How can unit rates and proportional reasoning be used to solve problems

Answer 1

Unit rates and proportional reasoning can be used to solve problems by finding the value of one unit and using that information to find the value of the entire quantity.

To solve problems using unit rates and proportional reasoning, follow these steps:

1. Identify the given quantities and what they represent.
2. Determine the relationship between the given quantities.
3. Find the unit rate by dividing one quantity by the other. This will help establish a ratio.
4. Use the unit rate to find the value of the unknown quantity. Multiply the unit rate by the known quantity to find the unknown quantity.
5. Check your answer by verifying that the relationship between the quantities remains the same.

For example, let's say you want to find the cost of 5 apples based on the given unit rate of 3 apples for $2.

1. Given information: 3 apples for $2
2. Relationship: 3 apples cost $2
3. Unit rate: Divide the cost by the number of apples, which gives us a unit rate of $2/3 apples.
4. Use the unit rate to find the cost of 5 apples: Multiply the unit rate by the number of apples, so the cost of 5 apples is (5 apples) * ($2/3 apples) = $10/3 = $3.33.
5. Verify: The relationship between the cost and the number of apples remains the same, as 3 apples would cost $2 and 5 apples would cost $3.33.

By using unit rates and proportional reasoning, you can solve a variety of problems involving different quantities and relationships between them.

Answer 2

One T-shirt is sold for every 5 people who attend a concert.

What is the ratio of people to T-shirts sold?

The ratio of people to T-shirts sold is
to

Answer 3

5:1

Answer 4

One T-shirt is sold for every 5 people who attend a concert.

What is one way to write the unit rate in words?
1 T-shirt for every 5 people
1 person per 5 T-shirts
5 T-shirts for each person
5 people per T-shirt

Answer 5

1 T-shirt for every 5 people