To solve the problem "What percent of 75 is 10?" follow these steps:
1. Identify the part and the whole in the question. Here, the part is 10 and the whole is 75.
2. To find what percentage one number is of another, you use the formula:
[tex]\[
\text{percentage} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100
\][/tex]
3. Substitute the given numbers into the formula:
[tex]\[
\text{percentage} = \left( \frac{10}{75} \right) \times 100
\][/tex]
4. Simplify the fraction and carry out the multiplication:
[tex]\[
\frac{10}{75} = 0.13333333333333334
\][/tex]
[tex]\[
0.13333333333333334 \times 100 = 13.333333333333334
\][/tex]
5. Therefore, 10 is 13.333333333333334 percent of 75.
Given the choices for the formula:
- [tex]\(p = 10 / 75\)[/tex] – This is the fraction part without multiplying by 100 to convert it into a percentage.
- [tex]\(r = 10 \times 75\)[/tex] – This does not relate to calculating percentages and is incorrect.
- [tex]\(p = 10 \times 75\)[/tex] – This too is incorrect for percentage calculation.
The correct expression to start solving this problem is:
[tex]\[
p = \frac{10}{75}
\][/tex]
And then, you multiply by 100 to get the percentage:
[tex]\[
\text{percentage} = \left( \frac{10}{75} \right) \times 100 = 13.333333333333334
\][/tex]
