Multiplying Decimals Made Easy!
Summary
TLDRThis 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
🔢 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.
📈 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.
📘 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.
Mindmap
Keywords
💡Decimal
💡Multiplying
💡Carrying Over
💡Decimal Point
💡Place Value
💡Alignment
💡Column
💡Carrying
💡Addition
💡Zero Placeholder
💡Intermediate 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
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