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
28.913.31+
0
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
159.372-
.0004 9 9 10
826.
0 1
5
Example 21.8 – 7.125
Homework Time
• Pg 112 Questions 1-20
Multiplying Decimals
Step 1:Multiply as if the factors were whole
numbers
Step 1: 8.5X2.54 2 5
1 7 0 0 2 1 2 5 next…..
Step 2:Count the total
decimals places in the factors
Step 2: 8.5
X2.5 4 2 5
1 7 0 0 2 1 2 5 next…..
Step 3:Give the product
the total decimal places of the factors
Step 3: 8.5
X2.5 4 2 5
1 7 0 0 2 1 .2 5
Examples
.25 x 4.2 85 x 4.36
Try These:
1. 4.8 2. 3.55 x 0.5 x .05
Practice, if m= 5.8
• 4.52m• 0.78m• 12.3m• 125.6m• 64m• 254m
Multiplying Decimals1
1) 0.6 x 0.4
2) 0.008 x 0.5
3) 3.0 x 0.074) 0.12 x 0.6
5) 5.23 x 1.2
6) 1.25 x 8
7) 23 x 0.25
8) 15.12 x 0.0069) 48 x 12.3
10)251 x 0.007
Multiplying Decimals2
1) 9.5 x 0.862) 4.3 x 9.53) 73 x 0.594) 59 x 0.755) 5.8 x 4.66) 52 x 0.937) 4.1 x 0.238) 0.31 x 4.6
9) 0.35 x 0.7010)4.7 x 5811)2.1 x 3212)5.4 x 1313)47 x 0.6814)8.2 x 7315)15 x 7.816)1.8 x 6.1
Dividing Decimals by Whole Numbers
Division Vocabulary
64.122
“Inside”Dividend
“Outside”Divisor
“Roof”Quotient
Step 1
4.264
Place the decimal point in the quotient above the decimal point in the dividend.
.
Step 2
Divide as with whole numbers.
4.264
6.6
-242424
0
-
Step 3
Check your answer. Multiply the
quotient by the divisor.
Your answer should be the dividend.
6.6
X 4
26.4
Now try these two.
6.85242.8
05.1352.61
How did you do?
Now you try.
6.128 374
Check your answers.
-3610-8
20-20
1.57512.6008 -8
46-40
60-56
40-40
4 3 7 0 09 2 5
.
.
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 Decimals1. 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
64.122.
Swingin’ Monkeys
64.122.Divisor
Moved (swung) the decimal point 1 place to the right
Swingin’
Monkey
Steps in Dividing Decimals
64.122. Dividend
Moved (swung) the decimal point 1 place to the right
Steps in Dividing Decimals – Swingin’ Monkeys
64.122.
3. Place (swing) the decimal point in the answer (quotient) lined up with the decimal point in the dividend (on the roof).
Steps in Dividing Decimals
4.1262
4. Now, divide as usual!
Steps in Dividing Decimals
4.12626
126
2
64
3
More Examples
• 12.45 ÷ 0.03• 0.2764 ÷ .0004
Remember: The more neatly you write and keep the numbers lined up, the BETTER!
Let’s Practice
Your Turn - Practice
1) 14.2 ÷ 0.2 =
2) 25.5 ÷ 1.5 =