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Multiplying Decimals

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WARM UP

564.76 – 332.78 = 231.98

34.84 + 17.69 + 20.7 = 73.23

2.45698 – 1.26589 = 1.19109

Is it true? 17.985 – 9.001 = 8.585 No

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Lets review what we did in the last lesson

To add decimals we need to align all decimal points in one line.

We start from the right end and the carry goes across the decimal point .

Lets try an example 3 5 . 1 4 5 1 4, 5 6 5 . 2 4 8 . 7

14, 6 0 9 . 0 8 5

1 1

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We Subtract Decimals in the same way

Align all decimals so that the decimal points are in a vertical line.

Add zeros to the right side of the decimal with fewer decimal places so that each decimal has the same number of decimal places.

Review

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Review

Lets try an example

2 9 6 . 7 0 - 8 5 . 6 2

Remember We add Zeros to the right side

of the decimal with fewer decimal places

2 1 1 . 0 8

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Modeling Multiplication of Decimals

Multiplying a Whole Number by a DecimalExample: 2 x 0.92

0.92 0.92

Move 8 squares

Shade 92 squares in each of two grids.

Move 8 hundredths from the second grid to fill the first grid.

Count the shaded square in the grids.

The shaded area is 1 whole and 84 hundredths, or 1.84

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Modeling Multiplication of Decimals

Multiplying DecimalsExample: 0.5 x 0.4

Shade 4 columns of a grid to represent 0.4

Shade 5 rows to represent 0.5. Use a different color or style.

The shadings overlap in 20 squares, representing 20 hundredths, or 0.20.So, 0.5 x 0.4 = 0.20

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Your Turn!

• 3 x 0.9 = 2.7• 0.8 x 0.5 = 4.00

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Lets Get Started !

Today we will learn about Multiplying Decimals

We are familiar with the multiplication of whole numbers .

To multiply decimal numbers we first ignore the decimals and multiply as usual

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Multiply Decimals

Starting on the right, multiply each digit in the top number by each digit in the bottom number just as you do with whole numbers

Now add the products.

Now place the decimal point in the answer by starting at the right and moving the number of places equal to the sum of the decimal places in both numbers multiplied.

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Let us understand it better with an example

We find the product of 0.03 x 0.002

 Ignore the decimal points and just multiply the two numbers

3 × 2 = 6

Together 0.03 and 0.002 have five digits after decimal places. Therefore, start from the right and move left five places and then place the decimal

We get 0.03 x 0.002 = 0.0 0 0 0 6

5 4 3 2 1 -> Counting Decimal places12 345

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Let us try another example

Find the product of

1.51 x 6.2

1. 5 1 (2 decimal places) 6. 2 (1 decimal place)

So the answer will have 3 decimal places.

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Solving the same example

1.5 1 x 6.2___________ 3 0 2 9 0 6 x__________ 9 3 6 2

Just count the numbers / places from right to left in both the numbers

to be multiplied ,and then add them and Insert the decimal after those

many places.

Multiply Decimals

1 23

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Lets take another example

Multiply 3.77 x (- 2.8)

3 .7 7 x 2.8 __________ 3 0 1 6 7 5 4 _________ -10 .5 5 6 ____________

Note the negative sign.

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When we multiply two numbers withSame sign we get +

And with Different sign we get -

Remember

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You try some !

0.0023 x 5.84 = 0.013432

0.00404 x 2 = 0.00808

0.3 x .028 = 0.0084

The number 5 times 0.5 equals 2.5

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Properties of Multiplication• Commutative property

– Changing the order of the factors does not change the product.

• 4.7 x 5 = 5 x 4.7

• Associative property– Changing the grouping of the factors does not change

the product.• (4.7 x 5) x 2 = 4.7 x (5 x 2)

• Identity property– The product of 1 and any number is that number.

• 4.7 x 1 = 1 x 4.7 = 4.7

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Properties of Multiplication

• Find 4 x (8 x $.25)= 4 x ($.25 x 8) Commutative property= (4 x $.25) x 8 Associative property= $1 x 8 Multiply inside the

parentheses– =$8 Identity property

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Your Turn!

• 2(5 x 2.3)

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BREAK TIME

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LETS PLAY A GAME

Click Here to Play

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Jose took $460 from his Uncle to buy a computer. He promised to return the money within a year. Jose returned $35.50 for five months and the remaining part of the year he returned $40 per month.

Find out how much money Jose still owes?

Jose still owes $2.50 to his uncle

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To correct the small difference between 365 days and 365.24 days , a leap year of 366 days is interposed every four years except in years that are divisible by 100 ,but not by 400. Why does this rule work ?

3 x 365 + 366 is slightly greater than 4 x 365.24

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Margaret works 7.5 hours a day for five days in a week and get paid $6.74/hr. How much does she make each day? What can she save in a year, if her monthly expenditure is $500.50

$50.55 a dayAssuming 4 weeks a month she makes $50.55 x 5 x 4=

$1011

Expenditure $500 So saving $1011 - $500.50 = $510.50 per monthAnd $510.50 x 12 = $6126 savings in a year.

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Assessment

1. Find each product.1. 0.018 x 4 = 0.0722. 1.9 x 9 = 17.13. 31 x 5.6= 173.6

2. Find each product.1. 0.12(0.96)=0.11522. 0.06(0.18)=0.01083. 0.486 x 0.9=0.4374

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Assessment

3. Complete and tell the property used.1. 2 x 79 x 0.5 = 79 x _ x 0.5 2; commutative2. (0.4 x 83) x 5 = 0.4 x (_ x 5) 83; associative

4. When you multiply two decimals between 0 and 1, is the product less than or greater than both factors? Less than both the factors; sample answer: 0.5 x 0.4 = 0.2; which is less than both 0.5 and 0.4

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Lets Review what we have learnt in this lesson

To multiply decimal numbers

Ignore the decimal points

Align them and multiply the numbers as whole numbers like this :

5 8 8.0 9 x 257.2

58809 x 2572 ______________ 15125648

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In the final product count how many decimal places are there on the right side of the decimal points in the two numbers that are multiplied

Now add them and place the decimal point in your answer so that there are those many numbers on the right.

. 588.09

x 257.2 ______________ 151256.748

RememberAlways count from right side

to put the decimal

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Be sure to practice what you have learned.

You had a Great Lesson Today