6.4: Homework
- Page ID
- 83016
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
- Start a new module on the front side of a new page and write the module number on the top center of the page.
- Answers without supporting work will receive no credit.
- Some solutions are given in the solutions manual.
- You may work with classmates but do your own work.
Mae had 72 lollipops and wanted to sell packages that had 4 lollipops in each package. How many packages could she make?
a. What division problem do you need to do to find the answer?
b. What interpretation of division does this word problem represent?
c. Explain how to use the correct interpretation to draw a picture to find the answer.
d. Draw a picture using the correct interpretation to help find the answer.
e. Write the multiplication problem shown by the picture:
f. Explain how you use the picture to find the answer to the problem. Be specific.
g. What is the answer to this problem?
Tina had 72 marbles and wanted to divide them up evenly amongst the 9 children in her class. How many marbles should each child receive?
a. What division problem do you need to do to find the answer? :
b. What interpretation of division does this word problem represent?
c. Explain how to use the correct interpretation to draw a picture to find the answer.
d. Draw a picture using the correct interpretation to help find the answer.
e. Write the multiplication problem shown by the picture:
f. Explain how you use the picture to find the answer to the problem. Be specific.
g. What is the answer to this problem?
Joan had 12 cups of sugar. A cookie recipe required 2/3 of a cup of sugar. How many recipes could she make?
a. What division problem do you need to do to find the answer? :
b. What interpretation of division does this word problem represent?
c. Explain how to use the correct interpretation to draw a picture to find the answer.
d. Draw a picture using the correct interpretation to help find the answer.
e. Write the multiplication problem shown by the picture:
f. Explain how you use the picture to find the answer to the problem. Be specific.
g. What is the answer to this problem?
a. Make up a word problem that would require using the partitioning of subsets interpretation of division and the division problem: \(20 \div 5\).
b. Draw a picture using this interpretation to find the answer.
c. Explain how you use the picture to find the answer to the problem. Be specific.
d. Write the multiplication problem shown by the picture.
e. What is the answer to this problem?
a. Make up a word problem that would require using the repeated subtraction interpretation of division and the division problem: \(20 \div 5\).
b. Draw a picture using this interpretation to find the answer.
c. Explain how you use the picture to find the answer to the problem. Be specific.
d. Write the multiplication problem shown by the picture.
e. What is the answer to this problem?
a. Make up a word problem that would require using the repeated subtraction interpretation of division and the division problem: \(6 \div 2/3\).
b. Draw a picture using this interpretation to find the answer.
c. Explain how you use the picture to find the answer to the problem. Be specific.
d. Write the multiplication problem shown by the picture.
e. What is the answer to this problem? ______
Draw a picture to do the division \(30 \div 2\) using
a. partitioning into subsets
b. repeated subtraction.
c. Which interpretation is easiest to draw and why?
Draw a picture to do the division \(32 \div 16\) using
a. partitioning into subsets
b. repeated subtraction.
c. Which interpretation is easiest to draw and why?
Fill in the blanks: \(637 \div 14\) = 45 r.7 means _____ \(\cdots\) _____ + _____ = ________
Someone was solving this problem: “Mark had 42 pencils and wanted to divide them up equally amongst his 3 children. How many pencils should he give each child?”
Which picture best represents a picture he might draw to find the solution?
To use the division interpretation of “partitioning into subsets”
a. would the number you are dividing by be the number of subsets or the amount in each subset?
b. After doing the division, would the answer be represented by the number of subsets or the amount in each subset?
To use the division interpretation of “repeated subtraction”,
a. would the number you are dividing by be the number of subsets or the amount in each subset?
b. After doing the division, would the answer be represented by the number of subsets or the amount in each subset?
For problems 13 – 17
a. Divide in the base given using repeated subtraction. All of your work must be shown. Show ALL steps.
b. Check each answer by multiplying the divisor by the quotient and then adding the remainder to see if this equals the dividend. All of your work must be shown. Do not skip any steps.
\(4320_{\text{seven}} \div 52_{\text{seven}}\)
\(2316_{\text{nine}} \div 7_{\text{nine}}\)
\(60382_{\text{eleven}} \div 21\text{T}_{\text{eleven}}\)
\(43401_{\text{five}} \div 444_{\text{five}}\) = _______
\(2020100_{\text{three}} \div 220_{\text{three}}\) = _______
Decide which of the following sets are closed under division. If it is closed under division, write "closed" and provide at least one example and compelling reason why you are sure it is closed. If it is not closed, write "not closed" and provide a counterexample.
| a. {-1} | b. {0} | c. {0, 1} |
| d. {-1, 1} | e. {1, 2, 3, 4, ...} |
Is division commutative?
Support your answer with either an example or a counterexample.
Is division associative?
Support your answer with either an example or a counterexample