Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.
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Transcript of Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.
![Page 1: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/1.jpg)
Adding, Subtracting, Multiplying, and Dividing Decimal Numbers
![Page 2: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/2.jpg)
Warm-Up• List the first 10 multiples of 8.• 8, 16, 24, 32, 40, 48, 56, 64, 72, 80• Count by 8s from 2 to 50.• 2, 10, 18, 26, 34, 42, 50• Simplify the fraction: 6/9• 2/3• Simply the fraction: 12/9• 1 1/3• Simply the fraction: 24/9• 2 2/3
![Page 3: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/3.jpg)
Place Value
• A whole number consisting of only one digit only has a number in the ones place.
• For example, 8 is a whole number consisting of only one digit; the 8 is in the ones place.
• A whole number consisting of two digits will have a number in the tens place and a number in the ones place.
• For example, 18 is a whole number consisting of two digits; the 1 is in the tens place and the 8 is in the ones place.
![Page 4: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/4.jpg)
Decimal Places
• When a decimal number has only one digit after the decimal, that number is in the tenths place.
• When a decimal number has two digits following the decimal, the numbers are in the tenths place and the hundredths place.
• Three digits after the decimal would fill the tenths, hundredths, and thousandths places.
![Page 5: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/5.jpg)
Aligning the Decimal, Place Value
• When adding or subtracting fractions, we align the decimal point because that will align the digits of the same place value.
• If we have a whole number without a decimal, we write in a decimal after the ones place.
• We can fill any decimal place with zero so that each number has the same place values filled with digits.
![Page 6: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/6.jpg)
Example
![Page 7: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/7.jpg)
Example
![Page 8: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/8.jpg)
Review
• Which digit in 4.65 has the same place value as the 2 in 12?
• 4, both the 4 and the 2 are in the ones place• Which digit in 13.65 has the same place value as
the 8 in 7.834?• 6, both the 6 and the 8 are in the tenths place• Which digit in 100.401 has the same place value
as the 9 in 834.229?• 1, both the 9 and the 1 are in the thousandths
place
![Page 9: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/9.jpg)
Practice
![Page 10: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/10.jpg)
Simplifying Numbers
• We communicate numbers in their simplest forms.
• One way to simplify numbers is to remove unnecessary zeroes.
• We can remove zeroes from the front of whole numbers.
• 0023 can be simplified by removing the zeroes in front of the tens and ones places, leaving 23.
![Page 11: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/11.jpg)
Simplifying Decimal Numbers
• We can also remove zeroes at the end of decimal numbers.
• 23.400 can be simplified by removing the two zeroes in the hundredths and thousandths places, leaving 23.4.
• 09.200 can be simplified by removing the zero in the ones place, hundredths place, and thousandths place, leaving 9.2.
![Page 12: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/12.jpg)
Practice
![Page 13: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/13.jpg)
Subtracting Decimal Numbers
• For some subtraction problems, we need to add decimal places to perform the subtraction.
• If we subtract 0.23 from 0.4, we first fill the hundredths place with a zero then we subtract.
![Page 14: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/14.jpg)
Example
![Page 15: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/15.jpg)
Example
![Page 16: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/16.jpg)
Practice
![Page 17: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/17.jpg)
Reading Decimal Numbers
• Use words to name 12.625.• twelve and six hundred twenty-five
thousandths
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Comparing Decimal Numbers
• When we compare the highest decimal place value, we see that 5 (in the tenths place) is greater than 4 (also in the tenths place).
![Page 19: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/19.jpg)
Ordering Decimal Numbers
![Page 20: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/20.jpg)
Practice
![Page 21: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/21.jpg)
Multiplying Decimal Numbers
![Page 22: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/22.jpg)
Multiplying Decimal Numbers
![Page 23: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/23.jpg)
Multiplying Decimal Numbers
![Page 24: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/24.jpg)
Multiplying Decimal Numbers• When we set up a decimal multiplication problem,
we do not line up the decimal points as we do in addition and subtraction.
• We just set up the problem as though it were a whole-number problem and then multiply.
• To place the decimal point in the answer, we first count the total number of decimal places in both factors.
• Then we insert a decimal point in the answer so that is has the same total number of decimal places as the factors.
![Page 25: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/25.jpg)
Examples
![Page 26: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/26.jpg)
Practice
![Page 27: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/27.jpg)
Zeroes as Placeholders
• Sometimes there are more decimal places in the factors than there are digits in the product.
• To complete the multiplication, we fill the empty place(s) with a zero(es).
![Page 28: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/28.jpg)
Zeroes as Placeholders
![Page 29: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/29.jpg)
Example
![Page 30: Adding, Subtracting, Multiplying, and Dividing Decimal Numbers.](https://reader036.fdocuments.us/reader036/viewer/2022081501/56649e6f5503460f94b6c97f/html5/thumbnails/30.jpg)
Practice