Transcript Tutorial 1c - C on T ech Math : : An application

Decimals: Add, Subtract, Multiply &
Divide
Lesson 1c
Adding & Subtracting Decimals
If you know how to add & subtract
whole numbers, you also know how to
add & subtract decimals.
Be sure to pay attention to place value,
add or subtract in each place, and
regroup when needed.
8.784 + 2.56 + 6.721
Adding & Subtracting Decimals
When adding or subtracting decimals:
1. Line up the decimal points.
2. Fill in zeros where no digits are
represented.
3. Use rules of adding or subtracting.
Addition:
Add up the thousandths. There are 5 thousandth.
Add the hundredths. There are 16 hundredths.
2
1
8.784
2.56 0
+ 6.721
18.06 5
• Since 16 hundredths is 1 tenth 6 hundredths, write 6 in the hundredths place. Write 1 as an
addend in the tenths place.
Add the tenths. There are 20 tenths.
• Since 20 hundredths is 2 ones 0 tenths, write 0 in the tenths place. Write 2 as an
addend in the ones place.
Add the ones. There are 18 ones.
So 8.784 + 2.56 + 6.721 = 18.065.
Adding & Subtracting Decimals
When adding or subtracting decimals:
1. Line up the decimal points.
2. Fill in zeros where no digits are represented.
3. Use rules of adding or subtracting.
Subtraction:
To subtract the thousandths, you will need more thousandths.
• Use one of the hundredths.
• Since 1 hundredth = 10 thousandths, change the number of the hundredths from 4 to 3 and
the number of thousandths from 0 to 10.
9
3 10 13
3 10
4.04 0
-2.681
1. 35 9
Now subtract. There are 9 thousandths.
Try to subtract the hundredths. You will need more hundredths.
•There are no tenths to use, so use a one. Change the number of ones from 4 to 3. Raise
the number of tenths from 0 to 9 and the number of hundredths from 3 to 13.
Subtract the hundredths. There are 5 hundredths.
Subtract the tenths. There are 3 tenths.
Subtract the ones. There is 1 one.
So 4.040 – 2.681 = 1.359
Addition Review
9.5
4.3 + 5.2
=
9.7
95
12.01
.10 + 12.1
=
12.2
13.1
103.01
.6 + 102.41
=
103.11
110.1
Subtraction Review
21.03
56.09 - 33.007
=
23.083
23.035
48.08
67.89 - 19.09
=
48.18
48.8
0.3
13.3 - 10.1 - 2.9
=
3.2
1.3
Multiplying with Decimals
You multiply decimals the same way that you multiply
whole numbers. The major difference is that you must
correctly place the decimal point in your answer.
Compare the two multiplications problems below:
29
x 55
1595
2.9
x 5.5
15.95
Each of the digits are the same. Each
of the steps are the same. But the
place values are different because of
the decimal points.
Multiply with Decimals
Placing the decimal point in the answer:
One method to decide where to place the decimal point in the
answer is by using an estimate.
Example 1:
You fill a bag with 2.30 pounds of tomatoes.
The cost is $1.85 per pound. How much
money do you spend?
To solve the problem, you can multiply 2.30
x 1.85.
Tomatoes
$1.85
Per Pound
Start with making an estimate. Multiply as you would whole
Use the estimate to place the
numbers.
decimal point.
The estimate was 4, so the decimal
2.30 x 1.85
185
point should go after the 4:

x 230
4.2550
2 x 2 = 4
42550
We can see that the answer will have The answer is 4.255. Since the answer needs to be in dollars
only one digit left of the decimal.
and cents round to the nearest cent. You spend $4.26.
Multiply with Decimals
Placing the decimal point in the answer:
Another method to decide where to place the decimal point in the answer is
by counting the number of places to the right of the decimal point in each
number.
The total tells you how many places there will be to the right of the decimal
point in your final answer.
Example 2:
Multiply 0.04 x 0.03
Multiply as if the numbers
where whole numbers.
4 x 3 = 12
Count the places to the right
of the decimal point in each
original number. Add.
0.04  2 decimal places
0.03  + 2 decimal places
4 decimal places
0.04 x 0.03 = .0012
Count the same number of places
from right to left in the answer, then
place the decimal point. (You may
need to fill places with zeros.)
0. 0.0.12.
..
Multiplication Review
8.75
4.75 • 4
=
16.75
19
.008808
.734 • .12
=
.08808
.8808
24.185
12.95 • 2.9
=
37.555
126.13
Dividing with Decimals
You divide decimals the same way that you divide
whole numbers. The major difference is that you must
correctly place the decimal point in your answer.
Compare the two division problems below:
37
14 518
-570
76
-76
0
3 .7
14 51.8
-57 0
76
-7 6
0
Each of the digits are the same. Each
of the steps are the same. But the
place values are different because of
the decimal points.
Dividing with Decimals
Dividing Decimals by Whole Numbers:
To divide a decimal by a whole number, you place the decimal point for the
answer directly above the decimal point in the dividend (the number you are
dividing into). Then you divide the same way you divide whole numbers.
Example 1:
You and three friends rent a ski boat for the day. The total cost is $178.16. If you
split the cost equally, how much does each person pay?
Divide the same way you divide
To solve the problem, you can divide 178.16  4. whole numbers.
4 4. 5 4
4 178.16
-16
18
Dividend
Divisor
-16
.
21
4 178.16
-20
16
The answer is 44.54. Each person pays $44.54.
-16
0
Write the decimal point for the
answer directly above the
decimal point in the dividend.
Dividing with Decimals
Dividing by Decimals:
To divide by a decimal, multiply the divisor (the number your dividing
by) and the dividend (the number you are dividing into) by the same
power of 10. You choose the power of ten that turns your
Write the decimal point on top
divisor into a whole number.
Example 2:
Dividend
Divisor
Divide 48  0.32
Multiply the divisor by a power Multiply the dividend by the
of 10 to make it a whole
same power of 10.
number.
0.32 x 100 = 32 (whole number)
Move the decimal point 2 places to
show this.
. 32
. . 48
directly above the new decimal
point in the dividend.
Divide the same way you divide
whole numbers.
150.
32 4800.
-32
48 x 100 = 4800
Move the decimal point 2 places to
160
show this.
-160
32 48. 00
..
48 x 0.32 = 150 0
Dividing with Decimals
Rounding your final answer:
When dividing decimals, you occasionally may need to round
your final answer. To round your final answer you will always
need to divide out the answer one decimal place past where
Write the decimal point on top directly above
you are rounding.
the new decimal point in the dividend.
Example 3: Divide 53  0.7
Divide the same way you divide whole numbers.
Round your answer to the nearest tenth.
Multiply the divisor by a power Multiply the dividend by the
of 10 to make it a whole
same power of 10.
number.
0.7 x 10 = 7 (whole number)
Move the decimal point 1 place to
show this.
.7. 53
53 x 10 = 530
Move the decimal point 1 place to
show this.
7 53 .0.
75. 7 1
7 530.00
-49
40
-35
50
-49
10
Dividing with Decimals
Rounding your final answer:
When dividing decimals, you occasionally may need to round
your final answer. To round your final answer you will always
need to divide out the answer one decimal place past where
Write the decimal point on top directly above
you are rounding.
the new decimal point in the dividend.
Example 3: Divide 53  0.7
Divide the same way you divide whole numbers.
Round your answer to the nearest tenth.
Since our answer must be rounded to the
nearest tenth, divide out to the hundredth.
Since a 1 is in the hundredth spot and it is
less than 5, then 75.71 rounds to 75.7 .
53 x 0.7  75.7
75. 7 1
7 530.00
-49
40
-35
50
-49
10
Division Review
Round your answers to the nearest hundredth
.05
63 3.09
=
.66
21
30.09
.7 21.06
=
300.8
3008
.38
.2 .32
=
1.6
3.8
Sorry!
Try a again.
Correct!!!