Multipying Multi-Digit Numbers

Key Concepts

• Multiplication with estimation for whole numbers with zeros
• Solve problems for multiplication with multi-digit number

Multiply whole numbers with zeros 

What is meant by whole numbers? 

Whole numbers are a set of numbers including all positive integers and 0.  

• Whole numbers are a part of real numbers that do not include fractions, decimals, or negative numbers.  
• Counting numbers are also considered as whole numbers. 

Example: Multiply 309 × 41 

Multiplication with estimation for whole numbers with zeros 

Estimation: 

An estimation is an approximate judgment or calculation, as of the value, amount, time, size, or weight of something. 

Example 1: 

A fruit seller, stacked 301 apples in one large basket.  He packed 34 baskets, how many apples did he pack? 

Solution: 

Step 1: Find 34 × 401. 

Estimate: 

30 × 400 = 12,000 

Step 2: 

Multiply by the ones. 

Re-group if necessary. 

Remember that multiplying with zero gives zero as the final product. 

Step 3:  

Multiply by the tens. 

Re-group if necessary. 

Add to get the final product. 

He packed 13,634 apples. 

Practice multiplying multi-digit numbers 

What is meant by multi digit numbers? 

Multi digit numbers means having more than one digit (number). 

Example: 3,456 

Multi digit numbers multiplication:  

Solve problems for multiplication with multi-digit number 

Example 1: 

Merci reads 6 fun facts every day at bedtime. How many fun facts will she read in 1,425 days? 

Solution: 

Find, 6 × 1,425 

Estimate: 

5 × 1,425 is about 5 × 1,400. 

She will read 8,550 fun facts in 1,425 days. 

Example 2: 

Charm has a tile store. She has 1,350 dozen varieties of tiles for sale. How many varieties are for sale? 

Solution: 

Find 12 × 1,350. 

Estimate 12 × 1,350 = 12 × 1300 = 15,600 

16, 200 varieties of tiles for sale.

Exercise

• Find the product. Estimate to check for reasonableness

• Estimate and then compute each product. Check that your answer is reasonable.

• Find the missing number.

• Find the missing numbers

• Determine the missing numbers

• A salesman sells 902 pieces of furniture. If he gets 23 reward points for each piece sold how many points does he earn?
• Avery says she has 105 dozen pearls for sale at her store. How many pearls are for sale?
• Robin learns 20 new words everyday. How many new words will he learn in 365 days?
• Mart’s salon givesa free goodie bag containing 10 finger rings to each customer who takes a fancy haircut. If 429 people got fancy haircuts at the shop, how many rings were given in all?
• Jack and Dwayne are preparing for their school’s winter bake sale. They have prepared 5,318  brownies. They plan on placing 24 brownies each into small bags to sell. How many bags  will they need?

What have we learned

• Understand whole numbers.
• Understand multidigit nubers.
• Understand estimation.
• Understand how to multiply whole numbers with zeros.
• Multiplication with estimation for whole numbers with zeros

Concept Map