#### Need Help?

Get in touch with us

# Multiply 3 Digit by 2 Digit Numbers

## Key Concepts

• Use partial products
• Use the standard algorithm

## What are the 3-digit numbers?

100 to 999 are the 3-digit numbers.

100 is the smallest 3-digit number.

999 is the largest 3-digit number.

### How to multiply a 3-digit number with a 2-digit number?

1. Multiply by the number in the ones place.
1. Put a zero below in the ones place.
1. Multiply by the number in the tens place.

For example, 324 × 46

## Use partial products

Example 1:

In an auditorium, there are 493 rows with 14 seats in each row. How many seats are available?

Solution:

Multiply 493 × 14

6, 902 seats are available.

Example 2:

Lenin bought a school bag. A bag cost is \$ 236. Find the cost of 47 such bags?

Solution:

Multiply 236 × 47

47 bags cost \$11,092.

### Use the standard algorithm

Example 1:

Charmin took her 735 students to the cricket stadium. Admission for each student was \$24. What was the total amount of money needed?

Solution:

Step 1: To use the standard algorithm, first multiply by the ones, regroup as needed.

4 × 5 ones= 20 ones or 2 tens

4 × 3 tens = 12 tens

12 tens + 2 tens = 14 tens.

14 tens = 1 hundred 4 tens.

4 × 7 hundred = 28 hundreds.

28 hundred + 1 hundred = 29 hundred.

Step 2: Multiply by the tens regroup as needed.

20 × 5 ones =100 ones

20 × 3 tens = 60 tens or 6 hundred.

20 × 7 hundreds = 140 hundreds or 14 thousand.

Step 3: Add to get the final product

\$17, 640 amount was needed.

Example 2:

Robert ordered 134 boxes of magnetics. There were 35 magnetic balls in each box. How many magnetic balls did he order?

Solution:

Step 1: To use the standard algorithm, first multiply by the ones, regroup as needed.

5 × 4 ones= 20 ones or 2 tens

5 × 3 tens = 15 tens

15 tens + 2 tens = 17 tens.

17 tens = 1 hundred 7 tens.

5 × 1 hundred = 5 hundreds.

5 hundred + 1 hundred = 6 hundred.

Step 2: Multiply by the tens regroup as needed.

30 × 4 ones =120 ones

30 × 3 tens = 90 tens or 9 hundred.

30 × 1 hundreds = 30 hundreds or 3 thousand.

3 thousand +1 thousand = 4 thousands.

Step 3: Add to get the final product.

Step 3: Add to get the final product.

He ordered 4,690 magnetic balls.

## Exercise

a.       3 1 5                                                 b.       4 9 6

× 7 7                                                            × 1  6

_________                                                         _________

_________                                                         _________

• Use partial products to find the product.

a.     8 6 7                                                 b.       5 4 8

× 6 3                                                            × 8  6

_________                                                         _________

_________                                                         _________

• Use standard algorithm model to find the product.

a.     9 9 1                                                 b.       5 4 0

× 4 4                                                            × 5  1

_________                                                         _________

_________                                                         _________

• Determine the missing digit in the following multiplication.

a.     3 8 2

× __ 4

_________

16,808

_________

• Determine the missing digit in the following multiplication.
• Find the product. Estimate to check for reasonableness.

a.     3 7 2

× 4 3

_________

_________

• Last month bakery sold 345 boxes of cupcakes. Each box has 15 cupcakes. How many cakes did the store sell in the last month? Find 15 x 345.
• Sally shoots an arrow 130 yards. Flame shoots her arrow 12 times as far. How far did  Flame’s arrow go
• Mother bought 35 large packets of spearmint bubble gum. If each packet contains pieces, how many pieces are there altogether?
• Laura sells home-made pizza sauce. If she uses 19 tomatoes to make one jar of sauce, how  many tomatoes do she need to make 115 jars?

### What have we learned

• Understand 3 digit numbers.
• Understand partial products.
• Multiplying 3-digit number by 2 digit numbers through partial product model.
• Identify the partial products.
• Multiplying 3-digit number by 2 digit numbers through standard algorithm model.

### Concept Map

#### Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […] #### Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem?  Right Angle Triangles A triangle with a ninety-degree […] #### Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]   