 # Operations with Decimals. Adding and Subtracting Decimals.

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Operations with 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 28.9 13.31+ 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 15 9.372 -.000 4 9 9 10 826. 01 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: 8.5 X2.5 4 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 0.07 4)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 0.006 9)48 x 12.3 10)251 x 0.007

Multiplying Decimals2 1)9.5 x 0.86 2)4.3 x 9.5 3)73 x 0.59 4)59 x 0.75 5)5.8 x 4.6 6)52 x 0.93 7)4.1 x 0.23 8)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 “Inside” Dividend “Outside” Divisor “Roof” Quotient

Step 1 Place the decimal point in the quotient above the decimal point in the dividend..

Step 2 Divide as with whole numbers. 6.6 -24 24 0 -

Now try these two. 42.82.61 How did you do?

Now you try.

Check your answers. -36 10 -8 20 -20 -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

Swingin’ Monkeys Divisor Moved (swung) the decimal point 1 place to the right Swingin’ Monkey

Steps in Dividing Decimals Dividend Moved (swung) the decimal point 1 place to the right

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).

Steps in Dividing Decimals 4. Now, divide as usual!

Steps in Dividing Decimals 6 12 6 2 6 4 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 =