(1.) Work the following addition problem in three different ways not using standard algorithms. In each case, explain carefully what you are doing and why it will give you a correct answer. The use the standard algorithm and try to explain why that works and why you have to carry .
64 + 37
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2.Work the following subtraction problem in three different ways not using standard algorithms. In each case, explain carefully what you are doing and why it will give you a correct answer. The use the standard algorithm and try to explain why that works and why you have to borrow
64 – 37
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3. Make up two real life words problems involving an addition .Make then different using different terms , different situations.Have fun ,use your imagination
. 4. Make up two real life words problems involving a subtraction ,
5. I have a bag that contains 50 coins. The total value of these coins is $1.00. How many quarters, dimes, nickels and pennies are in the bag? SHOW YOUR WORK, EXPLAIN YOUR THINKING.
(4.) Crack the code
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People have devised many kinds of secret codes to have private communications with each other, so that no one else can understand their messages. We will consider a letter-number code. where arithmetic problems are disguised by using letters. To use such a code you begin with an arithmetic problem such as:
35
+ 35
70
To create a coded version of the problem, you replace each digit with a letter, always using the same letter for that particular digit. For example you might replace 3 with A, 5 with D, 7 with O and 0 with H. If you do this, the addition problem becomes:
AD
+AD
OH
(In using such a code, you need to distinguish between the number ‘O’ and the letter ‘O’.)
The Rules
Problems like these usually follow certain rules:
- If a letter is used more than once in the same problem, it stands for the same number
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each time it is used.
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Different letters in the same problem always stand for different single digit numbers.
A letter standing for O never starts a number with more than one digit. For example, the problem can’t have a number like “05” (but it can use “507” or “80” or even simply “0”.)
The Problems (5 each)
See whether you can crack the codes for these problems based on the rules listed above. If you think there is only one right answer, prove it – that is, give a good explanation for your belief. If you think there are several possibilities, give them all and prove that there are no others. If you think. there is no possible answer prove that. You will need to keep careful track of how you arrive at your answers.
- ABB
– A
- ss
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+EE SST
- AB
+ BA ADE
Note: This is definitely harder than the previous ones. SEND
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+ MORE MONEY
f · r- ..
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