## Unit Rates and Ratios : The Relationship

#### Aligned To Common Core Standard:

**Grade 6 Proportional Relationships** - 6.RP.A.2

**What are Unit Rates?**-
When discussing unit rates, you need to first discuss rate, which is the ratio used for comparing different quantities. Unit rates define how much of the first quantity is compared to the one unit of the other. An example of unit rates is kilometer per hour, which shows how much distance (in km) is covered within an hour time. Unit rates and rates are used to solve several real-world problems. However, usually, real-world problems have different multiple-unit scenarios. Let us look at a few problems given below.
You can buy 5 kg of potatoes for $10. So, the single unit price of potato per kg is $10 รท 5 = $2 per kg of potatoes.
Another example is that you can paint 3 boards in 30 minutes. Here, the standard is to find how many boards you can paint in an hour. First, you know that 30 minutes times 2 is 60 minutes which is 1 hour. Now, if you combine your work for both 30 minutes, we can learn how much work we can do in an hour. The answer is 2 times 3 boards which equal to 6 boards. Therefore, you need to paint 6 boards in an hour.

### Printable Worksheets And Lessons

- Picnic Step-by-step
Lesson- Five bucks for a pizza pie... Can't beat that! How many
words can David write in a minute?

- Guided Lesson -
This is a regular potpourri of questions for you. We jump from word
problems to simple ratios.

- Guided Lesson Explanation
- I might have gone a little overboard on the question types here.
I have to admit that they are a bit drawn out.

- Practice Worksheet -
Word problems for you to walk through. They all assume that proportion
hold still.

- Matching Worksheet - This is the most random sheet I have ever created. It just came to me when I was written it.

#### Homework Sheets

We start with word problems and then move to easily definable proportion problems.

- Homework 1 - A shop keeper has 56 pens. He sold them for 280 dollars. How much did the shopkeeper charge for each pen?
- Homework 2 - How many seconds are there in 2 minutes?
- Homework 3 - 25 sticks are in 5 boxes. There are _____ sticks in each box.

#### Practice Worksheets

The problems focus on distance and length as the key measurement of focus.

- Practice 1 - A scooter can travel 100 km in 2 hours. How long will it take the scooter to travel 200 km?
- Practice 2 - How many meters are there in 856 cm?
- Practice 3 - The bunny eats 2 carrots in a day. How many carrots will he eat in 5 days?

#### Math Skill Quizzes

The quizzes mimic the other worksheets in this section, but we added some money type problems.

- Quiz 1 - There are a total of 50 bikes. 36 bikes are red and the others are black. How many black bikes are there?
- Quiz 2 - There are 150 students who went for a picnic in 6 buses. How many students are seated on each bus?
- Quiz 3 - 12 friends went for a dinner and they paid 600 dollars. How much did each friend contribute?