Question

y to solve the problem below. day, chloe spent $3\frac{1}{4}$ hours at the her family. then she spent $1\frac{2}{3}$ hours

Explanation:

Step1: Identify the operation

We need to add the two mixed numbers \( 3\frac{1}{4} \) and \( 1\frac{2}{3} \) to find the total time. First, convert the mixed numbers to improper fractions.
For \( 3\frac{1}{4} \): \( 3\times4 + 1 = 13 \), so \( 3\frac{1}{4}=\frac{13}{4} \).
For \( 1\frac{2}{3} \): \( 1\times3 + 2 = 5 \), so \( 1\frac{2}{3}=\frac{5}{3} \).

Step2: Find a common denominator

The denominators are 4 and 3, so the least common denominator (LCD) is \( 4\times3 = 12 \).
Convert \( \frac{13}{4} \) to twelfths: \( \frac{13}{4}=\frac{13\times3}{4\times3}=\frac{39}{12} \).
Convert \( \frac{5}{3} \) to twelfths: \( \frac{5}{3}=\frac{5\times4}{3\times4}=\frac{20}{12} \).

Step3: Add the fractions

Now add the two fractions: \( \frac{39}{12}+\frac{20}{12}=\frac{39 + 20}{12}=\frac{59}{12} \).

Step4: Convert back to mixed number (if needed)

\( \frac{59}{12}=4\frac{11}{12} \) (since \( 12\times4 = 48 \), \( 59 - 48 = 11 \)).

Answer:

The total time Chloe spent is \( 4\frac{11}{12} \) hours.