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# 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.

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