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 spends on his. 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 (1)
Convert the mixed number to an improper fraction: 1 4 1 = 4 5 .
Multiply Kyle's homework time by 4 5 : 3 2 × 4 5 = 12 10 .
Simplify the resulting fraction: 12 10 = 6 5 .
Jan spends 6 5 hours on her homework.
Explanation
Understanding the Problem Let's break down this word problem. We know Kyle's homework time and how Jan's homework time relates to Kyle's.
Identifying the Given Information Kyle spends 3 2 of an hour on homework. Jan spends 1 4 1 as much time as Kyle. We need to find out how much time Jan spends.
Converting Mixed Number to Improper Fraction First, we need to convert the mixed number 1 4 1 into an improper fraction. To do this, we multiply the whole number (1) by the denominator (4) and add the numerator (1): 1 × 4 + 1 = 5 . So, 1 4 1 = 4 5 .
Multiplying the Fractions Now, we multiply the time Kyle spends on homework by 4 5 to find the time Jan spends: 3 2 × 4 5 .
Performing the Multiplication To multiply fractions, we multiply the numerators and the denominators: 3 × 4 2 × 5 = 12 10 .
Simplifying the Fraction Now we simplify the fraction 12 10 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 12 ÷ 2 10 ÷ 2 = 6 5 .
Stating the Answer So, Jan spends 6 5 of an hour on her homework.
Examples
Understanding fractions is very useful in real life. For example, if you are baking a cake and the recipe calls for 3 2 cup of flour, but you only want to make half the recipe, you need to calculate half of 3 2 . This would be 2 1 × 3 2 = 3 1 cup of flour. Similarly, if you are splitting a pizza with friends and want to divide it equally, you are using fractions to determine how many slices each person gets. Fractions are also used in measurements, such as when building or sewing.
