To find the total amount of hair that Madelyn had cut off, we need to add the two measurements:
- The first cut: \(3 \frac{1}{2}\) inches
- The second cut: \(1 \frac{2}{3}\) inches
First, we can convert these mixed numbers into improper fractions.
For \(3 \frac{1}{2}\): \[ 3 \times 2 + 1 = 6 + 1 = 7 \quad \text{thus,} \quad 3 \frac{1}{2} = \frac{7}{2} \]
For \(1 \frac{2}{3}\): \[ 1 \times 3 + 2 = 3 + 2 = 5 \quad \text{thus,} \quad 1 \frac{2}{3} = \frac{5}{3} \]
Now we need to add \(\frac{7}{2}\) and \(\frac{5}{3}\). To do this, we need a common denominator. The least common multiple of 2 and 3 is 6.
Next, we convert both fractions:
\[ \frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6} \]
\[ \frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6} \]
Now we can add the two fractions: \[ \frac{21}{6} + \frac{10}{6} = \frac{21 + 10}{6} = \frac{31}{6} \]
Now we can convert \(\frac{31}{6}\) back to a mixed number. We divide 31 by 6: \[ 31 \div 6 = 5 \quad \text{with a remainder of} \quad 1 \] Thus, \[ \frac{31}{6} = 5 \frac{1}{6} \]
So, the total amount of hair Madelyn had cut off is \(5 \frac{1}{6}\) inches.
1 answer