Multiplying Decimals Made Easy!

Summary

This instructional video script teaches viewers how to multiply numbers with decimals. It begins with a simple example, explaining the process of multiplying 4.6 by 7, emphasizing the importance of carrying over numbers and placing the correct number of digits to the right of the decimal point in the final answer. The script progresses to more complex examples, such as multiplying 3.9 by 5.6 and 12.9 by 3.7, detailing each step of the multiplication process. It concludes with multiplying 14.56 by 8 and 13.79 by 5.46, highlighting the need to add zeros when moving to a new line and ensuring the total number of decimal places in the answer matches the sum of decimal places in the original numbers.

Takeaways

• 🔢 Multiplying decimals involves treating them like whole numbers until the end of the calculation.
• 📐 When multiplying, remember to carry over numbers as you would in whole number multiplication.
• 📝 After multiplying, align the decimal point in the product with the sum of the decimal places in the factors.
• 📈 For example, in 4.6 * 7, the product should have one digit after the decimal (since 4.6 has one).
• 📉 When multiplying larger numbers with decimals, like 3.9 * 5.6, you must account for all decimal places in the factors.
• 🔄 Carrying over is crucial; for instance, in 3.9 * 5.6, carrying over affects the next digit's calculation.
• 📑 When multiplying by a whole number followed by a decimal, like 12 * 3.7, treat the whole number as part of the decimal.
• 🔄 Always remember to add zeros when moving to a new line in the multiplication process.
• 📉 In problems with percentages, like 14.56% * 8, convert the percentage to a decimal before multiplying.
• 🔎 The final position of the decimal point in the product is determined by the total number of decimal places in the factors.
• 📐 For complex multiplications, like 13.79 * 5.46, ensure each step is clear and carry overs are accurately accounted for.

Q & A

What is the product of 4.6 and 7 according to the video?

The product of 4.6 and 7 is 32.2. The calculation involves multiplying 6 by 7 to get 42, then carrying over the 4, and multiplying 4 by 7 to get 28, adding the carried over 4 to get 32, and finally placing the decimal point one place to the right as there is one number to the right of the decimal in the original numbers.

How do you multiply 3.9 by 5.6 as demonstrated in the video?

To multiply 3.9 by 5.6, you first multiply the digits without considering the decimal points (9*6=54, write down 4 and carry over 5; 3*6=18, add 5 to get 23; 5*9=45, write down 5 and carry over 4; 5*3=15, add 4 to get 19). Then, align the decimal points according to the total number of decimal places in the original numbers (two in 3.9 and one in 5.6, so three in total), resulting in 21.84.

What is the final step when multiplying decimals as shown in the video?

The final step when multiplying decimals is to ensure that the number of digits to the right of the decimal point in your answer matches the total number of digits to the right of the decimal points in the original numbers.

Can you explain the process of multiplying 12.9 by 3.7 as described in the video?

To multiply 12.9 by 3.7, you multiply each digit of 12.9 by each digit of 3.7, carrying over as necessary (9*7=63, write down 3 and carry over 6; 2*7=14, add 6 to get 20, write down 0 and carry over 2; 1*7=7, add 2 to get 9; 3*9=27, carry over 2; 2*3=6, add 2 to get 8; 1*3=3). Then, add all the results together and place the decimal point two places to the right since there are two numbers to the right of the decimal point in total in the original numbers.

What is the significance of adding zeros when carrying over in decimal multiplication as explained in the video?

Adding zeros when carrying over in decimal multiplication is important for aligning the decimal places correctly. For each new line of multiplication, you add a zero to the end of the partial product to ensure the decimal point is placed accurately in the final result.

How does the video script guide you to multiply 14.56 by 8?

To multiply 14.56 by 8, you multiply each digit of 14.56 by 8 (8*6=48, carry over 4; 8*5=40, add 4 to get 44; 8*4=32, add 4 to get 36; 8*1=8, add 3 to get 11). Then, add all the partial products together, and place the decimal point three places to the right as the original numbers have a total of three digits to the right of the decimal point.

What is the product of 13.79 and 5.46 as shown in the video?

The product of 13.79 and 5.46 is 75.2934. This is calculated by multiplying each digit of 13.79 by each digit of 5.46, carrying over as necessary, and ensuring the final answer has four digits to the right of the decimal point, as both original numbers have two digits to the right of the decimal point.

How does the video emphasize the importance of decimal placement in multiplication?

The video emphasizes the importance of decimal placement by showing that the number of digits to the right of the decimal point in the final answer must match the total number of digits to the right of the decimal points in the original numbers being multiplied.

What is the rule for placing the decimal point in the final answer when multiplying decimals as per the video?

The rule for placing the decimal point in the final answer when multiplying decimals is to count the total number of digits to the right of the decimal points in both original numbers and place the decimal point in the answer with that many digits to the right.

Can you describe the step-by-step process of multiplying decimals as outlined in the video?

The step-by-step process of multiplying decimals involves: 1) Ignoring the decimal points and multiplying the numbers as whole numbers. 2) Carrying over as necessary during multiplication. 3) Adding zeros for each new line of multiplication. 4) Adding all partial products together. 5) Placing the decimal point in the final answer according to the total number of decimal places in the original numbers.

Outlines

00:00

🔢 Decimal Multiplication Basics

This paragraph introduces the process of multiplying numbers that include decimals. It begins with a simple example of multiplying 4.6 by 7. The explanation involves breaking down the multiplication into steps, starting with multiplying the digits to the right of the decimal point (6 * 7 = 42), then moving to the digits to the left (4 * 7 = 28), and finally combining these results while carrying over as necessary. The importance of aligning the decimal points in the final answer is emphasized, resulting in 32.2. The paragraph continues with another example multiplying 3.9 by 5.6, guiding through each step of the multiplication process, including carrying over numbers and adding zeros, to arrive at the final answer of 2184. The process is explained in a step-by-step manner, ensuring clarity and understanding.

05:03

📈 Advanced Decimal Multiplication

The second paragraph delves into more complex examples of decimal multiplication, such as multiplying 12.9 by 3.7 and 14.56 by 8. It illustrates the process of multiplying each digit, carrying over where necessary, and adding zeros when moving to the next line of the multiplication. The paragraph emphasizes the need to match the number of decimal places in the final answer to the sum of decimal places in the original numbers. For instance, when multiplying 12.9 by 3.7, the process involves carrying over numbers and adding zeros, resulting in the final answer of 47.73. The paragraph also covers the multiplication of 14.56 by 8, explaining how to handle the decimal and carry over numbers to get the final answer of 40.768. The focus is on accuracy and the correct placement of decimal points in the answers.

10:03

📘 Tips for Decimal Multiplication

The final paragraph offers tips for performing decimal multiplication. It advises on the importance of adding zeros when moving to new lines in the multiplication process, with the number of zeros increasing as you progress to subsequent lines. The paragraph also reiterates the critical aspect of ensuring the final answer has the correct number of decimal places, which should match the total number of decimal places in the original numbers involved in the multiplication. This guidance helps in maintaining accuracy throughout the multiplication process and achieving the correct result.

Keywords

💡Decimal

A decimal represents a fraction with a denominator that is a power of ten, typically written with a decimal point to the right of the integer part. In the context of the video, decimals are used in multiplication examples to demonstrate how to handle numbers with non-integer values. For instance, multiplying 4.6 by 7 involves carrying over digits and placing the decimal point appropriately in the final answer.

💡Multiplying

Multiplying is a mathematical operation where one number is added to itself a certain number of times, indicated by the other number. In the video, multiplying is the central operation being taught, with a focus on how to correctly handle the decimal points when multiplying numbers that include decimals.

💡Carrying Over

Carrying over is a process in arithmetic where a value exceeding the base (usually 10 for decimal numbers) is transferred to the next higher place value. The video script illustrates carrying over in the context of multiplying numbers with decimals, such as when multiplying 4.6 by 7, where the product of 42 is carried over to the next column.

💡Decimal Point

The decimal point is the symbol used to separate the integer part from the fractional part of a number. In the video, the importance of the decimal point is emphasized when determining where to place it in the final product after multiplying two numbers with decimals.

💡Place Value

Place value refers to the value of a digit based on its position within a number. The video script uses place value to explain how to multiply numbers with decimals, ensuring that the digits are aligned correctly before performing the multiplication.

💡Alignment

Alignment in multiplication refers to the arrangement of numbers so that corresponding place values are vertically aligned. The video script mentions alignment as a crucial step in multiplying numbers with decimals to ensure accuracy in the calculation.

💡Column

A column in multiplication is one of the vertical groups of numbers that are being multiplied. The video script uses the term 'column' to describe the process of multiplying numbers digit by digit, moving from one column to the next as you multiply.

💡Carrying

Carrying is the process of adding the value of one column to the next when the sum exceeds the base value (usually 10). The video script demonstrates carrying in the multiplication of decimals, such as when multiplying 3.9 by 5.6, where the product of 54 is carried over to the next higher place value.

💡Addition

Addition is the process of combining two or more numbers to find their total. In the video, addition is used after multiplying individual digits to sum the intermediate products and account for carrying over, as seen when adding 28 + 4 in the multiplication of 4.6 by 7.

💡Zero Placeholder

A zero placeholder is a zero used to hold the place in a number when there is no value for a particular digit. The video script mentions adding a zero when moving to the next higher place value in a multiplication problem, such as adding a zero before multiplying 3.9 by 5.6.

💡Intermediate Product

An intermediate product is the result of multiplying individual digits during the multiplication process. The video script describes how to handle intermediate products, such as the product of 54 in the multiplication of 3.9 by 5.6, before summing them to find the final product.

Highlights

Introduction to multiplying numbers with decimals

Basic example of multiplying 4.6 by 7

Explanation of carrying over numbers during multiplication

Result of 4.6 multiplied by 7 is 32.2

Second example multiplying 3.9 by 5.6

Detailed step-by-step multiplication process

Final answer for 3.9 multiplied by 5.6 is 21.84

Third example multiplying 12.9 by 3.7

Carry over technique in decimal multiplication

Final answer for 12.9 multiplied by 3.7 is 47.73

Fourth example multiplying 14.56 by 8

Carry over and addition in decimal multiplication

Final answer for 14.56 multiplied by 8 is 40.768

Harder example multiplying 13.79 by 5.46

Complex multiplication process with decimals

Final answer for 13.79 multiplied by 5.46 is 75.2934

Using a calculator to confirm the multiplication results

Instruction on adding zeros when moving to a new line in multiplication

Emphasis on the importance of decimal placement in the final answer

Transcripts

in this video we're going to focus on

multiplying numbers with decimals so

let's start with a basic example first

what is

4.6 multiplied

7 well first we need to multiply 6 * 7 6

* 7 is 42 so we need to put the first

number two and carry over the

four next let's multiply 4 * 7 4 * 7 is

28 and we need to add the four on top 28

+ 4 that's

32 now notice that we have one number to

the right of a decimal point so

therefore in our answer we should have

one number to the right of a decimal

point so the answer is

32.2 now let's try another

example let's multiply

3.9 by

5.6 feel free to try this one if you

want

to so first let's multiply 9 * 6 9 * 6

is 54 so we're going to write the four

and then we're going to carry over the

five next let's multiply 3 *

6 3 * 6 is 18 and 18 + 5 is 23

now let's move on to the five let's

multiply five and 9 5 * 9 is

45 so we need to write the five but we

need to add a zero first and then we'll

write the five carry over the

four next let's multiply 5 * 3 5 * 3 is

15 + 4 that's 19

now what we need to do is add 4 + 0 is 4

3 + 5 is 8 2 + 9 is 11 carry over the 1

1 + 1 is two now notice that we have two

numbers to the right of a decimal point

so therefore in our answer we should

have two numbers to the right of a

decimal point so the final answer is

2184 and that's

it now let's multiply 12

9 by

3.7 feel free to try this

problem so first let's multiply 9 * 7 9

* 7 is 63 so we're going to write the

three and carry over the

six next let's multiply 2 * 7 2 * 7 is

14 + 6 that's going to be 20 so we're

going to write the zero and carry over

the

two next we have 1 * 7 which is 7 + 2

that's equal to

9 now let's add a zero let's get rid of

these

numbers so now we're going to multiply 3

* 9 3 * 9 is

27 let's carry over the

two and then we'll multiply 2 * 3 which

is 6 6 + 2 that's

8 and then finally 1 * 3 which is just

three now let's add the numbers 3 + 0 is

3 0 + 7 is the same thing 9 + 8 is 17

carry over the one 3 + 1 is

4 now how many numbers do we have to the

right of a decimal point so here's one

and here's another one so we got two

numbers to the right of the decimal

point our final answer should be the

same so these two numbers are going to

be to the right of this decimal point

therefore the answer is

47.

73 let's continue working on some more

examples let's multiply 14.56%

8 * 6 8 * 6 is 48 let's carry over the

four next we have 8 * 5 which is 40 + 4

so that's uh

44 we're going to carry over the next

four and then 8 * 4 is 32 + 4 that's

36 so let's write 6 and then carry over

the

three 8 * 1 is 8 + 3 that's

11 so now let's

uh let's get rid of these

numbers let's add a zero and then let's

multiply 2 * 6 2 * 6 is 12 carry over

the 1 and then 2 * 5 is 10 + 1 that's 11

so let's carry over the next one 4 * 2

is 8 + 1 that's

9 and then 1 * 2 is just two so now we

can add so this is going to be 8 4 + 2

is 6 6 + 1 is 7 1 + 9 is 10 carry over

the 1 1 + 1 is 2 + 2 is

4 now where should we put the

decimal so looking at the original

problem the first number has two digits

to the right of a decimal point and the

second number only has one therefore our

final answer should have a total of

three numbers to the right of the

decimal

point so therefore the

answer is

40.

768 now let's move on to some harder

examples let's multiply 13

.79 by

5.46 so go ahead and try this

problem let's begin by multiplying 9 and

six 9 * 6 is 54 and let's add the five

on top next we have 7 * 6 which is 42 +

5 so that's uh 47

let's carry over the four and next we

have uh 6 * 3 which is 18 + 4 so that's

22 and now let's add the other two there

6 * 1 is 6 + 2 that's

8 now don't forget to add a

zero so we're done with six let's move

on to

four four * * 9 that's

36 so let's add a three and then 4 * 7

is 28 + 3 that's 31 so let's carry over

the other three and then 3 * 4 is 12 + 3

that's 15 so let's write five and carry

over the 1 1 * 4 is four + one that's

five so

now we're going to move on to

five let's get rid of the numbers on

top and let's add a zero actually this

time I'm going to add two

zeros so now 5 * 9 that's

45 and then 5 * 7 is 35 + 4 that's 39 9

carry over the three 5 * 3 is 15 + 3

that's

18 and then 5 * 1 is 5 + 1 that's six so

now let's add the numbers so this is

four four 7 + 6 is

13 and then 1 2 and 1 that's 4 + 5 is

9 8 + 5 is 13 + + 9 that's

22 8 and 2 is 10 + 5 that's 15 and 6 and

1 is

7 now where should we put the

decimal so looking at the original

numbers the first number has two numbers

to the right of the decimal point and

the second number also have two numbers

so therefore our final answer should

have a total of four digits

to the right of the decimal

point which means our answer is

75

2934 now if you have your calculator you

can confirm all of these

answers so if you type it in 13.79%

uh that contain decimal

numbers so every time you need to add a

new line don't forget to add a zero if

you're adding another line then once you

get to your third line you're adding two

zeros so don't forget about that step

and the last thing you have to keep in

mind is the numbers of or the amount of

numbers that is to the right of the

decimal point make sure that is equal to

the amount of numbers to the right of

the decimal point in your final answer