Adding, Subtracting, Multiplying, and Dividing Decimal Numbers

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

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.

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.

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.

Example

Example

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

Practice

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.

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.

Practice

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.

Example

Example

Practice

Reading Decimal Numbers

• Use words to name 12.625.• twelve and six hundred twenty-five

thousandths

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).

Ordering Decimal Numbers

Practice

Multiplying Decimal Numbers

Multiplying Decimal Numbers

Multiplying Decimal Numbers

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.

Examples

Practice

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).

Zeroes as Placeholders

Example

Practice