Select the TWO ratios that are equivalent to 3/9

Question

1/3
6/9
1/9
6/18

Answer 1

To find the ratios that are equivalent to \( \frac{3}{9} \), we can simplify \( \frac{3}{9} \) first:

\[ \frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3} \]

Now, we'll check the other options to see which are equivalent to \( \frac{1}{3} \) (and thus also to \( \frac{3}{9} \)).

1. \( \frac{1}{3} \) → This is equivalent to \( \frac{3}{9} \).
2. \( \frac{6}{9} \) → Simplifying \( \frac{6}{9} \): \[ \frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3} \quad (\text{not equivalent}) \]
3. \( \frac{1}{9} \) → This is clearly not equivalent to \( \frac{3}{9} \).
4. \( \frac{6}{18} \) → Simplifying \( \frac{6}{18} \): \[ \frac{6}{18} = \frac{6 \div 6}{18 \div 6} = \frac{1}{3} \quad (\text{equivalent}) \]

Therefore, the two ratios equivalent to \( \frac{3}{9} \) are:

• \( \frac{1}{3} \)
• \( \frac{6}{18} \)

Answer 2

Makynzie is making snacks for a party. She is going to make 20 sandwiches and 35 chicken wings. What is the ratio of chicken wings to sandwiches?
20:55
35:55
20:35
35:20

Answer 3

To find the ratio of chicken wings to sandwiches, we take the number of chicken wings (35) and the number of sandwiches (20).

The ratio is:

\[ \text{Ratio of chicken wings to sandwiches} = \frac{35}{20} \]

To express this as a ratio, we can write it as:

\[ 35:20 \]

Now, we can simplify this ratio by dividing both terms by their greatest common divisor (GCD), which is 5:

\[ \frac{35 \div 5}{20 \div 5} = \frac{7}{4} \]

So, the simplified ratio of chicken wings to sandwiches is \( 7:4 \).

However, the original question asked for the options given, which were:

• 20:55
• 35:55
• 20:35
• 35:20

The correct answer based on the number of items is \( 35:20 \).

So the final answer is:

35:20

Answer 4

Tony decides to make granola bars for breakfast. He follows a recipe that calls for 8 cups of rolled oats and 4 cups of almonds. What is the unit rate of rolled oats per 1 cup of almonds?
2 cups
4 cups
1/2 cup
32 cups

Answer 5

To find the unit rate of rolled oats per 1 cup of almonds, we can set up the ratio of rolled oats to almonds based on the amounts given in the recipe.

According to the recipe, there are:

• 8 cups of rolled oats
• 4 cups of almonds

We need to determine how many cups of rolled oats correspond to 1 cup of almonds.

To do this, we calculate the unit rate as follows:

\[ \text{Unit rate} = \frac{\text{Cups of rolled oats}}{\text{Cups of almonds}} = \frac{8 \text{ cups of rolled oats}}{4 \text{ cups of almonds}} \]

Now, simplify the ratio:

\[ \frac{8}{4} = 2 \]

This means that for every 1 cup of almonds, there are 2 cups of rolled oats.

So the unit rate of rolled oats per 1 cup of almonds is 2 cups.

Answer 6

Brynn is mowing the lawn. If it has taken 1/2 hour to mow 2/3 of the lawn, how long will it take to mow the entire lawn?
1/3 of an hour
3/4 of an hour
1 1/3 hours
1/6 of an hour

Answer 7

To find out how long it will take Brynn to mow the entire lawn, we can first determine the rate at which she is mowing the lawn and then use that rate to calculate the total time for the entire lawn.

1. Determine the rate of mowing:

   • If Brynn mows \( \frac{2}{3} \) of the lawn in \( \frac{1}{2} \) hour, she is mowing at the following rate:

   \[ \text{Rate} = \frac{\text{part of the lawn mowed}}{\text{time taken}} = \frac{\frac{2}{3}}{\frac{1}{2}} \]

   To divide by a fraction, we multiply by its reciprocal:

   \[ \text{Rate} = \frac{2}{3} \times \frac{2}{1} = \frac{4}{3} \text{ (lawn per hour)} \]

   This means Brynn mows \( \frac{4}{3} \) of the lawn in 1 hour.

2. Calculate the time to mow the entire lawn:

   • Since she can mow \( \frac{4}{3} \) of the lawn in 1 hour, we can find the time to mow 1 whole lawn by taking the reciprocal:

   \[ \text{Time to mow entire lawn} = \frac{1 \text{ lawn}}{\frac{4}{3} \text{ lawns/hour}} = \frac{3}{4} \text{ hours} \]

So it will take Brynn 3/4 of an hour to mow the entire lawn.

Answer 8

Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
No, the ratios are not equivalent.
Yes, the data table has a proportional relationship.
No, the table does not count consecutively.
No, the ratio 6 : 78 is not proportional to the other ratios.

Answer 9

To determine if the quantities in a data table represent a proportional relationship, we need to check if the ratios of the corresponding quantities are equivalent across the table.

However, you haven't provided the specific data from the table. Since I don't have that data, I can't analyze the ratios directly. Nevertheless, I can guide you on how to check for proportionality:

1. Calculate Ratios: For each pair of corresponding quantities in the table, calculate the ratio (e.g., if the first quantity is \( a \) and the second is \( b \), then the ratio is \( \frac{a}{b} \)).

2. Compare Ratios: Check to see if all ratios simplify to the same value. If all calculated ratios are equivalent, the relationship is proportional.

3. Determine the Conclusion:

   • If the ratios are equivalent, then you would select "Yes, the data table has a proportional relationship."
   • If the ratios are not equivalent, you can choose between the other options provided based on the observations (e.g., indicating a specific ratio that stands out as not proportional).

Please provide the specific values from the data table if you'd like a more detailed analysis.