmwith a Two-Digit Multiplier

You have learned to calculate multiplications such as 67 × 54 in parts.
You did two multiplications and then added.
It took three separate calculations.

In the usual, traditional way of multiplying there are also three separate calculations.
But this time ALL three calculations appear together.
Study 67 × 54 below.

 2       5  4 ×  6  7 3  7  8

 3   2       5  4 ×   6  7 3  7  8 3  2  4  0

 5  4 ×  6  7 3  7  8 + 3  2  4  0 3  6  1  8

First multiply  7 × 54
Pretend the 6 of
the 67 is not there.
Then multiply  60 × 54, but put the result
underneath the 378. Remember the zero.
Pretend the 7 of the 67 is not there!

Study these examples, too. Note the extra zero needed in the ones place on the second line!

5 × 34

20 × 34

 2       3  4 ×  2  5 1  7  0
 3  4 ×   2  5 1  7  0 6  8  0
 3  4 ×   2  5 1  7  0 +  6  8  0 8  5  0

4 × 63

90 × 63

 1       6  3 ×   9  4 2  5  2
 2       6  3 ×   9  4 2  5  2 5  6  7  0
 6  3 ×  9  4 2  5  2 + 5  6  7  0 5  9  2  2

1. Fill in the missing digits and complete the calculations.

 a. b. c. d. 2. Multiply.

 a. b. c. d. 3. Multiply. But first, estimate the result! Compare your final answer to your estimation. If there is a big
difference, you might have an error somewhere.

 a.  Estimate: ______ × ______     = __________ b.  Estimate: ______ × ______     = __________ c.  Estimate: ______ × ______     = __________ 5. Solve the word problems. Write a number sentence for each one.

 a.  How many eggs are in 15 dozen?     ___________________________________     Estimate: ___________________________ b. How many minutes are there in 21 hours?     ___________________________________     Estimate: ___________________________ c. The 455 pupils in a school are going to a zoo     by bus. One bus can seat 39 passengers. Are     11 buses enough to take them all?     ___________________________________     Estimate: ___________________________ d. Each month, Brenda earns \$21 from     watering the neighbor's flowers.     How much does she earn in a year?     ___________________________________     Estimate: ___________________________ 6. Multiply. Estimate the answer on the line.

 a.  51 × 19≈_________ b.  45 × 28≈_________ c.  12 × 18≈_________ d.  84 × 95 ≈_________ 7. Solve. Estimate before you calculate.

 a. Find the change, if a teacher buys 15 shirts         for \$17 each, and pays with \$300.       Estimation:  b. One year has 52 weeks. Sally pays \$98 weekly         in rent. How much will she pay in a year?        Estimation:

8. Calculate in the correct order.

 a.  60 × (10 + 20) × 2 = _________      30 × (40 – 40) × 2 = _________ b.  8 × (200 – 100) – 500 = _________      (800 – 200) × 20 + 100 = _________ Fill in the missing numbers in these multiplications:

 0 × 3 3 1 5

 6 7 × 4 0 0 2

 3 × 4 9 6

 8 4 × 5 4 7

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.

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