Write a division that represents the question: How many 3/8s are in 5/4?
The correct answer and explanation is:
Division Expression:
To represent the question “How many 3/8s are in 5/4?” using division, you write it as: 54÷38\frac{5}{4} \div \frac{3}{8}
Correct Answer:
54÷38=54×83=5×84×3=4012=103\frac{5}{4} \div \frac{3}{8} = \frac{5}{4} \times \frac{8}{3} = \frac{5 \times 8}{4 \times 3} = \frac{40}{12} = \frac{10}{3}
So, there are 103\frac{10}{3} or 3⅓ of the 3/8s in 5/4.
300-Word Explanation:
This problem is asking how many times the fraction 38\frac{3}{8} fits into the fraction 54\frac{5}{4}, which is a classic case of dividing fractions. Whenever you’re asked “how many of A are in B”, you model it with the division B ÷ A.
So we write: 54÷38\frac{5}{4} \div \frac{3}{8}
To divide by a fraction, you multiply by its reciprocal. The reciprocal of 38\frac{3}{8} is 83\frac{8}{3}. So: 54÷38=54×83\frac{5}{4} \div \frac{3}{8} = \frac{5}{4} \times \frac{8}{3}
Next, multiply the numerators and denominators: 5×84×3=4012\frac{5 \times 8}{4 \times 3} = \frac{40}{12}
This fraction can be simplified by dividing both numerator and denominator by 4: 40÷412÷4=103\frac{40 \div 4}{12 \div 4} = \frac{10}{3}
So, there are 10/3, or 3 whole groups and 1/3 of another, of the 3/8 portions in 5/4.
Think of it this way: if you had 5/4 cups of juice and you were pouring it into cups that each hold 3/8 of a cup, you’d be able to fill three full cups and have 1/3 of a cup’s worth left over. This is a great example of using division of fractions in real-life proportional reasoning.