Converting Fractions to Percentages and Vice Versa: Worded problems

To solve this problem, we'll determine the number of orange balls by calculating the fraction of the total number of balls:

• Step 1: Identify the total number of balls, $28$.
• Step 2: Note the fraction representing the orange balls, $\frac{1}{4}$.
• Step 3: Apply the formula to find the number of orange balls:
  Number of orange balls $= 28 \times \frac{1}{4}$

Now, let's perform the calculation:
$28 \times \frac{1}{4} = 28 \div 4 = 7$

Therefore, the number of orange balls in the box is $7$.

To solve this problem, we will determine the number of white balls in the box using a fraction of the total number of balls.

We are given the total number of balls in the box as 18, and we know that $\frac{2}{3}$ of these balls are white. To find the number of white balls, we follow these steps:

• Step 1: Identify the total quantity, which is 18 balls.
• Step 2: Use the given fraction $\frac{2}{3}$ to find the number of white balls.
• Step 3: Multiply the total number of balls by the fraction of white balls: $18 \times \frac{2}{3}$.

Perform the calculation:

$18 \times \frac{2}{3} = 18 \times 0.6667 = 12$

Alternatively, calculate directly using fractions:

$18 \times \frac{2}{3} = \frac{18 \times 2}{3} = \frac{36}{3} = 12$

Thus, the total number of white balls in the box is 12.

Therefore, the correct answer is choice 12.

To solve this problem, we will find a common equation to account for all students:

• Activity: Playing catch, Fraction: $\frac{1}{5}x$
• Activity: Playing soccer, Fraction: 20% of $x$ which is $\frac{1}{5}x$
• Activity: Watching a movie, Number: $15$ students

The total number of students involved is $x$. Thus, the setup for the equation is:

$\frac{1}{5}x + \frac{1}{5}x + 15 = x$

Simplify and solve for $x$:

$\frac{2}{5}x + 15 = x$

Subtract $\frac{2}{5}x$ from both sides:

$15 = x - \frac{2}{5}x$

$15 = \frac{3}{5}x$

To isolate $x$, multiply both sides by $\frac{5}{3}$:

$x = 15 \times \frac{5}{3}$

$x = 25$

Therefore, the total number of students is 25 students.