Multiplying Decimals Explained: A Step-By-Step Review | Understanding Decimal Multiplication

Summary

In 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

00:00

📘 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.

Keywords

💡Multiplying Decimals

Multiplying decimals is a mathematical operation that involves multiplying numbers that have decimal places. In the video, this concept is the central theme, as the instructor provides a tutorial on how to multiply numbers with decimals. The process involves removing the decimal points initially, performing the multiplication as if the numbers were whole numbers, and then placing the decimal point in the final answer based on the total number of decimal places in the original numbers.

💡Decimals

Decimals are numbers that represent fractions using a decimal point to separate the whole number from the fractional part. In the context of the video, decimals are the type of numbers being multiplied. The script explains that when multiplying decimals, you temporarily ignore the decimal points and treat the numbers as whole numbers until the multiplication is complete.

💡Middle School

Middle School refers to a stage of education that typically comes after elementary school and before high school. The video mentions middle school as one of the educational levels for which the tutorial on multiplying decimals is beneficial, indicating that the content is suitable for a range of learners, from younger students to adults.

💡High School

High School is the next stage of formal education after middle school, preparing students for higher education or the workforce. The video script mentions high school as part of the audience, emphasizing that the concept of multiplying decimals is a foundational skill that is important throughout a student's educational journey.

💡College

College refers to an institution of higher education that offers academic and often professional degrees. The video includes college students in its target audience, suggesting that the skill of multiplying decimals is relevant even at higher levels of education, possibly in various subjects like mathematics, engineering, or sciences.

💡Continuing Education

Continuing education encompasses educational programs and courses for adults who wish to continue their learning after their initial formal education has ended. The video script mentions continuing education to highlight that the tutorial is not only for traditional students but also for adults who may be returning to education or learning new skills.

💡Class

A class in the educational context refers to a group of students who are taught together. The video mentions classes to indicate that the tutorial on multiplying decimals is applicable across various classroom settings, whether it's in a physical classroom or an online learning environment.

💡Refresher

A refresher is a quick review or recap of previously learned material to help remember or understand it better. The video is described as a 'quick refresher,' implying that it is designed to help viewers quickly recall how to multiply decimals, which is a skill they might have learned earlier but need to revisit.

💡Whole Numbers

Whole numbers are numbers without fractions, including all positive integers, zero, and sometimes negative integers. In the video, the instructor advises to treat decimals as if they were whole numbers during the multiplication process, which simplifies the calculation by ignoring the decimal points initially.

💡Place Value

Place value is the value of a digit based on its position in a number. For example, the place value of '5' in the number 53 is different from its place value in 530. In the script, the instructor uses the concept of place value to explain how to correctly align and add the products when multiplying numbers that have been rewritten without decimal points.

💡Decimal Point

The decimal point is the symbol (.) used to separate the integer part of a number from the fractional part. In the context of the video, placing the decimal point correctly in the final answer after multiplication is a critical step. The instructor explains that the number of digits to the right of the decimal point in the original numbers determines where to place the decimal point in the result.

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