zMath 160  - Unit 10: Decimals: Equivalence and Multiplication

Modeling Multiplication of Decimals with Decimal Squares

Activity: Print out the decimal square (right-click, print) shown below to make a model of the given problem, and then complete the following steps:  Step #1: Horizontally (across), for 0.7, color seven (7) decimal strips the same color.  Step #2:  Vertically (up and down), for 0.6, color six (6) decimal strips a different color.  You will color some of the same squares that you colored in the first step. Step #3:  Count the number of squares that are filled with both colors.   These squares are the hundredths squares and each one represents one-hundredth. Note:  An example is provided in the lesson link to “Modeling Multiplication of Decimals”.


1)

Answer the following questions about the previous activity: 

          (a) How many hundredths squares are filled with both colors? 

          (b) What is the answer to the problem?


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2)

Write a multiplication sentence for the model shown below.


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3)

Write a multiplication sentence for the model shown below.


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Multiplying Decimals 


4)

Solve. Check for a reasonable answer through estimation.  0.7 × 0.8   


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5)

Solve. Check for a reasonable answer through estimation.  0.14 × 0.23


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6)

Solve. Check for a reasonable answer through estimation.  0.29 × 0.5


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More Decimal Multiplication


7)

Solve. Check for a reasonable answer through estimation.  78.5 × 3.95


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8)

Solve. Check for a reasonable answer through estimation.  3.48 × 39


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9)

Solve. Check for a reasonable answer through estimation.  6.89 × 2.3


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Equivalent Decimals


10)

Select the decimal that is not equivalent to 7.9.


11)

Simplify 8.30.


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12)

Find the products. Simplify the decimal.  6.43 × 10


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13)

Find the products. Simplify the decimal.  6.43 × 100


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14)

Find the products. Simplify the decimal.  6.43 × 1000


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15)

For problems #12 through #14, study the problems and the answers. Write a shortcut rule for placing the decimal point when multiplying by 10, 100 or 1000. 


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16)

Solve.


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17)

Solve.


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18)

Solve.


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19)

Solve.


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20)

Select the inverse of 6.


21)

Select the mixed fraction that is NOT equivalent to 8.


22)

Select the number that is closest to zero in value.


23)

Chris and Joni ran a 50 meter race. The wind was blowing against them at 1.8 kilometers per hour. Chris finished with a time of 6.5 seconds. Joni’s time was 0.43 seconds faster. What was Joni’s time for the race? Label answer correctly.


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24)

Study the pattern in the figure. How many blocks are needed to build a wall 10 blocks high? Explain how you figured the answer.


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25)

Refer to the pattern in the previous problem to answer the following questions: 

          (a) If 68 blocks were available; a wall could be built that is how many blocks high?

          (b) How many blocks would be left over? 


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