Transcript Adding and Subtracting Decimals

Operations with Decimals
Adding and Subtracting
Decimals
The Basic Steps:
• Line up the numbers by the
decimal point.
• Fill in missing places with
zeroes.
• Add or subtract.
Example: 28.9 + 13.31
28.90
+ 13.31
42.21
Example 17.548 + 126.1
Subtracting Across Zeroes
• If you have several zeroes in a
row, and you need to borrow,
go to the first digit that is not
zero, and borrow.
• All middle zeroes become 9’s.
• The final zero becomes 10.
Example: 15 – 9.372
0 14
9
9
10
15 .000
- 9.372
5 .6 28
Example 21.8 – 7.125
Practice
Homework Time
• Pg 112 Questions 1-20
Multiplying
Decimals
Step 1:
Multiply as if the factors
were whole numbers
Step 1:
8.5
X2.5
425
1700
2 1 2 5 next…..
Step 2:
Count the total
decimals places in the
factors
Step 2:
8.5
X2.5
425
1700
2 1 2 5 next…..
Step 3:
Give the product
the total decimal
places of the
factors
Step 3:
8.5
X2.5
425
1700
2 1 .2 5
Examples
 .25 x 4.2
 85 x 4.36
Try These:
1. 4.8
x 0.5
2. 3.55
x .05
Practice, if m= 5.8
•
•
•
•
•
•
4.52m
0.78m
12.3m
125.6m
64m
254m
Multiplying Decimals1
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
0.6 x 0.4
0.008 x 0.5
3.0 x 0.07
0.12 x 0.6
5.23 x 1.2
1.25 x 8
23 x 0.25
15.12 x 0.006
48 x 12.3
251 x 0.007
Multiplying Decimals2
1)
2)
3)
4)
5)
6)
7)
8)
9.5 x 0.86
4.3 x 9.5
73 x 0.59
59 x 0.75
5.8 x 4.6
52 x 0.93
4.1 x 0.23
0.31 x 4.6
9) 0.35 x 0.70
10) 4.7 x 58
11) 2.1 x 32
12) 5.4 x 13
13) 47 x 0.68
14) 8.2 x 73
15) 15 x 7.8
16) 1.8 x 6.1
Dividing Decimals by Whole
Numbers
Division Vocabulary
2 12.64
“Outside”
Divisor
“Inside”
Dividend
“Roof”
Quotient
Step 1
.
4 26.4
Place the decimal
point in the quotient
above the decimal
point in the dividend.
Step 2
6.6
4 26.4
-24
24
- 24
0
Divide as with whole
numbers.
Step 3
6.6
X 4
26.4
Check your answer.
Multiply the quotient
by the divisor.
Your answer should be
the dividend.
Now try these two.
42.8
2.61
2 85.6
5 13.05
How did you do?
Now you try.
4 37
8 12.6
Check your answers.
9.25
4 37.00
-36
10
-8
20
-20
1.575
8 12.600
-8
46
-40
60
-56
40
-40
Practice
•
•
•
•
23.5 ÷ 4
54 ÷ 7
124.6 ÷ 5
6523 ÷ 6
Dividing Decimals
“Swingin’ Monkeys”
Swinging Monkeys!
Follow these steps and you
will be great at dividing
decimals!
Remember: Whatever the
OUTSIDE monkeys do –
the INSIDE monkeys do
also!
Steps in Dividing Decimals
1. Make the divisor (outside number) a
whole number by moving (swingin’)
the decimal to the right as many
places as it takes to make it a
WHOLE NUMBER.
2. In MONKEY TERMS: Whatever the
outside monkey does (how far it
swings) the inside monkey does also.
Then the monkey climbs up and sits
on the roof!
Steps in Dividing Decimals –
Swingin’ Monkeys
.2 12.64
Swingin’ Monkeys
Divisor
.2 12.64
Moved (swung)
the decimal point
1 place to the
right
Steps in Dividing Decimals
Moved (swung)
the decimal point
1 place to the
right
.2 12.64
Dividend
Steps in Dividing Decimals –
Swingin’ Monkeys
3. Place (swing) the decimal point in the answer
(quotient) lined up with the decimal point in the dividend
(on the roof).
.2 12.64
Steps in Dividing Decimals
4. Now, divide as usual!
2 126.4
Steps in Dividing Decimals
63 2
2 126.4
12
6
6
4
More Examples
• 12.45 ÷ 0.03
• 0.2764 ÷ .0004
Let’s Practice
Remember: The more neatly you write and keep
the numbers lined up, the BETTER!
Your Turn - Practice
1) 14.2 ÷ 0.2 =
2) 25.5 ÷ 1.5 =