Converting Fractions to Percentages and Vice Versa: Calculate the percentage of the whole number

To solve the problem of finding 70% of 90, we will use the percentage calculation method:

• Step 1: Convert the percentage to a decimal. 70% is equivalent to $\frac{70}{100} = 0.70$.
• Step 2: Multiply the base number, 90, by the decimal equivalent of the percentage.

Let's perform the calculation:

$0.70 \times 90 = 63$

Therefore, 70% of 90 is $\mathbf{63}$.

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'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, let's begin by understanding the situation:

In Roberto's family, 75% of the members are women, and there are 9 men. We need to determine the number of females in the family.

• Step 1: Understand the percentage breakdown.

If 75% of the family are women, then 25% are men. This is because percentages of 100% are divided into parts that represent the whole group.

• Step 2: Set up the equation for men.

Since 25% of the family are men and there are 9 men, the equation for the total number of family members, $x$, based on the men is:

$0.25x = 9$

• Step 3: Solve for the total number of family members.

We solve the equation for $x$:

$x = \frac{9}{0.25} = 36$

This tells us that there are 36 members in the family.

• Step 4: Calculate the number of females.

Now, calculate the number of females, which is 75% of the total family:

$\text{Number of females} = 0.75 \times 36 = 27$

Therefore, the number of females in Roberto's family is 27.

To solve this problem, we'll perform a percentage calculation to determine how much Sebastian spends:

• Step 1: Identify the given information: Sebastian's salary is $5000$, and he spends 75% of it.
• Step 2: Calculate 75% of the salary. This is done using the formula: $\text{Amount spent} = \frac{75}{100} \times 5000$.

Now, let's perform the calculation:
Step 1: Using the formula, compute $\frac{75}{100} \times 5000$.

This calculation results in:

• $\frac{75}{100} = 0.75$
• $0.75 \times 5000 = 3750$

Therefore, the amount Sebastian spends per month is $3750$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the percentage of students who passed the test and calculate their number.
• Step 2: Find the number of students who failed by subtracting the number of students who passed from the total number of students.

Now, let's work through each step:
Step 1: We know 50% of the 48 students passed. To calculate this, convert 50% to a decimal by dividing by 100, giving us 0.50.
Multiply by the total number of students: $48 \times 0.50 = 24$
This means 24 students passed the test.

Step 2: To find how many students failed, subtract the number of students who passed from the total number of students:
$48 - 24 = 24$

Therefore, the number of students who failed the test is $24$.

To solve this problem, we will use the percentage relationship:

• Step 1: Convert the given percentage to a decimal:
  35% as a decimal is $0.35$ because $35\% = \frac{35}{100}$.
• Step 2: Use the relationship between the deposit and the total cost:
  The deposit is 35% of the total cost, so $0.35 \times \text{Total Cost} = 3500$.
• Step 3: Find the total cost by rearranging the formula and solving:
  Hence, $\text{Total Cost} = \frac{3500}{0.35}$.
• Step 4: Calculate:
  $\text{Total Cost} = \frac{3500}{0.35} = 10000$.

Therefore, the price of the computer is \text{\10,000} \).

The problem involves calculating a simple percentage discount. We start by determining 50% of the original fee.

• Step 1: Calculate the discount amount.
  $50\% \text{ of } 424 = 0.50 \times 424 = 212$
• Step 2: Calculate the registration fee at the open house.
  Since the open house discount is 50%, the registration fee would be:
  $424 - 212 = 212$

Therefore, the registration fees for the university at the open house are \212 \).

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Convert the percentage to a decimal
• Step 3: Use the percentage formula
• Step 4: Calculate the total number of students

Now, let's work through each step:
Step 1: The problem gives us the number of female students participating in the camp, which is 240.
Step 2: Convert the percentage of females into a decimal: $30\% = \frac{30}{100} = 0.30$.
Step 3: Apply the formula for total students:
$\text{Total number of students} = \frac{240}{0.30}$
Step 4: Perform the calculation:
$\frac{240}{0.30} = 800$
Thus, the total number of students participating in the summer camp is 800.

Therefore, the solution to the problem is 800.

To solve this problem, we'll follow these steps:

• Step 1: Define the total number of students in terms of those who received a gift.
• Step 2: Recognize that since 50% of students received a gift and 50% did not, the total student count is indicated by the sum of both groups.
• Step 3: Compute the total based on the fraction provided (50%).

Let's work through the steps:

Step 1: Let $x$ denote the total number of 7th grade students.

Step 2: 50% of the students received a gift, which means that:

$\frac{x}{2}$ students received the gift.

Similarly, $\frac{x}{2}$ students did not receive the gift.

Step 3: Since both parts are equal in size and constitute 50% each, multiplying by 2 will yield the full amount:

Therefore, $x = 2 \times \frac{x}{2}$.

To recover $x$, we simply recognize that $x$ itself is being split evenly; hence:

The total number of students $x = 100$.

Thus, the solution to the problem is $\mathbf{x = 100}$.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the number of white chairs from the given percentage.
• Step 2: Determine the number of black chairs by subtraction.

Let's work through each step:

Step 1: Calculate the number of white chairs.
The total number of chairs is 125. Since 60% of these chairs are white, we calculate the number of white chairs as follows:
$\text{White chairs} = 125 \times 0.60 = 75$

Step 2: Determine the number of black chairs.
Subtract the number of white chairs from the total number of chairs to find the number of black chairs:
$\text{Black chairs} = 125 - 75 = 50$

Therefore, the number of black chairs is 50.

To solve this problem, we'll follow these steps:

• Step 1: Identify the percentage of salary that is saved.
• Step 2: Calculate the amount saved using this percentage.

Let's start with Step 1:
Lucy spends 75% of her salary, so she saves $100\% - 75\% = 25\%$.

Now, Step 2:
We need to determine 25% of her monthly salary of 5000. We use the formula for finding a percentage of a number:

\( \text{Amount saved} = \frac{25}{100} \times 5000

Calculate the multiplication:

$\text{Amount saved} = 0.25 \times 5000 = 1250$

Therefore, Lucy saves \text{\1250} \) per month.

To solve the problem of finding the number of successful students, we need to follow these steps:

• Step 1: Understand that 50% of 48 students were successful.
• Step 2: Convert the percentage into a decimal or fraction. Since 50% is equivalent to $\frac{50}{100}$, we simplify it to $\frac{1}{2}$.
• Step 3: Apply the percentage formula by calculating $\frac{1}{2} \times 48$.

Now, let's calculate:

$\frac{1}{2} \times 48 = 24$

This calculation shows that 24 students were successful in the math test.

Therefore, the solution to the problem is $24$.

To solve this problem, follow these steps:

• Step 1: Identify the total number of tables in the room. There are 124 tables.
• Step 2: Determine the percentage of tables from the Netherlands. By calculation, it's $100\% - 75\% = 25\%$.
• Step 3: Find the numerical quantity of tables from the Netherlands. This involves taking 25% of the total tables:

$\text{Tables from Netherlands} = 124 \times \frac{25}{100}$

Calculating this, we have:

$\text{Tables from Netherlands} = 124 \times 0.25 = 31$

Thus, the number of tables from the Netherlands is $31$.

To solve the problem of finding the price of a shirt after a 30% discount, let's follow these clear steps:

• Step 1: Determine the discount amount using the formula: $\text{Discount Amount} = \text{Original Price} \times \left(\frac{\text{Discount Percentage}}{100}\right)$.
• Step 2: Calculate the price after discount: $\text{Price after Discount} = \text{Original Price} - \text{Discount Amount}$.
• Step 3: Verify this process with the problem requirements and check the options if provided.

Now, let's apply these steps:

Step 1: Calculate the discount amount:

The original price of the shirt is 160, and the discount percentage is 30%.

Using the formula, the discount amount is \( 160 \times \left(\frac{30}{100}\right) = 48 dollars.

Step 2: Find the final price after applying the discount:

The price after the discount becomes $160 - 48 = 112$ dollars.

Thus, the price of the shirt after applying the 30% discount is \112 \).

To solve this problem, we'll follow these steps:

• Step 1: Calculate the number of girls using the percentage provided.
• Step 2: Deduct the number of girls from the total number of students to find the number of boys.

Now, let's work through each step:
Step 1: The percentage of students that are girls is 30%. So, we find the number of girls by calculating:

$\text{Number of Girls} = 240 \times \left(\frac{30}{100}\right)$

Calculating this gives:

$\text{Number of Girls} = 240 \times 0.30 = 72$

Step 2: Subtract the number of girls from the total number of students to find the number of boys:
Number of Boys = Total Students - Number of Girls = 240 - 72 = 168

Therefore, the number of boys participating in the summer camp is $168$.

To solve this problem, we'll first determine the percentage of students who are girls and then use it to find the total number of students.

1. Determine the percentage of students who are girls. Since 80% of the students are boys, it follows that 20% are girls.

2. We know that 20% of the total number of students is equal to 12 (the number of girls). We can set up the equation:

$0.20 \times \text{Total students} = 12$

3. Solve for the total number of students:

$\text{Total students} = \frac{12}{0.20}$

$\text{Total students} = 60$

Therefore, the total number of students in the class is $60$.