Subtracting Decimals Explained: A Step-By-Step Review | Understanding Decimal Subtraction

Summary

In this educational video, Mr. J offers a concise review of decimal subtraction, ideal for middle school, high school, college, and adult learners. He demonstrates how to align decimals and use placeholder zeros for clarity, guiding viewers through two detailed examples. The video highlights common mistakes to avoid, such as not borrowing when necessary, and emphasizes the importance of accuracy in decimal subtraction.

Takeaways

• 📚 The video provides a quick review of subtracting decimals, suitable for middle school, high school, college, and adult learners.
• 🔢 To subtract decimals, align the decimal points to ensure proper place value alignment.
• 💡 Use placeholder zeros to make the decimals align neatly, especially when dealing with different decimal places.
• 🚫 Avoid the common mistake of dropping the zero in the hundredths place without borrowing, as this can lead to incorrect results.
• ✏️ When subtracting, start from the rightmost digit (hundredths place) and move left, borrowing as necessary.
• 📉 Subtract decimals vertically, similar to how you would add them, to maintain alignment and accuracy.
• 🔄 Remember that borrowing changes the value of the digits above; for example, borrowing from the tenths place changes a '9' to an '8'.
• 📈 After borrowing, subtract the new values in each place value, moving from the hundredths to the ones place.
• 💯 The final answer should have the decimal point aligned with the original problem, maintaining the decimal places.
• 📝 Practice is key to mastering decimal subtraction, and the video offers examples to help viewers understand the process.

Q & A

What is the main topic of the video?

The main topic of the video is a quick review of subtracting decimals.

Who is the target audience for this video?

The target audience includes middle school, high school, college students, and adults continuing their education.

What is the first example problem presented in the video?

The first example problem is subtracting 8 and 57 hundredths from 14 and 9 tenths.

Why is it important to line up the decimals when subtracting?

Lining up the decimals ensures that all the corresponding place values are aligned, making the subtraction process accurate and straightforward.

What is the purpose of using placeholder zeros in decimal subtraction?

Using placeholder zeros helps to align the decimal places correctly and avoid mistakes, especially when one number has fewer decimal places than the other.

What is the common mistake to avoid when subtracting decimals?

The common mistake to avoid is not borrowing correctly when there is a zero in the higher place value of the decimal. One should not simply drop the zero and proceed with the subtraction.

How does borrowing work in the context of the first example problem?

In the first example, borrowing is needed when subtracting in the hundredths place (0 minus 7) and the ones place (4 minus 8). The tens place is borrowed from to provide a value for subtraction.

What is the final answer to the first example problem in the video?

The final answer to the first example problem is 6 and 33 hundredths.

What is the second example problem in the video?

The second example problem is subtracting 59 and 8 tenths from 262 and 33 hundredths.

How is the decimal point handled during the subtraction process?

The decimal point is brought straight down into the answer after aligning the decimals and performing the subtraction in each place value.

What is the final answer to the second example problem in the video?

The final answer to the second example problem is 202 and 53 hundredths.

Outlines

00:00

📘 Subtracting Decimals Tutorial

This paragraph is a tutorial on subtracting decimals, aimed at various educational levels. The instructor begins by emphasizing the importance of aligning the decimal points when performing subtraction, using the example of 14.9 - 8.57. To avoid mistakes, the instructor suggests using placeholder zeros to align the numbers properly. They demonstrate the subtraction step by step, borrowing from the left when necessary, and highlight a common mistake of not borrowing when a zero appears in the higher place value. The solution to the example is 6.33.

05:00

🙌 Conclusion and Sign-off

The second paragraph is a brief conclusion and sign-off from the instructor. They thank the viewers for watching the tutorial on subtracting decimals and express a friendly farewell, indicating the end of the video.

Keywords

💡Decimals

Decimals are numbers that represent fractions with a denominator of 10, 100, 1000, etc. They are used to express values with a certain level of precision beyond whole numbers. In the video, decimals are the primary focus for the mathematical operations being taught, specifically subtraction. The script uses examples like '14 and 9/10' and '8 and 57/100' to demonstrate how to align and subtract decimals.

💡Subtracting

Subtracting is one of the four basic arithmetic operations, where you take one number away from another. In the context of the video, subtracting decimals is the main operation being reviewed. The script provides step-by-step instructions on how to subtract decimals, such as aligning them vertically and borrowing when necessary.

💡Aligning

Aligning in the context of decimals refers to the process of lining up the decimal points of two or more numbers to ensure that each place value is correctly positioned for operations. The video emphasizes the importance of aligning decimals when performing subtraction, as shown in the examples where the decimals are lined up before subtraction begins.

💡Placeholder Zeros

Placeholder zeros are zeros added to a number to align the decimal places correctly, especially when performing operations like subtraction. The video script explains that using placeholder zeros can help avoid common mistakes and ensure that the decimal alignment is correct, as illustrated when converting '14 and 9/10' to '14 and 9.00'.

💡Borrowing

Borrowing is a technique used in subtraction when the number in the higher place value is smaller than the number you are trying to subtract. The video script demonstrates borrowing with the example of '4 minus 8', where you borrow from the next higher place value to perform the subtraction correctly.

💡Tenths

Tenths refer to the first decimal place to the right of the decimal point, representing the value of 1/10. In the video, tenths are one of the decimal places that need to be aligned and operated on during subtraction, as shown in the example '14 and 9/10 minus 8 and 57/100'.

💡Hundredths

Hundredths are the second decimal place to the right of the decimal point, representing the value of 1/100. The video script uses hundredths in the subtraction examples to show how to align and subtract numbers with different decimal places.

💡Common Mistake

A common mistake in the context of the video refers to errors made during the subtraction process, such as not borrowing when necessary or misaligning decimals. The script points out the mistake of 'dropping the 7' in '0 minus 7' without borrowing, which would lead to an incorrect result.

💡Equivalent Decimal

An equivalent decimal is a decimal number that has the same value as another but is represented differently, often with additional zeros. The video script mentions that adding zeros to the right of a decimal does not change its value, which is why placeholder zeros can be used without affecting the outcome of the subtraction.

💡Vertical Subtraction

Vertical subtraction is a method of performing subtraction by writing numbers vertically and aligning the digits according to their place value. The video script uses vertical subtraction as the primary method for demonstrating how to subtract decimals, with clear examples shown step by step.

💡Decimal Point

The decimal point is the symbol used to separate the integer part of a number from its fractional part. In the video, the decimal point is crucial for aligning numbers during subtraction, as it determines where each decimal place should be positioned, as demonstrated in the examples provided.

Highlights

Introduction to subtracting decimals for various educational levels.

Importance of lining up decimals when subtracting to align all places properly.

Use of placeholder zeros to make decimal alignment clearer, without affecting the value.

Detailed breakdown of example 1: 14.9 - 8.57.

Borrowing explained: From tenths to hundredths place when performing subtraction (zero minus seven).

Clear steps for handling zeros and the significance of borrowing in subtraction.

Common mistake warning: Dropping digits during subtraction without borrowing can lead to incorrect results.

Detailed breakdown of example 2: 262.33 - 59.8.

Importance of using placeholder zeros again in the second example.

Borrowing from tenths place to hundredths in the second example.

Explanation of borrowing across places: borrowing from ones place to subtract in the second example.

Final answers for both examples demonstrated: 6.33 for the first and 202.53 for the second.

Encouragement to always use placeholder zeros to prevent mistakes.

Reminder to align the decimals correctly before performing any subtraction.

Conclusion with a recap of tips: Line up decimals, use placeholder zeros, and carefully borrow when needed.

Transcripts

[Music]

welcome to math with mr j

[Music]

in this video i'm going to go through a

quick review of subtracting 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

14 and 9 10 minus 8 and 57 hundredths

now just like when we add decimals when

we subtract decimals we need to line the

decimals up that's going to line up all

of our places so let's rewrite this

first problem vertically here lining up

the decimals so fourteen and nine tenths

minus

eight

and fifty-seven hundredths

so the decimals are lined up and that's

going to line up all of our places now

that problem looks a little offset

because 14 and nine-tenths goes to the

tenths place and then eight and 57

hundredths goes to the hundredths place

so just like when we add decimals we can

use placeholder zeros to have this look

more lined up so let's use a placeholder

zero in the hundredths place here and

then both of our decimals go to the

hundredths place remember zeros to the

right of a decimal do not change the

value that's an equivalent decimal and

does not change the value of the problem

at all now we're able to subtract so

we'll start with the hundredths place we

have zero minus seven which we need to

borrow so let's borrow from the nine

that's an eight now

and we have ten minus seven which is

three

then we move to the tenths place eight

minus five

three

bring our decimal straight down into the

answer the decimal is lined up

throughout the entire problem then we

move to the ones place four minus eight

we need to borrow from the tens place

here so that's a zero

and that's a fourteen so fourteen minus

eight is six

and we are done

six

and thirty three hundredths

now i do wanna mention one more thing

before moving on to number two and this

is going to be a common mistake that

you'll want to avoid and using

placeholder zeros will actually help you

avoid this mistake so let me rewrite the

problem here

real quick to the side so we have 14

and nine tenths minus

eight

and 57 hundredths

so dropping this 7 so starting with the

hundredths place and then just dropping

the 7 because there isn't anything above

it

is not correct we actually have zero

minus seven there

so we needed to borrow and you can see

we do not have a seven in the hundredths

place in our final answer so again avoid

the mistake of just dropping that number

because really we have zero minus seven

there and we need to borrow so be

careful of that

let's move on to number two where we

have

262 and 33 hundredths minus 59 and eight

tenths

so we will start by lining up our

decimals here

so

262 and 33 hundredths minus

59

and eight tenths

we can use a placeholder zero so these

both go to the hundredths and now we are

able to subtract so we'll start with the

hundredths three minus zero is three

the tenths place three minus eight well

we need to borrow so borrow from the two

that's a one

and we have a thirteen so thirteen minus

eight is five

we can bring our decimal straight down

into our answer

and now we have the ones place so 1

minus 9 we need to borrow so we'll

borrow from the 6

and we have 11 minus 9 which is

2.

then for the tens place we have 5 minus

5 which is 0.

and then lastly we have the hundreds

place where we have 2 minus nothing

under it so it's just two minus zero

which is two

and our final answer two hundred two and

fifty three hundredths so there you have

it there's a quick review of subtracting

decimals line the decimals up

use placeholder zeros if need be and

then subtract

i hope that helped

thanks so much for watching

until next time

peace

you