Question

part b
how many students chose math? which statement shows the correct solution and work?
show hints
\\(\frac{560}{100} \times 35 = 196\\) students
\\(\frac{35}{100} \times 560 = 196\\) students
\\(\frac{35}{560} \times 100 = 6.25\\) students
\\(\frac{560}{35} \times 100 = 1600\\) students

Explanation:

Step1: Understand the problem

We need to find the number of students who chose math. Typically, if 35% of students chose math and the total number of students is 560, we calculate 35% of 560. 35% is $\frac{35}{100}$.

Step2: Calculate the number of students

To find 35% of 560, we use the formula: $\frac{35}{100} \times 560$.
Calculating this: $\frac{35\times560}{100}=\frac{19600}{100} = 196$ students.
Now let's check each option:

• First option: $\frac{560}{100} \times 35$ is the same as $\frac{35\times560}{100}$ but the reasoning of the fraction is incorrect (it should be the percentage over 100 times total, not total over 100 times percentage, though numerically it's same, but the interpretation is wrong). But wait, no, actually $\frac{35}{100}\times560$ is the correct way. Wait, no, let's re - evaluate. The second option is $\frac{35}{100}\times560$, which is 35% of 560. The first option is $\frac{560}{100}\times35$, which is also 196, but the fraction represents total over 100 times percentage, which is not the standard way of calculating percentage. But the second option is the standard way of calculating a percentage of a number (percentage as a fraction over 100 times the total). The third option is $\frac{35}{560}\times100$, which is calculating what percentage 35 is of 560, not the number of students. The fourth option is $\frac{560}{35}\times100$, which is incorrect. So the correct option is the second one.

Answer:

$\boldsymbol{\frac{35}{100} \times 560 = 196}$ students (the second option: $\frac{35}{100} \times 560 = 196$ students)