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Models and Pictorials Warm-up Say Cheese! Powerpoint Multiplying Decimals Guided Practice Ice Cream Shop Say Cheese! (Warm Up) 1. Mr. Flanagan buys a 2½ pound wheel of cheese. His family eats 1⅓ of the wheel. How much cheese have they eaten? 2 12 x 113 = 52 1 4 2 10 x3 = 3 = 3 13 pounds 2. If each person in North America throws away 3⅔ pounds of garbage each day, how many pounds of garbage does each person throw away in a week? 3 23 x 7= 11 3 x 2 7 77 1 = 3 =25 3 pounds Decimal Times We can use what we learned about multiplying fractions to help us understand multiplying decimals. Use area models to multiply 0.5 x 0.3. 0.3 = 0.15 X 0.5 = X Adapted from CMP2, Bits & Pieces III Decimal Times Use area models to multiply 0.9 x 0.4. 0.9 X 0.4 = = X Adapted from CMP2, Bits & Pieces III 0.36 Decimal Times Use area models to multiply 0.7 x 0.8. 0.7 X 0.8 = = X Adapted from CMP2, Bits & Pieces III 0.56 Decimal Times What is the relationship between the products in Set A and the corresponding products in Set B. Set A Set B 0.5 x 0.3 = 0.15 5 x 3 = 15 0.9 x 0.4 = 0.36 9 x 4 = 36 0.7 x 0.8 = 0.56 7 x 8 = 56 The products in Set B are greater than the products in Set A, but they have the same digits. Adapted from CMP2, Bits & Pieces III Decimal Times What conclusion can we draw about multiplying decimals based on this relationship? Whether we are multiplying whole numbers or decimals, you start with multiplying the whole numbers. For example: 0.5 x 0.3, you start by multiplying 5 x 3. Adapted from CMP2, Bits & Pieces III Decimal Times So far we only dealt with decimals in the tenths place. Let’s use our calculator to explore what happens when we multiply decimals in the hundredths and thousandths place. What pattern do you notice? 0.05 x 0.03 = 0.0015 0.05 x 0.003 = 0.00015 0.005 x 0.003 = 0.000015 Possible answer: More digits behind the decimal in the problem results in more digits behind the decimal in the answer; or the total number of digits behind the decimal in the problem is the same as the number of digits behind the decimal in the answer. Adapted from CMP2, Bits & Pieces III Decimal Times With your partner, write an algorithm for multiplying any two decimal numbers. To multiply decimals, multiply the digits as if they were whole numbers; then count the number of digits behind the decimal point in both factors. That sum tells you how many digits are behind a the decimal point in the product. Adapted from CMP2, Bits & Pieces III Ice Cream Shop (Guided Practice) 1. Sweety’s Ice Cream Shop sells ice cream by the weight. They charge $2.95 per pound. Suppose your dish of ice cream weighs 0.42 pounds. How much will your ice cream cost? $2.95 x 0.42 = 1.239 (you will be charged $1.24) Ice Cream Shop (Guided Practice) 2. Aaron plans to buy new flooring for his rectangular office. His office is 7.9 meters by 6.2 meters. A. How many square meters of floor space does his office have? 7.9 m x 6.2 m = 48.98 sq. m B. Suppose flooring costs $5.90 per square meter. How much will the new flooring cost for Aaron’s office? 48.98 sq. m x $5.90 = $288.98