Kyle spends $\frac{2}{3}$ of an hour on homework. His sister, Jan, spends $1 \frac{1}{4}$ as much time on her homework as Kyle. How much time does Jan spend on her homework?
A. $1 \frac{3}{7}$ hours
B. $1 \frac{1}{6}$ hours
C. $\frac{5}{6}$ hours
D. $\frac{11}{15}$ hours
Answer (2)
Convert the mixed number to an improper fraction: 1 4 1 = 4 5 .
Multiply the time Kyle spends on homework by the improper fraction: 3 2 × 4 5 = 12 10 .
Simplify the resulting fraction: 12 10 = 6 5 .
Jan spends 6 5 of an hour on her homework.
Explanation
Kyle's Homework Time First, we need to determine how much time Kyle spends on his homework. The problem states that Kyle spends 3 2 of an hour on homework.
Jan's Homework Time Relative to Kyle's Next, we need to determine how much more time Jan spends on homework compared to Kyle. The problem states that Jan spends 1 4 1 as much time on her homework as Kyle.
Converting Mixed Number to Improper Fraction To find the amount of time Jan spends on homework, we need to multiply the time Kyle spends by 1 4 1 . First, convert the mixed number 1 4 1 to an improper fraction: 1 4 1 = 4 4 + 4 1 = 4 5 .
Multiplying Fractions Now, multiply the time Kyle spends on homework by 4 5 : 3 2 × 4 5 = 3 × 4 2 × 5 = 12 10 .
Simplifying the Fraction Simplify the fraction 12 10 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 12 10 = 12 ÷ 2 10 ÷ 2 = 6 5 .
Final Answer Therefore, Jan spends 6 5 of an hour on her homework.
Examples
Understanding fractions is essential in everyday life. For instance, when baking, you might need to halve a recipe that calls for 3 2 cup of flour. This means you need to calculate 2 1 of 3 2 , which is 2 1 × 3 2 = 3 1 cup. Similarly, when splitting a pizza with friends, knowing how to divide the pizza into equal fractions ensures everyone gets a fair share. These skills are also crucial in managing time, budgeting, and understanding proportions in various real-world scenarios.
Jan spends 6 5 of an hour on her homework, which is calculated by multiplying the time Kyle spends by 1 4 1 converted to an improper fraction of 4 5 . The final answer is 6 5 hours.
;
