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In this lesson, we will understand two multi-digit numbers, how to fluently perform the division and multiplication operations, and how to perform the four basic operations on decimals up to hundredths.
See the fact file below for more information on the operations with multi-digit numbers and decimals or alternatively, you can download our 37-page Operations with Multi-digit Numbers and Decimals
worksheet pack to utilise within the classroom or home environment.
Key Facts & Information
- Let us have a review first.
- 5 x 3 = 15
- Remember that in multiplication, we multiply the factors to get the product.
- Do you still remember how to multiply numbers?
- Let us have a brief recap.
- In multiplying by powers of 10, we always have to mind the number of zeros.
- 12 x 10 = ?
- We have only one zero. Therefore, we could already say that the product would have a zero at the rightmost side. Then, we proceed into multiplying 12 and 1, which would give us 12.
- 12 x 10 = 120
- Now, what if we have zeros in both factors?
- 30 x 10 = ?
- It is just the same as the previous one. We need to look at the number of zeroes, which is two, then we assume that we have two zeros at the rightmost part of the product. Then, we proceed into multiplying 3 and 1.
- 30 x 10 = 300
- But how do we multiply large numbers?
- Let us take the equation below as a sample.
- 512 x 46 = ?
- Seems complicated? We can write this equation in vertical form for it to look easier and less complicated.
- Now, we just have to do this step-by-step, number-by-number.
- Remember that we can expand 46 as 40 + 6.
- Therefore, we can say that we can solve this equation by rewriting it as:
- (512 x 6) + (512 x 40) = ?
- Now, doing it this way, we can first multiply 512 by 6 without minding the digit 4.
- Following the expanded form, we have to multiply 512 by 40, and then add the resulting product to the product of 512 times 6.
- These products are called partial products.
- We also have to keep in mind that we are multiplying 512 by 40, not by 4 only. Therefore, we have to add a zero at the rightmost part of that row.
- Now that we have taken into account the “0”, we can now proceed into multiplying 512 by 4.
- We now have the partial products, last step is to add them.
Therefore, the product of 512 and 46 is 23,552.
- In this section, we will establish methods on how to find quotients of whole numbers with up to four-digit dividends and two-digit divisors.
- First, we have to understand that multiplication and division are closely related. Therefore, we can use this to our advantage. How?
- 3355 ÷ 55 =?
- What if you already know that 55 multiplied by 61 is equal to 3355?
- Would this be relevant? Yes.
- Know that division is the reverse of multiplication, thus, we can rewrite the equation above as:
- 55 x A = 3355
- Wherein A is a variable.
- Since we already know that 55 times 61 would give us 3355, we can therefore already conclude that A stands for 61.
- 55 x 61 = 3355
- Thus, going back to the division equation, we would get:
- 3355 ÷ 55 = 61
- What if you do not have any idea that 55 times 61 is equal to 3355?
- We can use partial quotients. Partial quotients are just like partial products, here we take into account the place values of the numbers.
- To fully show how to use partial quotients, we will use the long division method.
- Now, we have a partial quotient of 6, but that doesn’t end there. We have to bring down 5, which will give us 55.
- From here, we need to divide 55 by 55.
- Therefore, 3355 ÷ 55 = 61.
- Adding decimals are just the same as adding whole numbers, but this time we have to take note of the decimal point.
- 500.12 + 9.98 = ?
- To make things easier, write them on top of each other.
- Then, make sure that the decimals points are aligned.
- The decimals points are going to be the guide.
- Then, perform addition as how you normally does to whole numbers.
- While performing addition, do not mind yet the decimal points.
- Then, after doing the addition, write the decimal point but make sure that it is still aligned with the other decimal points.
- In this section, we will get to know how to subtract decimals.
- 50.12 – 9.98 = ?
- But, we should still keep in mind the decimal points.
- Just like how we subtract whole number, we will just subtract decimals the same way.
- After doing so, make sure to align the decimal points and place a decimal point on the answer.
- Therefore, 50.12 minus 9.98 is equal to 40.14.
- In this section, we will establish understanding on how to multiply decimals.
- From the previous sections, we did addition and subtraction like how we normally do for whole numbers then later on applied the decimal points. This is also what we will do for multiplication.
- First, we multiply the numbers normally, ignoring first the decimal points.
- 11.31 x 7.11 = ?
- Let us first remove the decimal points and multiply the numbers normally.
- 1131 x 711 = 804141
- Note that for multiplication, we do not need to align the decimals points.
- What we need to do is to count the number of decimal points of the two factors.
- In total, we have four decimal places. With this in mind, remember the product that we got a while ago?
- Starting from the rightmost space (the one on the right of 1), we will count four steps (since we have a total of four decimal places) to the left. If we do this, we will end up in between 0 and 4. Therefore, we need to place the decimal point in that space.
- Therefore, the product if we multiply 11.31 and 7.11 is 80.4141.
- In this section, we will discuss how to divide decimals.
- Let us start first with dividing a whole number by a decimal.
- 15 ÷ 0.2 = ?
- Now, our first step is to “remove” the decimal point. To do this, we can multiply 0.2 by 10.
- 0.2 x 10 = 2
- But we have to keep in mind that we have to balance the numbers.
- Thus, we also need to multiply 15 by 10.
- 150 ÷ 2 = ?
- This way, it looks like our normal whole number now. Due to this modified equation, we can therefore easily perform division now.
- 150 ÷ 2 = 75
- Note that since both numbers are 10 times larger, the answer that we got is just the same as what we will get if we retained the original equation.
- 15 ÷ 0.2 = 75
- Now, let us try dividing a decimal by another decimal.
- 6.4 ÷ 0.4 = ?
- In this case, since both numbers (dividend and divisor) are decimals, we need just need to “remove” the decimals.
- To “remove” the decimal points, we need to multiply both numbers by 10.
- 6.4 x 10 = 64
- 0.4 x 10 = 4
- Now, we can rewrite the equation and perform division like how we perform it with whole numbers.
- 64 ÷ 4 = 16
- Just like in the previous example, the quotient that we got here is the same as the original equation, no modifications needed.
- 6.4 ÷ 0.4 = 16
Operations with Multi-digit Numbers and Decimals Worksheets
This is a fantastic bundle which includes everything you need to know about the operations with multi-digit numbers and decimals across 37 in-depth pages. These are ready-to-use Operations with Multi-digit Numbers and Decimals worksheets that are perfect for teaching students about the two multi-digit numbers, how to fluently perform the division and multiplication operations, and how to perform the four basic operations on decimals up to hundredths.
Complete List Of Included Worksheets
- Lesson Plan
- Operations with Multi-digit Numbers and Decimals
- Long Division
- Add Them
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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.