7.3: Appendix C

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Amy Lagusker
College of the Canyons

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Solutions for Partner Activities

Chapter 2

Section 2.3

Partner Activity 1

Step 1: Add up both lengths to find the total length

\[2 \dfrac{3}{4}+1 \dfrac{1}{2}=\dfrac{11}{4}+\dfrac{3}{2}=\dfrac{11}{4}+\dfrac{6}{4}=\dfrac{17}{4}=4 \dfrac{1}{4} \nonumber \]

Step 2: Divide the part by the whole

\[\dfrac{\text {Sam}}{\text {Total}}=\dfrac{2 \dfrac{3}{4}}{4 \dfrac{1}{4}}=2 \dfrac{3}{4} \div 4 \dfrac{1}{4}=\dfrac{11}{4} \div \dfrac{17}{4}=\dfrac{11}{4} \times \dfrac{4}{17}=\dfrac{11}{17} \approx 0.65=65 \% \approx \dfrac{2}{3} \nonumber \]

Partner Activity 2

\[\begin{array}{l}
\dfrac{1 \text { hour }}{84 \text { miles }+92 \text { miles }}=\dfrac{1 \text { hour }}{176 \text { miles }} \\
\rightarrow \dfrac{132 \text { miles needed in one hour }}{176 \text { miles total in one hour }}=\dfrac{3}{4} \text { hour }=45 \text { minutes }
\end{array} \nonumber \]

Partner Activity 3

$clipboard_ed5d202eb0ef532348c31d511d42f97ae.png$ $\begin{array}{c}
\rightarrow 5285 \div 5=1057=\text { first number } \\
1057 \times 4=4228=\text { second number } \\
\text { Check it! } 1057+4228=5285
\end{array} $

Section 2.4

Partner Activity 1

MMXLV = 1000+1000+(50-10)+5 = 2045
MDCCLXXXIX = 1000+500+200+50+30+(10-1) = 1789
1993 = 1000+(1000-100)+(100-10)+1+1+1 = MCMXCIII
5495 = 5000+(500-100)+(100-10)+5 = VCDXCV

Section 2.6

Partner Activity 1

1. $132_{\text {four}}$
2. $200313_{\text {four}}$
3. $100_{\text {four}}$
1. 15
2. 278
3. Undefined

Section 2.8

Partner Activity 1

$116_{\text {nine}}$
$1030_{\text {four}}$
$513_{\text {six}}$
$21_{\text {three}}$
$111110_{\text {two}}$

Chapter 3

Section 3.2

Partner Activity 1

Answer: 265

Partner Activity 2

Answers vary

Partner Activity 3

Section 3.4

Partner Activity 1

\[\begin{array}{l}
5 \div 0=\text { undefined } \\
0 \div 5=0 \\
0 \div 0=\text { indeterminate }
\end{array} \nonumber \]

We know that $18 \div 6=3$ because $3 \times 6=18$, therefore. Using a similar approach, we know that $5 \div 0 \neq 0$, since $0 \times 0 \neq 5$

Section 3.5

Partner Activity 1

$14.47
$3.65
$16.32

Partner Activity 2

$12 \times 6 = 72$
$10 \times 18 = 180$
$8 \times 8 = 64$

Partner Activity 3

321
229
15453

Section 3.6

Partner Activity 1

Answers vary. Samples are below:

Here to Baker, CA
The length of my bedroom
The weight of a 2nd grader

Section 3.7

Partner Activity 1

309.26
92.86%
114.06

Chapter 4

Section 4.2

Partner Activity 1

The denominator is VERY MUCH less than the numerator, i.e. $\dfrac{1}{10000}$
Both the denominator and the numerator are large numbers and they are very close in distance, i.e. $\dfrac{999}{1000}$
The numerator is roughly half of the denominator, i.e. $\dfrac{15}{31}$
The numerator is roughly a third of the denominator, i.e. $\dfrac{21}{60}$

Partner Activity 2

\[\dfrac{3}{8} \rightarrow \dfrac{1}{2}, \dfrac{5}{4} \rightarrow 1, \dfrac{2}{9} \rightarrow 0, \dfrac{4}{7} \rightarrow \dfrac{1}{2}, \dfrac{1}{3} \rightarrow \frac{1}{2} \nonumber \]

Section 4.3

Partner Activity 1

\[\dfrac{51}{684}+\dfrac{43}{684}+\dfrac{738}{684}=\dfrac{832}{684} \nonumber\]

\[\dfrac{1}{8}+\dfrac{4}{5}+\dfrac{1}{9}=\dfrac{1}{360}+\dfrac{ }{360}+\dfrac{ }{360}= \dfrac{45}{360}+\dfrac{288}{360}+\dfrac{40}{360}=\dfrac{373}{360} \nonumber \]

Partner Activity 2

Division works. The rest do not.

Chapter 5

Section 5.2

Partner Activity 1

Factors: 1, 2, 3, 5, 6, 10, 15, 30

First four multiples: 30, 60, 90, 120

Partner Activity 2

Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97

Partner Activity 3

0, 1, negative = neither. 2 is the first prime number.

Partner Activity 4

$85=5 \cdot 17$
$350=2 \cdot 5^{2} \cdot 7$
$60=2^{2} \cdot 3 \cdot 5$

Section 5.4

Partner Activity 1

2 feet; The GCF of (6, 8, 12) = 2

Partner Activity 2

Each packet contains 12 cards; The GCF of (24, 60, 48) = 12

Section 5.5

Partner Activity 1

120 cookies; The LCM of (15, 24) = 120

Partner Activity 2

$\dfrac{1}{12}$
$\dfrac{1}{6}$
14

Chapter 6

Section 6.2

Partner Activity 1

$clipboard_e16301d31a71f88c6aa04060facf19713.png$
$clipboard_e2d617da3db818022a989bf2a6bc18d01.png$
Does not exist

Partner Activity 2

A square is a rectangle
Parallelogram
A regular has all same sides and all same angles

Partner Activity 3

180
540
2340
360

Partner Activity 4

Section 6.3

Partner Activity 1

Area is base times height, two dimensions
Volume is base times height times width, three dimensions

Partner Activity 2

About $12 \text { units}^2$

Partner Activity 3

$52 \text { units}^2$

Partner Activity 4

$24 \text { units}^3$

Section 6.4

Partner Activity 1

$\dfrac{5}{9}$ yards
84480 feet

Section 6.5

Partner Activity 1

$1200 \text { inches}^2$
$225 \text { feet}^2$
$196838560.5 \text { miles}^2$
$37.68 \text { inches}^3$

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