Confidential1 Multiplying Decimals

Confidential2 WARM UP – = = – = Is it true? – = No

Confidential3 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 , ,

Confidential4 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

Confidential5 Review Lets try an example Remember We add Zeros to the right side of the decimal with fewer decimal places

Confidential6 Modeling Multiplication of Decimals Multiplying a Whole Number by a Decimal Example: 2 x 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

Confidential7 Modeling Multiplication of Decimals Multiplying Decimals Example: 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 So, 0.5 x 0.4 = 0.20

Confidential8 Your Turn! 3 x 0.9 = x 0.5 = 4.00

Confidential9 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

Confidential10 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.

Confidential11 Let us understand it better with an example We find the product of 0.03 x Ignore the decimal points and just multiply the two numbers 3 × 2 = 6 Together 0.03 and 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 = > Counting Decimal places12 345

Confidential12 Let us try another example Find the product of 1.51 x (2 decimal places) 6. 2 (1 decimal place) So the answer will have 3 decimal places.

Confidential13 Solving the same example x 6.2 ___________ x __________ 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 \ \ \

Confidential14 Lets take another example Multiply 3.77 x (- 2.8) x 2.8 __________ _________ ____________ Note the negative sign.

Confidential15 When we multiply two numbers with Same sign we get + And with Different sign we get - Remember

Confidential16 You try some ! x 5.84 = x 2 = x.028 = The number 5 times 0.5 equals 2.5

Confidential17 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

Confidential18 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

Confidential19 Your Turn! 2(5 x 2.3)

Confidential20 BREAK TIME

Confidential21 LETS PLAY A GAME Click Here to Play

Confidential22 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

Confidential23 To correct the small difference between 365 days and 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 is slightly greater than 4 x

Confidential24 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 $ $50.55 a day Assuming 4 weeks a month she makes $50.55 x 5 x 4= $1011 Expenditure $500 So saving $ $ = $ per month And $ x 12 = $6126 savings in a year.

Confidential25 Assessment 1.Find each product x 4 = x 9 = x 5.6= Find each product (0.96)= (0.18)= x 0.9=0.4374

Confidential26 Assessment 3.Complete and tell the property used. 1.2 x 79 x 0.5 = 79 x _ x 0.5 2; commutative 2.(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

Confidential27 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 : x x 2572 ______________

Confidential28 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 x ______________ Remember Always count from right side to put the decimal

Confidential29 Be sure to practice what you have learned. You had a Great Lesson Today