17 Homework
Use the set theory definition of addition or subtraction to add or subtract each of the following. Define appropriate sets and show work. Refer back to pages 2 and 3 for addition and pages 41 and 42 for subtraction if you need help getting started.
- [latex]5+3[/latex]
- [latex]5-4[/latex]
Verify each of the following:
- [latex]79>66[/latex]
- [latex]34<88[/latex]
State whether each set is closed under addition and/or subtraction of whole numbers. Provide an example if it is closed, or provide a counterexample if it is not closed.
- {0}
- {0, 2, 4, …}
Add the following in the system in which the numbers are given. Show work.
a. Egyptian
𓁨 𓂭 𓂭 𓂭 𓂭 𓂭 𓂭 ∩ ∩ ⃒ ⃒ ⃒ ⃒ + 𓂭 𓂭 𓂭 𓂭 ∩ ∩ ∩ ∩ ∩ 𓏲 𓏲 𓏲
b. Egyptian
𓏲 𓏲 𓏲 𓏲 𓏲 𓏲 ∩ ∩ ∩ ∩ ⃒ ⃒ ⃒ ⃒ + 𓏲 𓏲 𓏲 ∩ ∩ ∩ ∩ ∩ ⃒ ⃒ ⃒ ⃒ ⃒ ⃒ ⃒ ⃒
c. Mayan
d. Mayan
Subtract the following in the system in which the numbers are given. Show work.
a. Egyptian
𓆼 𓆼 ∩ ∩ ⃒ ⃒ ⃒ ⃒ – ∩ ∩ ∩ ∩ ∩ ∩ ∩ ∩ 𓏲 𓏲 𓏲 𓏲 𓏲 𓏲
b. Egyptian
𓏲 𓏲 𓏲 𓏲 𓏲 𓏲 ∩ ∩ ∩ ∩ ⃒ ⃒ ⃒ ⃒ – 𓏲 𓏲 𓏲 ∩ ∩ ∩ ∩ ∩ ⃒ ⃒ ⃒ ⃒ ⃒ ⃒ ⃒ ⃒
c. Mayan
For each pair of numbers, add them together. Then subtract the smaller number from the larger number. Show work and check your answer.
#6
[latex]5432_{\text{six}}[/latex] and [latex]2453_{\text{six}}[/latex]
#7
[latex]5\text{T}4_{\text{twelve}}[/latex] and [latex]387_{\text{twelve}}[/latex]
Question #8
Add 5643 + 7885 using each algorithm from this module. State the method for each.
Question #9
Subtract 3586 from 8204 each algorithm from this module. State the method for each.
Question #10
Write the addition table for Base Four.
Question #11
Someone does the following computation in a certain base, but is making a mistake. What base were they working in and what is the mistake? 132 + 243 = 320. What is the correct answer? Be sure to show work.
Question #12
Someone used the directed vector to do a subtraction problem. What was the subtraction problem used?
Question #13
Find the answer to the following subtraction problems by using directed vectors on the number line in conjunction with the missing addend approach. Draw the vectors.
- [latex]10-4[/latex]
- [latex]6-11[/latex]
Question #14
In what number base or bases between 2 and 13 are each of the following calculations valid?
a.
[latex]\begin{align*} 57 &\\ \underline {+\; 64}&\\ 132 & \end{align*}[/latex]
b.
[latex]\begin{align*} 341 &\\ \underline {+\; 524}&\\ 865 & \end{align*}[/latex]
c.
[latex]\begin{align*}101 &\\ \underline {+\; 111}&\\ 212 & \end{align*}[/latex]
d.
[latex]\begin{align*} \text{T}4 &\\ \underline {+\; 58}&\\ 12\text{W} & \end{align*}[/latex]