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Operations with Decimals

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Adding and Subtracting Decimals

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The Basic Steps: Line up the numbers by the decimal point. Fill in missing places with zeroes. Add or subtract.

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Example: 28.9 + 13.31 28.9 13.31+ 0 42.21

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Example 17.548 + 126.1

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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.

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Example: 15 – 9.372 15 9.372 -.000 4 9 9 10 826. 01 5

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Example 21.8 – 7.125

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Practice

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Homework Time Pg 112 Questions 1-20

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Multiplying Decimals

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Step 1: Multiply as if the factors were whole numbers

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Step 1: 8.5 X2.5 4 2 5 1 7 0 0 2 1 2 5 next…..

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Step 2: Count the total decimals places in the factors

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Step 2: 8.5 X2.5 4 2 5 1 7 0 0 2 1 2 5 next…..

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Step 3: Give the product the total decimal places of the factors

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Step 3: 8.5 X2.5 4 2 5 1 7 0 0 2 1.2 5

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Examples .25 x 4.2 85 x 4.36

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Try These: 1. 4.8 2. 3.55 x 0.5 x.05

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Practice, if m= 5.8 4.52m 0.78m 12.3m 125.6m 64m 254m

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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

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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

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Dividing Decimals by Whole Numbers

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Division Vocabulary “Inside” Dividend “Outside” Divisor “Roof” Quotient

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

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

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Step 3 Check your answer. Multiply the quotient by the divisor. Your answer should be the dividend. 6.6 X 4 26.4

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Now try these two. 42.82.61 How did you do?

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Now you try.

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Check your answers. -36 10 -8 20 -20 -8 46 -40 60 -56 40 -40

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Practice 23.5 ÷ 4 54 ÷ 7 124.6 ÷ 5 6523 ÷ 6

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Dividing Decimals “Swingin’ Monkeys”

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Swinging Monkeys! Follow these steps and you will be great at dividing decimals! Remember: Whatever the OUTSIDE monkeys do – the INSIDE monkeys do also!

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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!

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Steps in Dividing Decimals – Swingin’ Monkeys

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

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

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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).

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

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Steps in Dividing Decimals 6 12 6 2 6 4 3

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More Examples 12.45 ÷ 0.03 0.2764 ÷.0004

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Remember: The more neatly you write and keep the numbers lined up, the BETTER! Let’s Practice

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Your Turn - Practice 1)14.2 ÷ 0.2 = 2)25.5 ÷ 1.5 =

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