Question

1. it took luis $4\frac{1}{2}$ hours to drive to windsor. later that day she drove $2\frac{2}{3}$ hours to waterloo.

(a) how long did he drive in total?
(b) how much longer was his drive to windsor compared to his drive to waterloo?

Explanation:

Part (a)

Step1: Convert mixed numbers to improper fractions

To add \( 4\frac{1}{2} \) and \( 2\frac{2}{3} \), first convert them to improper fractions.
For \( 4\frac{1}{2} \): \( 4\times2 + 1 = 9 \), so \( 4\frac{1}{2}=\frac{9}{2} \).
For \( 2\frac{2}{3} \): \( 2\times3 + 2 = 8 \), so \( 2\frac{2}{3}=\frac{8}{3} \).

Step2: Find a common denominator

The least common denominator of 2 and 3 is 6.
Convert \( \frac{9}{2} \) to sixths: \( \frac{9}{2}=\frac{9\times3}{2\times3}=\frac{27}{6} \).
Convert \( \frac{8}{3} \) to sixths: \( \frac{8}{3}=\frac{8\times2}{3\times2}=\frac{16}{6} \).

Step3: Add the fractions

Now add the two fractions: \( \frac{27}{6}+\frac{16}{6}=\frac{27 + 16}{6}=\frac{43}{6} \).

Step4: Convert back to mixed number

Convert \( \frac{43}{6} \) to a mixed number: \( 43\div6 = 7 \) with a remainder of 1, so \( \frac{43}{6}=7\frac{1}{6} \).

Step1: Convert mixed numbers to improper fractions

We already know \( 4\frac{1}{2}=\frac{9}{2} \) and \( 2\frac{2}{3}=\frac{8}{3} \) from part (a).

Step2: Find a common denominator

The least common denominator of 2 and 3 is 6.
Convert \( \frac{9}{2} \) to sixths: \( \frac{9}{2}=\frac{27}{6} \).
Convert \( \frac{8}{3} \) to sixths: \( \frac{8}{3}=\frac{16}{6} \).

Step3: Subtract the fractions

Subtract the two fractions: \( \frac{27}{6}-\frac{16}{6}=\frac{27 - 16}{6}=\frac{11}{6} \).

Step4: Convert back to mixed number

Convert \( \frac{11}{6} \) to a mixed number: \( 11\div6 = 1 \) with a remainder of 5, so \( \frac{11}{6}=1\frac{5}{6} \).

Answer:

The total driving time is \( 7\frac{1}{6} \) hours.

Part (b)