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mathematics
contemporary mathematics
Contemporary Mathematics 1st Edition OpenStax - Solutions
Explain the error in the following calculation: \(15_{12} \times 7_{12}=105_{12}\)
Explain the error in the following calculation: \(45_{8} \times 6_{8}=94_{8}\).
In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for base 6 ?
In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for base 14 ?
In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for base 2 ?
Consider the answers from Exercise 24 and Exercise 26.Which base do you think would be more efficient: base 10, base 6 , or base \(2 ?\)Data from Exercises 24In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for
\(11_{2} \times 11_{2}\)Use the multiplication table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the multiplication table for the given base.
\(101_{2} \times 10_{2}\)Use the multiplication table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the multiplication table for the given base.
\(11011_{2} \times 1011_{2}\)Use the multiplication table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the multiplication table for the given base.
\(1011_{2} \times 1010101_{2}\)Use the multiplication table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the multiplication table for the given base.
Convert \(1011_{2}\) and \(1010101_{2}\) to base 10 . Then multiply those base 10 numbers. Next, convert the answer you got for Exercise 31 to base 10.Do these numbers match?Data from Exercises 31\(1011_{2} \times 1010101_{2}\)Use the multiplication table that you created from Exercise 4 to perform
\(19_{16} \times 5_{16}\)Use the multiplication table that you created from Exercise 3 to perform the indicated base 16 operations.Data from Exercises 3base 16 Create the multiplication table for the given base.
\(3 \mathrm{~B}_{16} \times \mathrm{A}_{16}\)Use the multiplication table that you created from Exercise 3 to perform the indicated base 16 operations.Data from Exercises 3base 16 Create the multiplication table for the given base.
\(25_{16} \times 16_{16}\)Use the multiplication table that you created from Exercise 3 to perform the indicated base 16 operations.Data from Exercises 3base 16 Create the multiplication table for the given base.
\(\mathrm{C}_{16} \div 4_{16}\)Use the multiplication table that you created from Exercise 3 to perform the indicated base 16 operations.Data from Exercises 3base 16 Create the multiplication table for the given base.
\(43_{5} \times 32_{5}=126_{5}\)Explain how you know an error was committed without performing the operation in the given base.
\(5_{14} \times 9_{14}=45_{14}\)Explain how you know an error was committed without performing the operation in the given base.
What does it mean when we say a number is written in base 7 ?
What does it mean when we say a number is written in base 12 ?
How many symbols are there in a base 3 system? What are they?
How many symbols are there in a base 15 system? What are they?
List the numbers, up to 100 , in the base 5 system.
List the numbers, up to 100 , in the base 2 system.
\(14_{5}\)Convert the number into a base 10 number.
\(21_{6}\)Convert the number into a base 10 number.
\(12_{3}\)Convert the number into a base 10 number.
\(34_{5}\)Convert the number into a base 10 number.
\(14_{8}\)Convert the number into a base 10 number.
789 Convert the number into a base 10 number.
\(3 \mathrm{~B}_{12}\)Convert the number into a base 10 number.
\(241_{6}\)Convert the number into a base 10 number.
\(101_{2}\)Convert the number into a base 10 number.
\(4 A 7_{14}\)Convert the number into a base 10 number.
8049 Convert the number into a base 10 number.
\(101001_{2}\)Convert the number into a base 10 number.
\(3223_{6}\)Convert the number into a base 10 number.
14367 Convert the number into a base 10 number.
\(8 \mathrm{AOBD}_{15}\)Convert the number into a base 10 number.
\(110202_{3}\)Convert the number into a base 10 number.
\(100 \mathrm{~A} 4_{12}\)Convert the number into a base 10 number.
\(1010000101_{2}\)Convert the number into a base 10 number.
12 into base 4 Convert the base 10 number into the given base.
25 into base 2 Convert the base 10 number into the given base.
43 into base 12 Convert the base 10 number into the given base.
153 into base 5 Convert the base 10 number into the given base.
203 into base 2 Convert the base 10 number into the given base.
431 into base 4 Convert the base 10 number into the given base.
543 into base 12 Convert the base 10 number into the given base.
1,023 into base 2 Convert the base 10 number into the given base.
2,876 into base 4 Convert the base 10 number into the given base.
1,765 into base 5 Convert the base 10 number into the given base.
1,993 into base 7 Convert the base 10 number into the given base.
2,000 into base 2 Convert the base 10 number into the given base.
4,368 into base 12 Convert the base 10 number into the given base.
12,562 into base 16 Convert the base 10 number into the given base.
When converting from base 10 to base 6 , a student finds the following remainders: \(3,1,3,6\). How do you know that a mistake was made?
When converting from base 10 to base 4, a student finds the following remainders: \(0,0,3,7,2\). How do you know a mistake was made?
Suppose a base 12 number is converted into a base 10 number, and one of the digits is A. Was an error committed? How do you know?
Suppose a base 10 number is converted into a base 5 number and one of the digits is 6 . Was an error committed? How do you know?
Suppose a base 2 number is converted into a base 10 number, and the base 10 number has more digits that the base 2 number. Was an error committed? How do you know?
Suppose a base 16 number is converted to base 2, and the base 2 number has fewer digits than the base 16 number. Was an error committed? How do you know?
25 Convert the Hindu-Arabic number into a Mayan number.
71 Convert the Hindu-Arabic number into a Mayan number.
400 Convert the Hindu-Arabic number into a Mayan number.
723 Convert the Hindu-Arabic number into a Mayan number.
67Convert the Hindu-Arabic number to a Babylonian number.
135 Convert the Hindu-Arabic number to a Babylonian number.
781 Convert the Hindu-Arabic number to a Babylonian number.
10,952 Convert the Hindu-Arabic number to a Babylonian number.
base 5 Create the addition table for the given base.
base 3 Create the addition table for the given base.
base 16 Create the addition table for the given base.
base 2 Create the addition table for the given base.
\(4_{6}+3_{6}\)Perform the indicated base 6 operation.
\(14_{6}+25_{6}\)Perform the indicated base 6 operation.
\(31_{6}+3_{6}\)Perform the indicated base 6 operation.
\(43_{6}+34_{6}\)Perform the indicated base 6 operation.
\(532_{6}+23_{6}\)Perform the indicated base 6 operation.
\(254_{6}+143_{6}\)Perform the indicated base 6 operation.
\(20_{6}-3_{6}\)Perform the indicated base 6 operation.
\(23_{6}-5_{6}\)Perform the indicated base 6 operation.
\(5_{12}+6_{12}\)Perform the indicated base 12 operation.
\(3_{12}+A_{12}\)Perform the indicated base 12 operation.
\(34_{12}+7_{12}\)Perform the indicated base 12 operation.
\(76_{12}+B_{12}\)Perform the indicated base 12 operation.
\(59_{12}+1 A_{12}\)Perform the indicated base 12 operation.
\(\mathrm{A} 1_{12}+36_{12}\)Perform the indicated base 12 operation.
\(53_{12}-9_{12}\)Perform the indicated base 12 operation.
\(2 \mathrm{~B}_{12}-7_{12}\)Perform the indicated base 12 operation.
Explain two ways to detect an error in arithmetic in bases other than base 10.
Explain the error in the following calculation: \(28_{13}+47_{13}=75_{13}\).
Explain the error in the following calculation: \(36_{7}+23_{7}=597\).
In base 10 addition, there are 100 addition rules plus a rule for carrying a 1.How many addition rules are there for base 6 ?
In base 10 addition, there are 100 addition rules plus a rule for carrying a 1.How many addition rules are there for base 14 ?
In base 10 addition, there are 100 addition rules plus a rule for carrying a 1.How many addition rules are there for base \(2 ?\)
\(101_{2}+111_{2}\)Use the addition table that you created from Exercise 4 to perform the indicated base 2 operations.
\(1011_{2}+10011_{2}\)Use the addition table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the addition table for the given base.
\(11111_{2}+11111_{2}\)Use the addition table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the addition table for the given base.
\(1010101_{2}+1010101_{2}\)Use the addition table that you created from Exercise 4 to perform the indicated base 2 operations.Data from Exercises 4base 2 Create the addition table for the given base.
\(29_{16}+38_{16}\)Use the addition table that you created from Exercise 3 to perform the indicated base 16 operations.Data from Exercises 3base 16 Create the addition table for the given base.
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