In this Grade 4 Saxon Math lesson from Chapter 6, students learn how to multiply three-digit numbers by a one-digit number using the standard multiplication algorithm, including how to carry digits when a partial product results in a two-digit answer. The lesson also applies this skill to multiplying dollar-and-cent amounts and using compatible numbers for mental math estimation.
Section 1
📘 Multiplying Three-Digit Numbers
When we multiply a three-digit number using pencil and paper, we multiply the ones digit first. Then we multiply the tens digit. Then we multiply the hundreds digit.
Next, you'll use this process to solve multiplication problems with three-digit numbers, including those involving money and carrying.
Section 2
Multiplying three-digit numbers
To multiply a three-digit number, you multiply in order, from right to left. First multiply the ones digit, then the tens digit, and finally the hundreds digit. If a product in any column is a two-digit number, you write the ones digit down and carry the tens digit over to the next column on the left.
Example 1: To solve , first multiply . Write down 2, carry over 1. Then, , plus the carried 1 is 10. Write down 0, carry over 1. Finally, , plus the carried 1 is 7. The answer is .
Example 2: For , start with . Write 4, carry 2. Next, , plus 2 is 20. Write 0, carry 2. Lastly, , plus 2 is 23. The final product is .
Think of it like stacking blocks, starting from the right! You handle the ones first, then the tens, then the hundreds. If a stack gets too high (more than 9), you just carry the extra bundle of ten over to the next stack. This keeps everything organized and leads you to the correct grand total.
Section 3
Multiplying money
Multiplying money, like an amount in dollars and cents, is almost identical to multiplying whole numbers. The key difference is that you must place a decimal point two places from the right in your final answer. This correctly separates the dollars from the cents, ensuring the value is accurate for currency calculations.
Example 1: To find the cost of 3 tickets at 3.75 dollars each, you calculate . Then, place the decimal two spots from the right. The total cost is 11.25 dollars.
Example 2: For 5 items at 4.25 dollars each, you calculate . Placing the decimal point two places from the right gives you a total cost of 21.25 dollars.
Multiplying money is just regular multiplication in a fancy suit! Calculate the product as if there were no decimal point. Once you have your total, place the decimal point two spots from the right. This magical dot transforms your pile of digits back into proper dollars and cents, ready for spending.
Section 4
Multiplying by 10
To multiply any whole number by 10, there is a simple and effective shortcut you can use for quick mental math. You just take the original number and place a single zero at the very end of it. This method instantly gives you the correct product without needing to perform the full multiplication process.
Example 1: To find out how many people pass through a gate in 10 minutes at a rate of 100 people per minute, you multiply . Just add a zero to 100 to get people.
Example 2: If you have 45 packs of trading cards and each pack has 10 cards, you can find the total by calculating cards.
Multiplying by 10 is like a magic trick! You don't need a calculator, just a zero. Take any number, add a zero to its right side, and voilà—you've made it ten times bigger. It is a handy shortcut that makes you look like a math wizard and works every single time for whole numbers.
Section 5
Estimate products
When an exact answer isn't necessary, you can estimate a product by using compatible numbers. A compatible number is a number that is close to the original factor but is much easier to work with, especially for mental math. Common compatible numbers are those that end in a zero or five, simplifying the calculation.
Example 1: To estimate the perimeter in feet of an area that is 256 yards, you can use the compatible number 250. Since each yard is 3 feet, you calculate feet.
Example 2: To estimate the cost of four gallons of milk at 2.47 dollars per gallon, round 2.47 dollars to 2.50 dollars. Then, multiply dollars for an approximate cost.
Why wrestle with tricky numbers when you can use their friendly neighbors? To estimate a product, swap out a difficult number for an easier, 'compatible' one nearby (like turning 256 into 250). This makes the math simple enough to do in your head, giving you a quick and reasonably close answer.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
Expand to review the lesson summary and core properties.
Section 1
📘 Multiplying Three-Digit Numbers
When we multiply a three-digit number using pencil and paper, we multiply the ones digit first. Then we multiply the tens digit. Then we multiply the hundreds digit.
Next, you'll use this process to solve multiplication problems with three-digit numbers, including those involving money and carrying.
Section 2
Multiplying three-digit numbers
To multiply a three-digit number, you multiply in order, from right to left. First multiply the ones digit, then the tens digit, and finally the hundreds digit. If a product in any column is a two-digit number, you write the ones digit down and carry the tens digit over to the next column on the left.
Example 1: To solve , first multiply . Write down 2, carry over 1. Then, , plus the carried 1 is 10. Write down 0, carry over 1. Finally, , plus the carried 1 is 7. The answer is .
Example 2: For , start with . Write 4, carry 2. Next, , plus 2 is 20. Write 0, carry 2. Lastly, , plus 2 is 23. The final product is .
Think of it like stacking blocks, starting from the right! You handle the ones first, then the tens, then the hundreds. If a stack gets too high (more than 9), you just carry the extra bundle of ten over to the next stack. This keeps everything organized and leads you to the correct grand total.
Section 3
Multiplying money
Multiplying money, like an amount in dollars and cents, is almost identical to multiplying whole numbers. The key difference is that you must place a decimal point two places from the right in your final answer. This correctly separates the dollars from the cents, ensuring the value is accurate for currency calculations.
Example 1: To find the cost of 3 tickets at 3.75 dollars each, you calculate . Then, place the decimal two spots from the right. The total cost is 11.25 dollars.
Example 2: For 5 items at 4.25 dollars each, you calculate . Placing the decimal point two places from the right gives you a total cost of 21.25 dollars.
Multiplying money is just regular multiplication in a fancy suit! Calculate the product as if there were no decimal point. Once you have your total, place the decimal point two spots from the right. This magical dot transforms your pile of digits back into proper dollars and cents, ready for spending.
Section 4
Multiplying by 10
To multiply any whole number by 10, there is a simple and effective shortcut you can use for quick mental math. You just take the original number and place a single zero at the very end of it. This method instantly gives you the correct product without needing to perform the full multiplication process.
Example 1: To find out how many people pass through a gate in 10 minutes at a rate of 100 people per minute, you multiply . Just add a zero to 100 to get people.
Example 2: If you have 45 packs of trading cards and each pack has 10 cards, you can find the total by calculating cards.
Multiplying by 10 is like a magic trick! You don't need a calculator, just a zero. Take any number, add a zero to its right side, and voilà—you've made it ten times bigger. It is a handy shortcut that makes you look like a math wizard and works every single time for whole numbers.
Section 5
Estimate products
When an exact answer isn't necessary, you can estimate a product by using compatible numbers. A compatible number is a number that is close to the original factor but is much easier to work with, especially for mental math. Common compatible numbers are those that end in a zero or five, simplifying the calculation.
Example 1: To estimate the perimeter in feet of an area that is 256 yards, you can use the compatible number 250. Since each yard is 3 feet, you calculate feet.
Example 2: To estimate the cost of four gallons of milk at 2.47 dollars per gallon, round 2.47 dollars to 2.50 dollars. Then, multiply dollars for an approximate cost.
Why wrestle with tricky numbers when you can use their friendly neighbors? To estimate a product, swap out a difficult number for an easier, 'compatible' one nearby (like turning 256 into 250). This makes the math simple enough to do in your head, giving you a quick and reasonably close answer.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter