Which multiplication equation represents the question: how many 3/8s are in 5/4?
The correct answer and explanation is:
Correct Multiplication Equation:
To answer the question “How many 3/8s are in 5/4?”, we rewrite it as a multiplication problem: (54÷38)=xcan be rewritten as38×x=54\left( \frac{5}{4} \div \frac{3}{8} \right) = x \quad \text{can be rewritten as} \quad \frac{3}{8} \times x = \frac{5}{4}
So, the multiplication equation that represents the question is: 38×x=54\frac{3}{8} \times x = \frac{5}{4}
Solution:
To solve for xx: x=54÷38=54×83=4012=103x = \frac{5}{4} \div \frac{3}{8} = \frac{5}{4} \times \frac{8}{3} = \frac{40}{12} = \frac{10}{3}
So, there are 103\frac{10}{3} (or 3 and 1/3) pieces of 38\frac{3}{8} in 54\frac{5}{4}.
300-Word Explanation:
This question is essentially asking how many times the fraction 38\frac{3}{8} fits into another fraction, 54\frac{5}{4}. This is a classic example of a division of fractions. However, instead of writing it as a division problem, the question asks for a multiplication equation that represents the situation.
To find such an equation, consider the unknown number of times 38\frac{3}{8} fits into 54\frac{5}{4}. Let this unknown number be xx. If you take xx groups of 38\frac{3}{8}, then you will get 54\frac{5}{4}: 38×x=54\frac{3}{8} \times x = \frac{5}{4}
This equation perfectly represents the original question. We’re multiplying 38\frac{3}{8} by some number to find 54\frac{5}{4}, and solving for that number tells us how many 38\frac{3}{8}’s are in 54\frac{5}{4}.
To solve, we isolate xx by dividing both sides of the equation by 38\frac{3}{8}, which is the same as multiplying by its reciprocal: x=54÷38=54×83=4012=103x = \frac{5}{4} \div \frac{3}{8} = \frac{5}{4} \times \frac{8}{3} = \frac{40}{12} = \frac{10}{3}
This means there are 103\frac{10}{3} or 3 and 1/3 groups of 38\frac{3}{8} in 54\frac{5}{4}.