Question

Write the ratio that compares 36 social media posts to 16 social media posts using fractional notation. Simplify the improper fraction to lowest terms.(1 point)
Write the ratio 12:36 as an equivalent ratio of x:3.(1 point)
How do you write 4 is to 16 as 12 is to 48 as a proportion in fractional notation? Do not simplify your answer.
A company pays their employees $20 per hour. Using fractional notation, write a proportion that represents how long an employee must work to make $80. Use x to represent the unknown number of hours.(1 point)
Which of the following, Option 1 or Option 2, is a proportion?

Option 1: 7/8=20/22

Option 2: 7/8=21/24

Answer 1

1. **Ratio Comparison**:
The ratio comparing 36 social media posts to 16 social media posts in fractional notation is:
\[
\frac{36}{16}
\]
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 4:
\[
\frac{36 \div 4}{16 \div 4} = \frac{9}{4}
\]
Therefore, the simplified ratio is \(\frac{9}{4}\).

2. **Equivalent Ratio**:
To write \(12:36\) as an equivalent ratio of \(x:3\), we start by setting up the proportion:
\[
\frac{12}{36} = \frac{x}{3}
\]
Cross-multiplying gives:
\[
12 \cdot 3 = 36 \cdot x
\]
Simplifying the left side:
\[
36 = 36x
\]
Dividing by 36:
\[
x = 1
\]
Therefore, the equivalent ratio is \(1:3\).

3. **Proportion in Fractional Notation**:
To write "4 is to 16 as 12 is to 48" in fractional notation, we can express it as:
\[
\frac{4}{16} = \frac{12}{48}
\]

4. **Proportion for Employee Pay**:
If a company pays their employees $20 per hour, to find how long an employee must work to make $80, we set up the proportion:
\[
\frac{20}{1} = \frac{80}{x}
\]
This can be rewritten as:
\[
\frac{20}{1} = \frac{80}{x}
\]

5. **Identifying the Proportion**:
We need to determine which option is a proportion:
- **Option 1**: \( \frac{7}{8} = \frac{20}{22} \)
- **Option 2**: \( \frac{7}{8} = \frac{21}{24} \)

To check both options, we can cross-multiply:

**Option 1**:
\[
7 \cdot 22 \quad \text{(154)} \quad \text{and} \quad 8 \cdot 20 \quad \text{(160)}
\]
These are not equal, so this is not a proportion.

**Option 2**:
\[
7 \cdot 24 \quad \text{(168)} \quad \text{and} \quad 8 \cdot 21 \quad \text{(168)}
\]
These are equal, so this is a proportion.

Therefore, **Option 2** is a proportion.

Answer 2

Describe three ways to write the ratio that compares 4 electronic devices for every 3 people.(1 point)
How do you write 5 is to 1 as 20 is to 4 as a proportion in fractional notation?(1 point)
You fill your car with 15 gallons of gas at a cost of $45. Using fractional notation, how do you write a proportion that shows how much 5 gallons of gas will cost? Use x to represent the unknown cost.(1 point)
Determine if 2.5/10=?12/48 or 2.5/2=?12/24 is a proportion.(1 point)
Determine if one, both, or neither of the following is a proportion. 16/8=?24/12, 8/4=?12/6 (1 point)

Answer 3

1. **Three Ways to Write the Ratio of 4 Electronic Devices for Every 3 People**:
- As a fraction: \(\frac{4}{3}\)
- In colon notation: \(4:3\)
- In words: "4 electronic devices for every 3 people"

2. **Proportion in Fractional Notation (5 is to 1 as 20 is to 4)**:
To express "5 is to 1 as 20 is to 4" as a proportion in fractional notation:
\[
\frac{5}{1} = \frac{20}{4}
\]

3. **Proportion for Gas Cost**:
If you fill your car with 15 gallons of gas for $45, to write a proportion showing how much 5 gallons will cost (using \(x\) for the unknown cost):
\[
\frac{15}{45} = \frac{5}{x}
\]

4. **Determining if Proportions are Equal**:
We check whether \( \frac{2.5}{10} = \frac{12}{48} \) or \( \frac{2.5}{2} = \frac{12}{24} \) is a proportion by cross-multiplying:

- **For \( \frac{2.5}{10} = \frac{12}{48} \)**:
\[
2.5 \cdot 48 = 120 \quad \text{and} \quad 10 \cdot 12 = 120
\]
Since both sides are equal, this is a proportion.

- **For \( \frac{2.5}{2} = \frac{12}{24} \)**:
\[
2.5 \cdot 24 = 60 \quad \text{and} \quad 2 \cdot 12 = 24
\]
Since both sides are not equal, this is not a proportion.

Therefore, **only the first statement is a proportion**.

5. **Proportion Check**:
To determine if one, both, or neither of the following is a proportion:
- **Option 1**: \( \frac{16}{8} = \frac{24}{12} \)
\[
16 \cdot 12 = 192 \quad \text{and} \quad 8 \cdot 24 = 192
\]
Since both sides are equal, this is a proportion.

- **Option 2**: \( \frac{8}{4} = \frac{12}{6} \)
\[
8 \cdot 6 = 48 \quad \text{and} \quad 4 \cdot 12 = 48
\]
Since both sides are equal, this is also a proportion.

Therefore, **both statements are proportions**.