Basics of Fractions: Drawing, Unit Fractions, Partitioning, Equal Parts

Partition Regions into Equal Parts

Prior Knowledge:

1. Identify each colored part of the following shapes.          

2. What part does the cake shape represent?

3. What fraction does the doughnut have?

4. How many parts does the pizza have?

Answers:

1. Circle – 1 part

Kite – 3 parts

Arrow – half part

Hexagon – 6 parts

2. 1 part

3. Whole part

4. 1 part

Introduction:

What are fractions?

Fractions are numbers that represent a part of the whole.

Real-world Example:

An apple is divided into slices of the whole

A pizza is divided into two equal parts. Each part is equal to half of the whole pizza.

Fraction of a Whole

When we divide a whole into equal parts, each part is a fraction of the whole.

Fraction Partitioning:

A whole fraction is divided into multiples of the unit fraction.

Example: Dividing a room into separate areas.

Example:

Draw lines to divide the shapes into 8 equal parts. Then write the fraction that represents 1 part.

Divide the given grid into 8 equal parts.

All parts have an equal area.

Each part is one-eighth of the area of the whole.

One-eighth can be written as a fraction.

Fractions and Regions

Unit Fraction

A unit fraction is any fraction with 1 as its numerator (top number) and a whole number as the denominator (bottom number).

Example:  1/4 (one quarter), which has a numerator of 1

Example:

Mrs. Gracia served part of a pan of cakes to a friend. What does each part of the whole pan represent? What part was served? What part is left?

The whole pan is divided into 6 equal parts. Each part is  1/6 of the whole.

6 pieces of 1/6 is 6/6. So, the whole is 6/6.

 The unit fraction is 1/6.

The number below the bar in a fraction shows the number of equal parts in the whole. It is called the denominator.

If 2 pieces of 1/6 is 2/6, then 2/6 of the pan was served.

If 4 pieces of 1/6 is 4/6, then 4/6 of the pan is left.

The number above the bar in a fraction shows the number of pieces of the unit fraction. It is called the numerator.

Understand the Whole Number 

Find 6/3 equivalent to a whole number

Here the denominator is 3

That means each part is 1/3 of the whole

We have six  1/3 parts because the numerator is 6. So, the area model for the six  1/3 parts is:

Notice how you can combine three 1/3 parts to make one whole.

How many wholes do you have now?

You have 2 wholes.

That means 6/3 is equivalent to 2 wholes.

Example:

Mr. John drew a picture on the board.

Then he asked her students what fraction it represented.

• Nathan said that the picture represents 2/6. Label the picture to show how Nathan’s answer can be correct.
• Victor said that the picture represents 2/3. Label the picture to show how Victor’s answer can be correct.

Solution:

Nathan’s picture represents 2/6 of the given drawing, which means that all six squares together make up the whole, and two of these squares have been shaded: 

Victor’s picture represents 2/3 of the given drawing, which means there are 3 squares that make a whole, so the two shaded squares represent two out of three.

Exercise:

Gilly and Luke went to the school library one fine morning. They planned to read books that day and borrow books to read during the winter. Answer the following questions:

1. Of the 10 books on fairy tales, Gilly borrowed 3. What fraction of the books on fairy tales did she borrow?
2. Gilly found 15 books on underwater life and brought 7 of these to the table. What fraction of the books on underwater life did she bring to the table?
3. Luke saw 9 books about the Solar System and its 9 planets. These were thick books and so he thought that 2 of these would be enough. What fraction of the solar system books did he borrow?
4. Luke also checked out books about land and sea animals. There were 20 books on land animals and 4 books on sea animals. He chose to borrow 7 books on animals. What fraction of the books on animals did Luke borrow?
5. Lastly, Gilly and Luke found a book on Greek mythology and the 12 most important Greek myths. The book had 120 pages. Gilly and Luke read 40 pages of the book. What fraction of the book did they read?

One fine spring morning, best friends Abby and Jessica went to the amusement park to enjoy some amazing rides. Answer the following questions:

6. Wanting to take things slowly, they first tried the carousel. There are 48 people in line. If 28 of them are kids, what is the fraction of people in line for the carousel that are kids?

7. Next, they decided to try the log ride. They were required to wear life vests to ensure their safety. There are 27 life vests available and 15 of them are colored yellow. What fraction of the life vests are not yellow?

8. After the log ride, they decided to grab something to eat. They bought 2 whole pizzas each. Abby had each of her whole pizzas sliced into four while Jessica had each of hers sliced into 8. Which of them ate more if Abby ate one whole pizza and 3 slices while Jessica ate one whole pizza and 5 slices?

9. Full from eating, they decided to rest by a pond full of ducks. There are 16 ducks in the pond and 8 of them are male. What is the fraction of male ducks in the pond? What is the fraction of female ducks?

10. Lastly, they rode the roller coaster. The roller coaster train is composed of 21 cars. If there are 12 empty cars, what is the fraction of empty cars in the roller coaster train?

11. Full from eating, they decided to rest by a pond full of ducks. There are 16 ducks in the pond and 8 of them are male. What is the fraction of male ducks in the pond? What is the fraction of female ducks?

12. Lastly, they rode the roller coaster. The roller coaster train is composed of 21 cars. If there are 12 empty cars, what is the fraction of empty cars in the roller coaster train?

What We Have Learned:

• Draw whole numbers as fractions
• Understand unit fractions
• Differentiate between numerator and denominator fractions
• Partition and regions of a whole
• Divide the whole fractions into equal parts

Concept Map: