Question

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1. during a trip, martha drove $\frac{1}{6}$ of the time, chris drove $\frac{1}{4}$ of the time, and juan drove the rest of the time. what fraction of the time did juan drive?
2. gilberto worked $3\frac{1}{4}$ hours on thursday, $4\frac{2}{5}$ hours on friday, and $6\frac{1}{2}$ hours on saturday. how many hours did he work

Explanation:

For Question 12:

Step1: Find total driven fraction

$\frac{1}{6} + \frac{1}{4}$
First find a common denominator (12):
$\frac{1\times2}{6\times2} + \frac{1\times3}{4\times3} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12}$

Step2: Subtract from total time (1)

$1 - \frac{5}{12}$
Rewrite 1 as $\frac{12}{12}$:
$\frac{12}{12} - \frac{5}{12} = \frac{7}{12}$

Step1: Convert mixed numbers to improper fractions

$3\frac{1}{4} = \frac{13}{4}$, $4\frac{2}{5} = \frac{22}{5}$, $6\frac{1}{2} = \frac{13}{2}$

Step2: Find common denominator (20) and convert

$\frac{13\times5}{4\times5} = \frac{65}{20}$, $\frac{22\times4}{5\times4} = \frac{88}{20}$, $\frac{13\times10}{2\times10} = \frac{130}{20}$

Step3: Sum the fractions

$\frac{65}{20} + \frac{88}{20} + \frac{130}{20} = \frac{65+88+130}{20} = \frac{283}{20}$

Step4: Convert back to mixed number

$\frac{283}{20} = 14\frac{3}{20}$

Answer:

$\frac{7}{12}$

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For Question 13: