The Standard Multiplication Algorithm
with 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

Then add.

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

Add.

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

Add.

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.

2. Multiply.

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

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.

Learn more and see the free samples!

See more topical Math Mammoth books

Math Lessons menu

Place Value Grade 1 Using a 100-bead abacus in elementary math Teaching tens and ones Practicing with two-digit numbers Counting in groups of ten Skip-counting practice (0-100) Comparing 2-digit numbers Cents and dimes Grade 2 Three-digit numbers Comparing 3-digit numbers Grade 3 Place value with thousands Comparing 4-digit numbers Rounding & estimating Rounding to the nearest 100 Grade 4 Place value - big numbers	Add & subtract lessons Grade 1 Missing addend concept (0-10) Addition facts when the sum is 6 Addition & subtraction connection Grade 2 Fact families & basic addition/subtraction facts Sums that go over over the next ten Add/subtract whole tens (0-100) Add a 2-digit number and a single-digit number mentally Add 2-digit numbers mentally Regrouping in addition Regrouping twice in addition Regrouping or borrowing in subtraction Grade 3 Mental subtraction strategies Rounding & estimating	Multiplication Grade 3 Multiplication concept as repeated addition Multiplication on number line Commutative Multiply by zero Word problems Order of operations Structured drill for multiplication tables Drilling tables of 2, 3, 5, or 10 Drilling tables of 4, 11, 9 Grade 4 Multiplying by whole tens & hundreds Distributive property Partial products - the easy way Partial products - video lesson Multiplication algorithm Multiplication Algorithm — Two-Digit Multiplier Scales problems - video lesson Estimation when multiplying
Division Grade 3 Division as making groups Division/multiplication connection Division is repeated subtraction Zero in division Division that is not exact (remainder) Divisibility Grade 4 How to teach long division Long division as repeated subtraction Why long division works Zero in dividend Remainder & long division Two-digit divisor Review of division topics Divisibility Divisibility within 0-1000 Divisibility rules Prime factorization 1 Prime factorization 2 Sieve of Eratosthenes	Fraction Lessons Understanding fractions Finding fractional parts with division Mixed numbers Fractions to mixed numbers and vv. Adding like fractions Equivalent fractions Adding unlike fractions 1 Adding unlike fractions 2: Finding the common denominator Adding mixed numbers Subtracting mixed numbers Subtracting mixed numbers 2 Measuring in inches Comparing fractions Simplifying fractions Multiply fractions by whole numbers Multiply fractions by fractions Multiplication and area Simplify before multiplying Dividing fractions by whole numbers Dividing fractions: fitting the divisor Dividing fractions: reciprocal numbers Dividing fractions: using the shortcut	Geometry Lessons Lines, rays, and angles Measuring angles Parallel & perpendicular Acute, obtuse, and right triangles Angle sum of a triangle Equilateral & isosceles triangles Circles Symmetry Altitude of a triangle Polygons Perimeter Area of rectangles Area of right triangles Area of parallelograms Area of triangles Area versus Perimeter Angles in Polygons (PDF) Review: Area of Polygons (PDF) Surface Area (PDF)
Decimals Lessons Decimals videos Decimals (1 decimal digit) Decimal place value (1 decimal digit) Decimals (2 decimal digits) Decimal place value (2 decimal digits) Decimals (3 decimal digits) Add & subtract (1 decimal digit) Add & subtract (2 decimal digits) Add and subtract decimals — practice Comparing decimals Multiply a decimal by a whole number Multiply decimals by decimals Divide decimals—mental math Divide decimals by decimals Multiply and divide decimals by 10, 100, and 1000 Decimals review lesson	Percents Lessons How to teach proportions Percent - the basic concept Percentage of a number—mental math How to calculate a percentage of a number How to calculate percentages Basics of percent of change	General Four habits of highly effective math teaching Why are math word problems SO difficult for children? Hint: it has to do with a "recipe" that many math lessons follow. The do's and don'ts of teaching problem solving in math Advice on how you can teach problem solving in elementary, middle, and high school math. How to set up algebraic equations to match word problems Students often have problems setting up an equation for a word problem in algebra. To do that, they need to see the RELATIONSHIP between the different quantities in the problem. This article explains some of those relationships. Seven reasons behind math anxiety and how to prevent it Mental math "mathemagic" with Arthur Benjamin (video) Keeping math skills sharp in the summer Geometric vanish puzzles Science resources Short reviews of the various science resources and curricula I have used with my own children.

The Standard Multiplication Algorithmwith a Two-Digit Multiplier

Math Mammoth Multiplication 2

The Standard Multiplication Algorithm
with a Two-Digit Multiplier