In previous grades, you used models to represent fractions. For example, you can use a fraction square to represent 4 over 5 4 5 . Remember that if the square represents one whole unit, the denominator tells you how many equal-sized parts that the square should be divided into. The numerator tells you how many of these equal-sized parts will be shaded.

You also investigated problems involving partitioning, or separating, objects among different numbers of people. For example, consider the problem below.

To represent this partitioning, you can use fraction circles. Partition each of the four pizzas into three parts, and assign each part to one person.

The person represented by the blue portions of each pizza receives four slices that are each equivalent to 1 over 3 1 3 of a pizza.

The image below links to an interactive that you can use to investigate ways to partition different numbers of pizzas among different people. Click on the image and the interactive will open in a new browser tab or window. Use the interactive to investigate how to divide 2 pizzas among 3 people, 4 pizzas among 3 people, and 5 pizzas among 3 people. Also investigate how you could divide different numbers of pizzas among 4 people. Use the check boxes to reveal the expressions related to each model.

Interactive popup. Assistance may be required.

Need additional directions?

Use the interactive to model different combinations of pizzas and people. Use the model to complete the table shown below in your notes. Use the situation to create a division number sentence for each combination. Then, use the table to answer the questions that follow.

Interactive popup. Assistance may be required.

Check Your Answer

Number of Pizzas	Number of People	Fractional Part	Division Number Sentence
4	3	4 over 3 4 3	4 ÷ 3
5	3	5 over 3 5 3	5 ÷ 3
5	2	5 over 2 5 2	5 ÷ 2
3	4	3 over 4 3 4	3 ÷ 4

• How does the numerator of the fractional part compare to the number sentence?

  Interactive popup. Assistance may be required.

  Check Your Answer

  The numerator of the fractional part is the same as the dividend in the number sentence.

• How does the denominator of the fractional part compare to the number sentence?

  Interactive popup. Assistance may be required.

  Check Your Answer

  The denominator of the fractional part is the same as the divisor in the number sentence.

Pause and Reflect

In general, how would you write a fraction to represent the division number sentence a ÷ b?

Interactive popup. Assistance may be required.

Check Your Answer

a over b a b

Practice

1. Write a number sentence that represents the fraction 7 over 9 7 9 .

   Interactive popup. Assistance may be required.

   Need a hint?

   Which part of a division number sentence does the numerator represent? The denominator?
   Interactive popup. Assistance may be required.

   Check Your Answer

   7 ÷ 9
2. Madison collects marbles. In her collection, 17 out of 34 marbles are cat’s-eye marbles. Write a fraction and a number sentence that represents the portion of her marble collection that is cat’s-eye marbles.

   Interactive popup. Assistance may be required.

   Need a hint?

   What do the numerator and denominator in a fraction represent? How do the numerator and denominator compare to a division number sentence?
   Interactive popup. Assistance may be required.

   Check Your Answer

   17 over 34 17 34 = 17 ÷ 34
3. Duc had piano practice 13 days in April. April has 30 days. Write a number sentence that represents the fraction of the total number of days in April on which Duc had piano practice.

   Interactive popup. Assistance may be required.

   Need a hint?

   Which part of a division number sentence does the numerator represent? The denominator?
   Interactive popup. Assistance may be required.

   Check Your Answer

   13 ÷ 30