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In this lesson, we will utilize your place value understanding and properties of operations to perform multi-digit arithmetic equations. In addition, we will fluently add and subtract whole numbers, multiply multi-digit numbers by a one-digit number, and find whole number quotients and remainders with up to four-digit dividends and one-digit divisors.
See the fact file below for more information on the multi-digit arithmetic operations or alternatively, you can download our 37-page Multi-Digit Arithmetic Operations worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
PLACE VALUE PARTIAL SUMS
- One way to solve for the sum of two large numbers is to use partial sums.
- In this section, we will try to understand how place value partial sums work.
- Place value partial sums is a method of breaking down numbers into expanded form and adding them like place values.
- Let’s use the addition equation provided below.
- 729 + 243 = ?
- How do we expand numbers?
- 700 + 20 + 9
- 200 + 40 + 3
- Note that we already have numbers holding the hundreds place value, tens place value, and ones place value. We can now add them by place values.
- 700 + 200 = 900
- 20 + 40 = 60
- 9 + 3 = 12
ADDING FOUR-DIGIT NUMBERS
- First, we add the digits in the ones place. Next, we add the tens.
- Next, work on the hundreds place and then on thousands place .
SUBTRACTING FOUR-DIGIT NUMBERS
- Subtracting four-digit numbers is just like subtracting smaller numbers.
MULTIPLICATION PATTERNS ACROSS PLACE VALUES
- 10 x 6 = ?
- 100 x 6 = ?
- 1000 x 6 = ?
- All of these numbers multiplied by 6 starts with 1. The number of zeros increase by 1 in each equation. This means, the place value of number 1 increases in each equation.
- 10 – The value of 1 is 1 ten.
- 100 – The value of 1 is 1 hundred.
- 1000 – The value of 1 is 1 thousand.
- Translating the first equation, it would become:
- 1 ten x 6
- 1 ten x 6 = 6 tens
- 10 x 6 = 60
- For the second equation, it would be:
- 1 hundred x 6.
- 1 hundred x 6 = 6 hundreds
- 100 x 6 = 600
- Can you figure out the pattern for the third equation?
- As the place value of the number that’s being multiplied increases, the number of zeros also increase. When completing patterns in multiplication, always look for the rule based on the place values of the numbers.
THREE-DIGIT BY ONE-DIGIT MULTIPLICATION
- When multiplying a three-digit number by a one-digit number, multiply the one-digit number with each of the digits in the three-digit number, starting from the right or from the ones place.
- Let’s take a look at this example.
- 310 x 2 = ?
- The first thing you need to do is to arrange the numbers in column form.
- Write the three-digit number at the top and the one-digit number at the bottom.
- Make sure to align 2 with 0. Both digits must be in the ones place or at the rightmost side.
- First, multiply 0 and 2. Let’s write their product in the ones place.
- Next, multiply 1 and 2, then write the answer in the tens place.
- Lastly, multiply 3 and 2. Write 6 in the hundreds place.
FOUR-DIGIT BY ONE-DIGIT DIVISION
- Let’s solve for the quotient of 8.356 and 4.
- First, let’s arrange the problem in long division form.
- Look at the first digit on the left. How many 4’s can you get from 8?
- We write 2 on top, as quotient, and the product of 2 and 4 below the 8.
- Next, we subtract this product from the digit in the dividend (8) to get the remainder.
- Let’s bring down the next digit, 3. How many 4’s can you get from a 3?
- None right? So, we write 0 on top, as a quotient.
- When the quotient for any digit in long division is 0, we divide the next digit along with it.
- Let’s bring down the next digit, 5. Let’s divide 35 by 4. How many 4’s can you get from 35?
- We write 8 on top, as quotient, and the the product of 8 and 4 under the 35. Next, subtract their product, 32, from 35.
- Finally, let’s bring down the last digit, 6. Since we have a remainder 3 from the difference of 35 and 32, we will combine 3 with 6, and divide them by 4.
- 36 divided by 4 is 9. We write 9 on top, as quotient, and the product of 9 and 4 below the 36. Then, we subtract.
- The quotient when 8,356 is divided by 4 is 2,089 and the remainder is 0.
Multi-Digit Arithmetic Operations Worksheets
This is a fantastic bundle which includes everything you need to know about the multi-digit arithmetic operations across 37 in-depth pages. These are ready-to-use Multi-Digit Arithmetic Operations worksheets that are perfect for teaching students about the place value understanding and properties of operations to perform multi-digit arithmetic equations. In addition, we will fluently add and subtract whole numbers, multiply multi-digit numbers by a one-digit number, and find whole number quotients and remainders with up to four-digit dividends and one-digit divisors.
Complete List Of Included Worksheets
- Lesson Plan
- Multi-Digit Arithmetic Operations
- Find the Sum
- Find the Difference
- Find the Product
- Find the Quotient
- Quotient and Remainders
- Multiplying Multiples
- Missing Subtraction
- Missing Multiples
- Write the Equation
- Word Problems
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Link will appear as Multi-Digit Arithmetic Operations Facts & Worksheets: https://kidskonnect.com - KidsKonnect, June 1, 2020
Use With Any Curriculum
These worksheets have been specifically designed for use with any international curriculum. You can use these worksheets as-is, or edit them using Google Slides to make them more specific to your own student ability levels and curriculum standards.