Question

1. $r + 6\frac{7}{10} = 1\frac{1}{15}$

Explanation:

Step1: Isolate the variable $r$

Subtract $6\frac{7}{10}$ from both sides.
$r = 1\frac{1}{15} - 6\frac{7}{10}$

Step2: Convert to improper fractions

Rewrite mixed numbers as fractions.
$r = \frac{16}{15} - \frac{67}{10}$

Step3: Find common denominator

Use 30 as the common denominator.
$r = \frac{32}{30} - \frac{201}{30}$

Step4: Subtract the fractions

Calculate the difference of the numerators.
$r = \frac{32 - 201}{30} = \frac{-169}{30}$

Step5: Convert to mixed number

Rewrite the improper fraction.
$r = -5\frac{19}{30}$

Answer:

$r = -5\frac{19}{30}$ or $r = -\frac{169}{30}$