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Multiplication and Division of Decimals
Back to Algebra–Ready Review Content.
47
7x
9
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
9For example,
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
4x7=28
9For example,
6
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28
9For example,
6
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28 7x7=49,
9For example,
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28 7x7=49,
49+2=51
9For example,
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28 7x7=49,
1
record
the 1
49+2=51
9For example,
carry
the 5
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28 7x7=49,
1
record
the 1
carry
the 5
49+2=51
9
9x7=63,
63+5= 68
For example,
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28 7x7=49,
1
record
the 1
carry
the 5
49+2=51
9
9x7=63,
63+5= 68
8
record
the 8
carry
the 6
6
For example,
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
6
we start the multiplication by
multiplying the top with the
bottom right most digit.
47
7x
8
record
the 8
carry
the 2
4x7=28 7x7=49,
1
record
the 1
carry
the 5
49+2=51
9
9x7=63,
63+5= 68
8
record
the 8
carry
the 6
6When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example,
6
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
1
record
the 1
9
8
record
the 8
carry
the 6
6
6x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
4x6=24
1
record
the 1
9
8
record
the 8
carry
the 6
6
6x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
4x6=24
1
record
the 1
←record
9
8
record
the 8
carry
the 6
6
6
carry
the 2
4
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
4x6=24 7x6=42,
1
record
the 1
←record
42+2=44
9
8
record
the 8
carry
the 6
6
6
carry
the 2
4
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
carry
the 4
4x6=24 7x6=42,
1
record
the 1
←record
42+2=44
9
8
record
the 8
carry
the 6
6
6
carry
the 2
44
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
carry
the 4
4x6=24 7x6=42,
1
record
the 1
←record
42+2=44
9
9x6=54
54+4= 58
8
record
the 8
carry
the 6
6
6
carry
the 2
44
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example, 47
7
8
record
the 8
carry
the 4
4x6=24 7x6=42,
1
record
the 1
←record
42+2=44
9
9x6=54
54+4= 58
8
record
the 8
carry
the 6
6
6
carry
the 2
4485
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example,
Because we are in a
place value system, the
result of the multiplication
must be placed in the correct slots,
so it is shift one place to the left.
47
7
8
record
the 8
carry
the 4
4x6=24 7x6=42,
1
record
the 1
←record
42+2=44
9
9x6=54
54+4= 58
8
record
the 8
carry
the 6
6
6
carry
the 2
Finally, we obtain the answer
by adding the two columns.
4485+
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
we start the multiplication by
multiplying the top with the
bottom right most digit.
When this is completed, we
proceed with the multiplication to
the next digit of the bottom number.
For example,
Because we are in a
place value system, the
result of the multiplication
must be placed in the correct slots,
so it is shift one place to the left.
47
7
8
record
the 8
carry
the 4
4x6=24 7x6=42,
1
record
the 1
←record
42+2=44
9
9x6=54
54+4= 58
8
record
the 8
carry
the 6
6
6
carry
the 2
Finally, we obtain the answer
by adding the two columns.
4485
8526 5
+
x
Let's review the multiplication of two
multiple digit numbers. Such a problem
is treated as multiple problems of
multiplying with a single digit number.
Multiplication and Division of Decimals
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer.
Multiplication and Division of Decimals
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer.
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7
47
7
81
9
866
4485
8526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer.
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7
Ignore the decimal points and multiply
974 x 67 = 65258.
I. count the total number of places to the right of the decimal point in both
decimal numbers,
47
7
81
9
866
4485
8526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7
Ignore the decimal points and multiply
974 x 67 = 65258. Put back the decimal
points to count the number of places after
them, which is 3.
I. count the total number of places to the right of the decimal point in both
decimal numbers,
47
7
81
9
866
4485
8526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7
Ignore the decimal points and multiply
974 x 67 = 65258. Put back the decimal
points to count the number of places after
them, which is 3.
..
There are 3
places after the
decimal point
I. count the total number of places to the right of the decimal point in both
decimal numbers,
II. take the decimal point at the right end of their product, count to the left
the same total–number of places, to place the decimal point.
47
7
81
9
866
4485
8526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7.
.
There are 3
places after the
decimal point
Ignore the decimal points and multiply
974 x 67 = 65258. Put back the decimal
points to count the number of places after
them, which is 3.
I. count the total number of places to the right of the decimal point in both
decimal numbers,
II. take the decimal point at the right end of their product, count to the left
the same total–number of places, to place the decimal point.
47
7
81
9
866
4485
8526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7.
.
There are 3
places after the
decimal point
Move the decimal point of the product
3 places to the left for the answer.
Ignore the decimal points and multiply
974 x 67 = 65258. Put back the decimal
points to count the number of places after
them, which is 3.
I. count the total number of places to the right of the decimal point in both
decimal numbers,
II. take the decimal point at the right end of their product, count to the left
the same total–number of places, to place the decimal point.
47
7
81
9
866
4485
526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7.
.
There are 3
places after the
decimal point
Move the decimal point of the product
3 places to the left for the answer.
So move the decimal point
3 places left.
.. 8
Ignore the decimal points and multiply
974 x 67 = 65258. Put back the decimal
points to count the number of places after
them, which is 3.
I. count the total number of places to the right of the decimal point in both
decimal numbers,
II. take the decimal point at the right end of their product, count to the left
the same total–number of places, to place the decimal point.
47
7
81
9
866
4485
526 5
x
To multiply two decimal numbers, do exactly the same–then insert
the decimal point in the product at the correct place for the final
answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example A. Multiply 9.74 x 6.7.
.
There are 3
places after the
decimal point
Move the decimal point of the product
3 places to the left for the answer.
So move the decimal point
3 places left.
.. 8
Hence 9.74 x 6.7 = 65.258
Ignore the decimal points and multiply
974 x 67 = 65258. Put back the decimal
points to count the number of places after
them, which is 3.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
Remove the trailing 0’s to the right for the multiplication decimal numbers.
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
So move the decimal point
two places left to place the
decimal point.
0. 8 4.
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
So move the decimal point
two places left to place the
decimal point.
0. 8 4.
b. Multiply 0.00012 x 0.00700.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
So move the decimal point
two places left to place the
decimal point.
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.
8 4.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
So move the decimal point
two places left to place the
decimal point.
8 4. = 12 x 7
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.
There are eight places after the decimal points so move the point eight
place left and fill in 0’s as we move:
8 4.
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
So move the decimal point
two places left to place the
decimal point.
8 4. = 12 x 7
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.
There are eight places after the decimal points so move the point eight
place left and fill in 0’s as we move:
8 4.
0.0 0 0 0 0 0
8 places
Multiplication and Division of Decimals
Example B. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places
after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
So move the decimal point
two places left to place the
decimal point.
8 4. = 12 x 7
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.
There are eight places after the decimal points so move the point eight
place left and fill in 0’s as we move:
8 4.
0.0 0 0 0 0 0
8 placesHence 0.00012 x 0.00700 = 0.00000084.
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual
651.3
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual
651.3
= 1.3 ÷ 65651.3
Calculate
by long division.
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual
651.3
)6 5 1 . 3= 1.3 ÷ 65
651.3
Calculate
by long division.
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3
.
= 1.3 ÷ 65651.3
Calculate
by long division. the decimal point place
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3
0 . 0
= 1.3 ÷ 65651.3
Calculate
by long division. the decimal point place
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3 0
0 . 0
= 1.3 ÷ 65651.3
Calculate
by long division. the decimal point place
Pack trailing 0’s
so it’s enough to
enter a quotient
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3 01 3 0
2.
0
= 1.3 ÷ 65651.3
Calculate
by long division. the decimal point place
00 Pack trailing 0’s
so it’s enough to
enter a quotient
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3
Calculate
by long division. the decimal point place
00 Pack trailing 0’s
so it’s enough to
enter a quotient
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
Example C. a. Compute 0.0013 ÷ 0.00065
We change a problem of dividing two decimal numbers to a problem that is
a decimal number divided by an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3
Calculate
by long division.
00
the decimal point place
Pack trailing 0’s
so it’s enough to
enter a quotient
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
Example C. a. Compute 0.0013 ÷ 0.00065
We change a problem of dividing two decimal numbers to a problem that is
a decimal number divided by an integer. Write the problem as a fraction then
move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3
Calculate
by long division.
0.00065
0.0013Write 0.0013 ÷ 0.00065 as
00
the decimal point place
Pack trailing 0’s
so it’s enough to
enter a quotient
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
Example C. a. Compute 0.0013 ÷ 0.00065
.
move 5 places so the numerator is an integer.
We change a problem of dividing two decimal numbers to a problem that is
a decimal number divided by an integer. Write the problem as a fraction then
move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3
Calculate
by long division.
0.00065
0.0013Write 0.0013 ÷ 0.00065 as . =
.65
13.
0 0
00
the decimal point place
Pack trailing 0’s
so it’s enough to
enter a quotient
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
Example C. a. Compute 0.0013 ÷ 0.00065
.
move 5 places so the numerator is an integer.
We change a problem of dividing two decimal numbers to a problem that is
a decimal number divided by an integer. Write the problem as a fraction then
move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3
Calculate
by long division.
0.00065
0.0013Write 0.0013 ÷ 0.00065 as =
.65
13.
0 0= 2
Hence 0.0013 ÷ 0.00065 = 2
00
the decimal point place
Pack trailing 0’s
so it’s enough to
enter a quotient
.
Multiplication and Division of Decimals
Example B. Compute by long division.
To divide a decimal number by an integer, do long division as usual and
leave the decimal point in the same position for the quotient .
Example C. a. Compute 0.0013 ÷ 0.00065
.
move 5 places so the numerator is an integer.
We change a problem of dividing two decimal numbers to a problem that is
a decimal number divided by an integer. Write the problem as a fraction then
move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3
Calculate
by long division.
0.00065
0.0013Write 0.0013 ÷ 0.00065 as =
.65
13.
0 0= 2
Hence 0.0013 ÷ 0.00065 = 2
00
the decimal point place
Pack trailing 0’s
so it’s enough to
enter a quotient
.
Multiplication and Division of Decimals
Example C. b. Compute 0.00013 ÷ 0.65
Multiplication and Division of Decimals
Example C. b. Compute 0.00013 ÷ 0.65
0.65
0.00 013Write 0.00013 ÷ 0.65 as
Multiplication and Division of Decimals
Example C. b. Compute 0.00013 ÷ 0.65
.move 2 places
0.65
0.00 013Write 0.00013 ÷ 0.65 as .
= .65
0 013.
Multiplication and Division of Decimals
Example C. b. Compute 0.00013 ÷ 0.65
.move 2 places
)65 0 .1 3
0.65
0.00 013Write 0.00013 ÷ 0.65 as .
= .65
0 013.
Calculate this by long division:
Multiplication and Division of Decimals
Example C. b. Compute 0.00013 ÷ 0.65
.move 2 places
)65 0 .1 3 0
1 3 0
0 20 .0
0
0.65
0.00 013Write 0.00013 ÷ 0.65 as .
= .65
0 013.
Hence 0.0013 ÷ 0. 65 = 0.002.
Calculate this by long division:
