32 multiplication and division of decimals
TRANSCRIPT
Multiplication and Division of Decimals
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
7x8
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
7x8
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
7x8
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
7x8
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
7x8
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
7x8
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
7x8
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
78
record the 8
1
record the 1
9
8
record the 8
carry the 6
66x
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
78
record the 8
4x6=24
1
record the 1
9
8
record the 8
carry the 6
66
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
78
record the 8
4x6=24
1
record the 1
←record
9
8
record the 8
carry the 6
66
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
78
record the 8
4x6=24 7x6=42,
1
record the 1
←record
42+2=44 9
8
record the 8
carry the 6
66
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
78
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
66
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
78
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
66
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
78
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
66
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
78
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
66
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
78
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
66
carry the 2
Finally, we obtain the answer by adding the two columns.
44
85
85 2 6 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
47781
9
866
448585 2 6 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 6.7Ignore 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,
47781
9
866
448585 2 6 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 6.7Ignore 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,
47781
9
866
448585 2 6 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 6.7Ignore 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.
47781
9
866
448585 2 6 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.
47781
9
866
448585 2 6 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 product3 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.
47781
9
866
44855 2 6 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 product3 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.
47781
9
866
44855 2 6 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 product3 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 0.700Remove 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 0.700Remove 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 0.700Remove 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 ÷ 65651.3Calculate
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 ÷ 65651.3Calculate
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 ÷ 65651.3Calculate
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 . 30 . 0
= 1.3 ÷ 65651.3Calculate
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 00 . 0
= 1.3 ÷ 65651.3Calculate
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 ÷ 65651.3Calculate
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 ÷ 65651.3Calculate
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 ÷ 65651.3Calculate
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 ÷ 65651.3Calculate
by long division.
0.000650.0013Write 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 ÷ 65651.3Calculate
by long division.
0.000650.0013Write 0.0013 ÷ 0.00065 as
. = .
6513 .
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 ÷ 65651.3Calculate
by long division.
0.000650.0013Write 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 ÷ 65651.3Calculate
by long division.
0.000650.0013Write 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 DecimalsExample C. b. Compute 0.00013 ÷ 0.65
Multiplication and Division of DecimalsExample C. b. Compute 0.00013 ÷ 0.65
0.650.00 013Write 0.00013 ÷ 0.65 as
Multiplication and Division of DecimalsExample C. b. Compute 0.00013 ÷ 0.65
. move 2 places
0.650.00 013Write 0.00013 ÷ 0.65 as .
= . 650 013.
Multiplication and Division of DecimalsExample C. b. Compute 0.00013 ÷ 0.65
. move 2 places
)65 0 .1 3
0.650.00 013Write 0.00013 ÷ 0.65 as .
= . 650 013.
Calculate this by long division:
Multiplication and Division of DecimalsExample C. b. Compute 0.00013 ÷ 0.65
. move 2 places
)65 0 .1 3 01 3 0
0 20 . 0
0
0.650.00 013Write 0.00013 ÷ 0.65 as .
= . 650 013.
Hence 0.0013 ÷ 0. 65 = 0.002.
Calculate this by long division: