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)

Question

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.