Fractions of a whole: modeling word problems

key notes :

What is a fraction? A fraction represents part of a whole. Here are some examples of fractions.

A circle split into two equal parts with the right half shaded and labeled with the fraction one over two. A second circle split into four equal parts with three of the fourths shaded and labeled with the fraction three over four. A third circle split into six equal parts with four of the sixths shaded and labeled with the fraction four over six.

In a fraction, the top number is called the numerator. The bottom number is called the denominator.

The fraction three fourths with the three labeled as the numerator and the four labeled as the denominator.

💡 A fraction model represents a part of a whole.

Learn with an example

Elizabeth is selling jars of homemade jam at the Good Earth Farmers Market. Before any shoppers arrive, she uses masking tape to divide her table into 2 equal sections. She fills 1 section of the table with jars of blueberry jam.

Which model represents the fraction of the table that Elizabeth fills with jars of blueberry jam?

The table is the whole.

Elizabeth divides the table into 2 equal sections. The model should have 2 equal parts.

She fills 1 section of the table with jars of blueberry jam.

So, shade 1 part of the model.

This model shows 1/2. It represents the fraction of the table that Elizabeth fills with jars of blueberry jam.

Eliza keeps frogs and turtles as pets. Eliza’s pets live in a long tank. The tank is divided into 3 equal parts. Turtles live in 1 part.

Which model represents the fraction of the tank that turtles live in?

The tank is the whole.

The tank is divided into 3 equal parts. The model should have 3 equal parts.

turtles live in 1 part .

so, shade 1 part of the model .

This model shows 1/3 . It represents the fraction of the tank that turtles live in.

Elsie is using a long wooden board to fix a broken fence. She saws the board into 4 equal pieces. Elsie uses 1 piece to fix the front of the fence.

Which model represents the fraction of the board that Elsie uses to fix the front of the fence?


The board is the whole.

Elsie saws the board into 4 equal pieces. The model should have 4 equal parts.

elsie uses 1 plece to fix the front of the fence .

so, shade 1 part of the model .

This model shows 1/4 . It represents the fraction of the board that Elsie uses to fix the front of the fence.

Let’s practice!