Multiplying Decimals Explained: A Step-By-Step Review | Understanding Decimal Multiplication
Summary
TLDRIn this educational video, Mr. J offers a quick review on multiplying decimals, suitable for middle school to adult learners. He demonstrates how to eliminate decimals initially, multiply as with whole numbers, and then correctly place the decimal point in the answer by counting the digits after the decimal in the original problem. The video provides two detailed examples to illustrate the process, aiming to make the concept clear and accessible.
Takeaways
- 📘 **Remove Decimals First**: When multiplying decimals, start by ignoring the decimal points and treat the numbers as whole numbers.
- 🔢 **Multiply as Whole Numbers**: Perform the multiplication as you would with integers, focusing on the numerical values without considering the decimal places.
- 📌 **Count Decimal Places**: After the multiplication, count the total number of decimal places in the original numbers to determine where to place the decimal in your answer.
- 📐 **Align Decimal Places**: Ensure the number of decimal places in your final answer matches the sum of the decimal places in the original problem.
- 📝 **Carry Over Correctly**: When multiplying, remember to carry over numbers as you would in whole number multiplication.
- 🔄 **Add Zeros for Place Value**: When moving to the next digit in multiplication, add a zero for each place value you move to the left.
- 📉 **Handle Carried Numbers**: After carrying over, continue the multiplication process, adding the carried numbers to the subsequent results.
- 🎯 **Final Decimal Placement**: Place the decimal point in your final answer based on the count of original decimal places, not on the multiplication result itself.
- 📖 **Review Examples Carefully**: The script provides detailed examples to demonstrate the process of multiplying decimals, which is crucial for understanding the method.
- 👨🏫 **Educational for All Ages**: The method is applicable to anyone from middle school to adults continuing education, making it a universal mathematical skill.
Q & A
What is the primary focus of the video 'Math with Mr. J'?
-The primary focus of the video is to provide a quick review of multiplying decimals, which is helpful for middle school, high school, college, and adult learners.
What is the first step recommended in multiplying decimals according to the video?
-The first step recommended in multiplying decimals is to remove any decimals within the problem and treat the numbers as whole numbers for multiplication.
How does the video illustrate the multiplication of decimals with the first example?
-The video illustrates the multiplication of decimals by converting 'six and seven tenths times four' to '67 times 4', then multiplying as if they were whole numbers, and finally placing the decimal in the answer based on the original problem.
What is the result of the first example in the video?
-The result of the first example, '67 times 4', is '26.8', which is calculated by multiplying as whole numbers and then placing the decimal one place from the right to account for the single decimal in the original problem.
How does the video handle the multiplication of decimals with more than one decimal place?
-The video handles the multiplication of decimals with more than one decimal place by first removing the decimals, multiplying the resulting whole numbers, and then counting the total number of decimal places in the original numbers to determine where to place the decimal in the answer.
What is the final answer for the second example provided in the video?
-The final answer for the second example, '521 times 38', is '19.798', which is calculated by multiplying as whole numbers and then placing the decimal three places from the right to match the total number of decimal places in the original problem.
What is the significance of counting the number of digits to the right of the decimal in the original problem?
-Counting the number of digits to the right of the decimal in the original problem is significant because it determines how many digits should be to the right of the decimal in the final answer after multiplying.
How does the video ensure the accuracy of the decimal placement in the final answer?
-The video ensures the accuracy of the decimal placement by matching the number of digits to the right of the decimal in the final answer to the total number of decimal places in the original problem.
What is the main takeaway from the video regarding multiplying decimals?
-The main takeaway from the video is that when multiplying decimals, one should remove the decimals, multiply as if they were whole numbers, and then place the decimal in the answer according to the total number of decimal places in the original numbers.
What is the purpose of the placeholder zero mentioned in the video?
-The purpose of the placeholder zero mentioned in the video is to maintain the correct place value when multiplying numbers that have been rewritten without decimals, ensuring the accuracy of the multiplication.
How does the video conclude the process of multiplying decimals?
-The video concludes by emphasizing the process of removing decimals, multiplying as whole numbers, and then placing the decimal in the answer to match the original problem's decimal places, and encourages viewers to practice this method.
Outlines
📘 Decimal Multiplication Basics
This paragraph introduces a tutorial on multiplying decimals, suitable for middle school, high school, college, and adult learners. It emphasizes the importance of removing decimals from the problem initially and then multiplying as if dealing with whole numbers. The focus is on understanding how to place the decimal point in the final answer by counting the number of digits to the right of the decimal in the original problem. An example is given where 'six and seven tenths times four' is simplified to multiplying 67 by 4, resulting in 26.8. The process involves carrying over and aligning the decimal point based on the number of decimal places in the original numbers.
Mindmap
Keywords
💡Multiplying Decimals
💡Decimals
💡Middle School
💡High School
💡College
💡Continuing Education
💡Class
💡Refresher
💡Whole Numbers
💡Place Value
💡Decimal Point
Highlights
Introduction to a quick review of multiplying decimals
Relevance for middle school, high school, college, and adult education
Removing decimals to simplify multiplication
Multiplication of whole numbers as an initial step
Placing the decimal in the answer after multiplication
Example 1: Multiplying six and seven tenths by four
Rewriting the problem as 67 times 4
Multiplication process: 4 times 7 equals 28
Carry over the 2 from 4 times 7 to 4 times 6
Final multiplication result before placing the decimal
Determining the number of decimal places in the answer
Final answer for example 1: 26.8
Example 2: Multiplying five and twenty one hundredths by three and eight tenths
Rewriting the problem as 521 times 38
Multiplication process: 8 times 1 equals 8, 8 times 2 equals 16
Carry over and multiplication with the hundreds place
Final multiplication result before placing the decimal for example 2
Determining the number of decimal places in the answer for example 2
Final answer for example 2: 19.798
Summary of the method: remove decimals, multiply, then place the decimal
Thank you and sign-off for the video
Transcripts
[Music]
welcome to math with mr j
[Music]
in this video i'm going to go through a
quick review of multiplying decimals
this should be helpful for anyone
looking for a quick refresher whether
you're in middle school high school
college continuing your education as an
adult really no matter what class or
goal you are working towards here are a
couple of examples to get this down
let's jump into number one where we have
six and seven tenths times four now the
first thing that we're going to do when
we have a multiplication problem that
involves decimals we're going to remove
any decimals within the problem so we're
going to multiply just like we would if
we had whole numbers let's set this up
and rewrite number 1 as
67
times
4
so again remove any decimals we're going
to worry about placing the decimal in
our answer once we multiply so once we
remove the decimals we can multiply so
we'll start with 4 times 7
which is 28
so carry that 2 and then we have 4 times
6 which is 24 plus that 2 is 26.
now we're done multiplying so we can
place our decimal in our answer so we
take a look at the original problem and
see how many digits are behind or are to
the right of a decimal well one we have
this seven right here to the right of a
decimal so our answer is going to have
one digit to the right or behind the
decimal so one digit would be this eight
so we can place our decimal in between
the six and the
eight
our final answer 26 and eight tenths
let's move on to number two where we
have five and twenty one hundredths
times three and eight tenths so let's
remove the decimals and rewrite this
problem
so 521
times
38.
now we're ready to multiply so 8 times 1
is 8.
8 times 2 is sixteen
put our six
carry the one and then eight times five
is forty plus that one
is forty one
so we are done with the eight and we are
done with this carried one so we're
going to move over to the three we're
moving one place value to the left so we
need our placeholder zero here and now
we multiply starting with three times
one which is three
three times two is six
and then three times five is fifteen
now we add
so eight plus zero is eight
six plus three is nine
one plus six is seven
four plus five is nine
and then we have a one
so once we get to this point we look at
our original problem and see how many
digits are to the right or are behind a
decimal well this 2 would be 1 this one
would be 2
and then this 8 would be 3. so we have 1
2
3 digits behind or to the right of a
decimal so our answer needs 3 digits to
the right of the decimal so we have 1
two
three digits
our decimal is going to go between the
nine and the seven
our final answer 19 and 798
thousandths
so there you have it there's a quick
review of multiplying decimals remove
the decimals
multiply as you normally would with
whole numbers and then place your
decimal in the answer look at the
original problem see how many digits are
to the right or are behind a decimal and
then your answer is going to match that
i hope that helped
thanks so much for watching
until next time
peace
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