\frac{5}{16} \div \frac{1}{3} = h Step 2: \frac{16}{5} \times \frac{3}{1} = h Step 3: \frac{48}{5} = h Answer: \frac{9}{5} = h What was Joylin’s first error? She switched the divisor and the dividend when creating an equation She replaced both the divisor and the dividend with their reciprocals She multiplied the two numerators and the two denominators to generate She reduced the improper fraction incorrectly when getting her final answer
Step 1: \frac{5}{16} \div \frac{1}{3} = h Step 2: \frac{16}{5} \times \frac{3}{1} = h Step 3: \frac{48}{5} = h Answer: \frac{9}{5} = h What was Joylin’s first error? She switched the divisor and the dividend when creating an equation She replaced both the divisor and the dividend with their reciprocals She multiplied the two numerators and the two denominators to generate She reduced the improper fraction incorrectly when getting her final answer
The Correct Answer and Explanation is:
Correct Answer:
She replaced both the divisor and the dividend with their reciprocals.
Explanation
In the given problem, we are looking at a sequence of steps to solve a fraction division problem:
Step 1:
516÷13=h\frac{5}{16} \div \frac{1}{3} = h
This is set up correctly. The rule for dividing fractions is to multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). In other words: 516÷13=516×31\frac{5}{16} \div \frac{1}{3} = \frac{5}{16} \times \frac{3}{1}
However, in Step 2, Joylin writes: 165×31=h\frac{16}{5} \times \frac{3}{1} = h
This is where the first error occurs. Instead of keeping the dividend as 516\frac{5}{16}, she incorrectly flipped it to 165\frac{16}{5}. That means she replaced both the dividend and the divisor with their reciprocals, not just the divisor, which is the correct procedure.
The correct process should be:
- Start with 516÷13\frac{5}{16} \div \frac{1}{3}
- Multiply the dividend by the reciprocal of the divisor: 516×31=1516\frac{5}{16} \times \frac{3}{1} = \frac{15}{16}
- So the correct answer is: h=1516h = \frac{15}{16}
Instead, Joylin’s incorrect Step 2 gives: 165×31=485\frac{16}{5} \times \frac{3}{1} = \frac{48}{5}
Then, in Step 3, she claims that 95=h\frac{9}{5} = h, which is also incorrect. It appears she tried to simplify 485\frac{48}{5}, but did it incorrectly, possibly by mistaking it for a different fraction altogether.
Therefore, Joylin’s first error was that she replaced both the divisor and the dividend with their reciprocals—an incorrect application of the rules for dividing fractions.
