To perform the subtraction of \(5\) wholes and \(2\) thirds minus \(3\) wholes and \(1\) sixth, we can first convert everything into improper fractions.
-
Convert the whole numbers and fractions to improper fractions:
-
\(5\) wholes and \(2\) thirds can be converted as follows: \[ 5 = \frac{5 \times 3}{3} = \frac{15}{3} \] So, \(5\) wholes and \(2\) thirds is: \[ 5 \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{17}{3} \]
-
\(3\) wholes and \(1\) sixth can be converted as follows: \[ 3 = \frac{3 \times 6}{6} = \frac{18}{6} \] So, \(3\) wholes and \(1\) sixth is: \[ 3 \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6} \]
-
-
Now we need to subtract \(\frac{19}{6}\) from \(\frac{17}{3}\). To do this, we need a common denominator. The least common multiple of \(3\) and \(6\) is \(6\).
-
Convert \(\frac{17}{3}\) to have a denominator of \(6\): \[ \frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6} \]
-
Now perform the subtraction: \[ \frac{34}{6} - \frac{19}{6} = \frac{34 - 19}{6} = \frac{15}{6} \]
-
Simplify \(\frac{15}{6}\): \[ \frac{15}{6} = \frac{5}{2} \]
Thus, the final result of \(5\) wholes and \(2\) thirds minus \(3\) wholes and \(1\) sixth is: \[ \frac{5}{2} \quad \text{or} \quad 2 \frac{1}{2} \text{ (as a mixed number)} \]