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

Practice

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 =