## Unit Rates and Ratios of Fractions

#### Aligned To Common Core Standard:

**Grade 7 Proportional Relationships** - 7.RP.A.1

What is the Difference Between Unit Rates and Ratios of Fractions? When it comes to relationships, both ratios and rates are a means of expressing relationships between two or more quantities. They are used to compare numbers. Though they sound a lot like each other, rates and ratios are two different concepts of mathematics. If you are ever faced with a problem that asks you to determine both the rate and ratio, you might get confused. Therefore it's time to understand the difference between rates and ratio. The ratio is basically used to express the relationship between two numbers. For instance, you have three water bottles and five lunchboxes. You can compare these two using ratio. To analyze the ratio between the water bottles and lunch boxes, we divide the set of each item. It's from 3 to 5 or 3:5 or 3/5. All these are forms to express a ratio. The ratio can be expressed as a fraction, as a decimal or even or as a decimal. Rate, on the other hand, is a bit different than the ratio. You can even call it is a special ratio. It is the comparison of measurements having separate units, like cents and grams.

### Printable Worksheets And Lessons

- Fence Painting Step-by-step
Lesson- Who knew that painting a fence could get so complicated?

- Guided Lesson
- Eating bananas, running, and baking batches of cookies.

- Guided Lesson Explanation
- Flipping the fractions is where most kids lose this one. Just
remind them to snap their fingers when trying to divide.

- Practice Worksheet
- These problems all involve time. It is pretty evident that people
are big on saving time; says the girls writing worksheets to make
your day go by faster.

- Matching Worksheet - A word of caution: I removed the units in order to require students to actually do the problems. Tell your kids that fact and give them extra credit for adding the units.

#### Homework Sheets

We use all word problem formats to work on splitting up whole numbers and fractions.

- Homework 1 - Roger went to the market to get some oranges. He bought 3/4 of a bushel of oranges. He shared the oranges with 60 people. How much of the bushel will each person get?
- Homework 2 - Tabitha can deliver 7 pizzas in 1/2 of an hour. How long will it take to her deliver 20 pizzas?
- Homework 3 - Eric bought a packet of toffees for his friend. The packet had 2/6 of a pound of toffee. He broke the toffee into 7 equal paper baggies. What is the weight of one of those baggies?

#### Practice Worksheets

On the practice sheets I focused on using different forms of notation for fractions. I would stress that you show those forms to students.

- Practice 1 - Jackson ran 3/2 of a mile in 1/2 of an hour; compute the unit rate (miles per hour) as a complex fraction.
- Practice 2 - Nelson measured out 2/4 of a cup of vinegar to be added evenly to 3 clothes washers. How much vinegar goes in each washer?
- Practice 3 - 1/4 of the students in guitar class attended class today. Only 3/4 of the students share guitars. What fraction of the class shares guitars?

#### Math Skill Quizzes

The first and third quiz are lengthy. I made the second quiz quick in case you are looking for just a short review.

- Quiz 1 - Lana drank 1/4 of a cup of milk in 1/12 of a minute. How many minutes will it take her to drink a full cup of milk?
- Quiz 2 - Isaac used 1/3 of an ounce of almonds to make 1/12 of a pound of cake. How many ounces of almonds are needed to make a cake?
- Quiz 3 - If you split 2/3 of a ton of dirt into 9 piles, how much dirt would be in each pile?