Question

4 the table below shows the length of several roads. what is the combined length of all the roads? the combined length is road distance (in miles) road 1 $3\frac{2}{6}$ road 2 $1\frac{1}{5}$ road 3 $6\frac{4}{8}$ road 4 $9\frac{2}{3}$

Explanation:

Step1: Simplify each mixed number

Road 1: $3\frac{2}{6} = 3\frac{1}{3} = \frac{10}{3}$
Road 2: $1\frac{1}{5} = \frac{6}{5}$
Road 3: $6\frac{4}{8} = 6\frac{1}{2} = \frac{13}{2}$
Road 4: $9\frac{2}{3} = \frac{29}{3}$

Step2: Find common denominator (30)

Convert fractions to 30 denominator:
$\frac{10}{3} = \frac{100}{30}$, $\frac{6}{5} = \frac{36}{30}$, $\frac{13}{2} = \frac{195}{30}$, $\frac{29}{3} = \frac{290}{30}$

Step3: Sum all fractions

$\frac{100 + 36 + 195 + 290}{30} = \frac{621}{30}$

Step4: Simplify the total

$\frac{621}{30} = 20\frac{21}{30} = 20\frac{7}{10}$? Correction:
Wait, recalculate sum: $10+9=19$, $6=6$, $13/2=6.5$; $19+6+6.5=31.5$? No, correct sum:
$3\frac{1}{3} + 9\frac{2}{3} = 13$; $1\frac{1}{5} + 6\frac{1}{2} = 1.2 + 6.5 = 7.7$; $13 + 7.7 = 20.7 = 20\frac{7}{10}$? No, $1\frac{1}{5}=6/5=1.2$, $6\frac{1}{2}=13/2=6.5$, sum $1.2+6.5=7.7$; $3\frac{2}{6}+9\frac{2}{3}=3\frac{1}{3}+9\frac{2}{3}=13$; total $13+7.7=20.7=20\frac{7}{10}$? Wait, $3\frac{2}{6}=3.333...$, $1\frac{1}{5}=1.2$, $6\frac{4}{8}=6.5$, $9\frac{2}{3}=9.666...$; sum: $3.333+1.2=4.533$; $6.5+9.666=16.166$; total $4.533+16.166=20.699≈20.7=20\frac{7}{10}$

Wait, exact fraction sum:
$\frac{10}{3} + \frac{6}{5} + \frac{13}{2} + \frac{29}{3} = (\frac{10+29}{3}) + \frac{6}{5} + \frac{13}{2} = \frac{39}{3} + \frac{12 + 65}{10} = 13 + \frac{77}{10} = 13 + 7\frac{7}{10} = 20\frac{7}{10}$

Final exact answer: $20\frac{7}{10}$ miles or 20.7 miles.

Corrected Step3:
Combine like fractions first:
$\frac{10}{3} + \frac{29}{3} = \frac{39}{3} = 13$
$\frac{6}{5} + \frac{13}{2} = \frac{12 + 65}{10} = \frac{77}{10} = 7\frac{7}{10}$
Step4: Sum the results: $13 + 7\frac{7}{10} = 20\frac{7}{10}$

Final Answer:

$20\frac{7}{10}$ miles (or 20.7 miles)

(Revised):

Step1: Simplify mixed numbers

Road1: $3\frac{2}{6}=3\frac{1}{3}=\frac{10}{3}$; Road2: $1\frac{1}{5}=\frac{6}{5}$; Road3: $6\frac{4}{8}=6\frac{1}{2}=\frac{13}{2}$; Road4: $9\frac{2}{3}=\frac{29}{3}$

Step2: Add like fractions

$\frac{10}{3}+\frac{29}{3}=\frac{39}{3}=13$

Step3: Add remaining fractions

$\frac{6}{5}+\frac{13}{2}=\frac{12+65}{10}=\frac{77}{10}=7\frac{7}{10}$

Step4: Sum total lengths

$13 + 7\frac{7}{10}=20\frac{7}{10}$

Answer:

22 miles