Sid has a bag with 100 marbles. There are 40 red marbles and 60 blue marbles in the bag.
1. What percentage of red marbles are there in the bag?
2. Write the percentage of blue marbles in the bag:
a. as a fraction with denominator 100
b. as a fraction in simplest form
c. as a ratio
d. as a decimal number

Answer

Let's solve the problem step by step.

### Step 1: Calculate the percentage of red marbles in the bag.
To find the percentage of red marbles, we use the formula:

\[ \text{Percentage of red marbles} = \left( \frac{\text{Number of red marbles}}{\text{Total number of marbles}} \right) \times 100 \]

Given:
- Number of red marbles = 40
- Total number of marbles = 100

Substituting the values:

\[ \text{Percentage of red marbles} = \left( \frac{40}{100} \right) \times 100 = 40\% \]

### Step 2: Calculate the percentage of blue marbles in the bag.
To find the percentage of blue marbles, we use the same formula:

\[ \text{Percentage of blue marbles} = \left( \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} \right) \times 100 \]

Given:
- Number of blue marbles = 60

Substituting the values:

\[ \text{Percentage of blue marbles} = \left( \frac{60}{100} \right) \times 100 = 60\% \]

### Step 3: Write the percentage of blue marbles as a fraction with denominator 100.
The percentage of blue marbles is already expressed as a fraction with a denominator of 100:

\[ \text{Fraction with denominator 100} = \frac{60}{100} \]

### Step 4: Write the percentage of blue marbles as a fraction in simplest form.
To simplify the fraction \(\frac{60}{100}\):

1. Find the greatest common divisor (GCD) of 60 and 100, which is 20.
2. Divide both the numerator and the denominator by 20:

\[ \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \]

### Step 5: Write the percentage of blue marbles as a ratio.
The ratio of blue marbles to the total marbles can be expressed as:

\[ \text{Ratio} = 3:5 \]

### Step 6: Write the percentage of blue marbles as a decimal number.
To convert the fraction \(\frac{3}{5}\) to a decimal:

\[ \frac{3}{5} = 0.6 \]

### Final Answers:
1. Percentage of red marbles: **40%**
2. Percentage of blue marbles:
a. As a fraction with denominator 100: **\(\frac{60}{100}\)**
b. As a fraction in simplest form: **\(\frac{3}{5}\)**
c. As a ratio: **3:5**
d. As a decimal number: **0.6**