# Interpret Fractions as Division of Numerator by the Denominator Worksheets

When fractions were first introduced to you; they were most likely presented as being a series of parts of a whole value. An example may be explained with one of our favorite foods. A whole pizza is made up of 8 slices. This means that 1 slice (part) is represented by the fraction 1/8^{th}. When we truly look at the exact nature of fraction it is in fact a quotient that express the parts divided by the whole value. The numerator represents the dividend and the denominator represents the divisor. In a way a fraction serves two purposes in math it represents and expression of a system or an operation. We can use this to our advantage to manipulate fractions and solve real world problems with ease. These worksheets will have students look at the concept of a fraction differently. This will prepare us for some basic pre-algebra skills.

### Aligned Standard: Grade 5 Fractions - 5.NF.3

- Fractions of Squares Step-by-step Lesson- We give you a line up of squares and ask you what fraction is yellow?
- Guided Lesson - We touch on more deep thinking fraction based problems. We give you everyday scenarios on this one.
- Guided Lesson Explanation - More of a verbal walk through on these problems. A little less intensive explanation.
- Practice Worksheet - I just realized that I really got carried away with the squares, as far as repetition. I'll write a few more in this section soon.
- Matching Worksheet - Match the fraction, whole number, and/or range to the problem that fits best.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Whatever number the problem is drawing attention to will automatically be your numerator.

- Homework 1 - What fractions of the triangle are orange?
- Homework 2 - If 2 people want to divide 37-kgs of rice equally by weight, how many kgs of wheat should each person get? Between what two whole numbers does your answer lie?
- Homework 3 - Count the total number of squares. We find that there are 5 squares. This is the denominator of fraction.

### Practice Worksheets

You will find some complex word problems for this grade level here.

- Practice 1 - If 4 children want to divide 42 pencils equally. How many pencils should each person get? Between what four whole numbers does your answer lie?
- Practice 2 - If 2 people want to divide 29 soda bottles equally, how many bottles should each person get? Between what two whole numbers does your answer lie?
- Practice 3 - What fraction of the circles are purple?

### Math Skill Quizzes

I feel like I covered this skill in every way that I can think of.

- Quiz 1 - Jack prepared lemon tea for a party. He used 12 ounces of lemon and 150 ounces of water. He has a measuring cup that is in units of cups.
- Quiz 2 - What fraction of the pentagons are yellow?
- Quiz 3 - If 2 people want to divide 93 chocolate equally, how many chocolate should each person get? Between what two whole numbers does your answer lie?

### Equating a Fraction to a Division Problem

Division is an operation where you determine how many times a value will fit into a different value. In a way you are breaking the numerator (parts) into a set number of groups (denominator). If you really look at a fraction, it is a quotient operation. When we begin to understand this relationship between fractions and the division operation, we can process some more advanced applications of math and apply it algebraic to solve problems. Look at how the two resemble one another in the diagram below:

## How to Determine the Fraction of a Data Set (Group)

Analyzing grouped data to find out the trends that define it is one of the fundamental concepts in statistics. It has a seemingly endless number of applications in our day-to-day lives. When kids are learning different ways to analyze data, they must develop strong concepts of determining the fraction of a group. The great thing about making sense of data sets is that there is not one correct way to do anything.

Example: Consider the following data set; 2, 1, 3, 2, 4, 5, 2, 1, 53, 4, 5, 1, 3, 12, 9, 10, 21, 2, 10, 17

What is the fraction of 2s in this data set?

Solution:

**Step 1: Organize the Data** - When analyzing the data, the first step is to organize it properly. You can arrange the data in ascending order, descending order, or stem-and-leaf plot; it is entirely up to you. Without organizing the data, the chances of errors are very high.

1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 9, 10, 10, 12, 17, 21, 53

**Step 2: Count the 2s** - The next step is to count the number of times 2 appears in the data set. In this case, you see that the number 2 repeats four times in this data.

**Step 3: Create a Fraction and Simplify** - The next step is to create a fraction; (Number of times 2 appears in the data)/(total number of values in data) = 4/20. The fraction can be simplified to 1/5, which is the fraction of 2s in the data. These worksheets and quick lessons help students understand the meaning and purpose of various fractions.