# Comparing Fractions

As we begin to better understand the concept of fractions and parts of wholes the natural sense of direction is to begin to compare them. When you first begin to put two fractions next to each, students can be confused as to how the two interrelate. If that is the case, we encourage teachers to use visuals with their students to help bring these things to life. We then review the concept of the parts of fractions and explain the bottom value (denominator) indicates the total number of parts that is equal to one complete unit. The top value (numerator) indicates the number of parts that this value consists of. These worksheets and lessons will help students learn how to compare these values with both like and unlike denominators. We also explore where whole numbers and mixed numbers come into play here.

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

- Models and Fractions Step-by-step Lesson- We have you convert from models to fractions and then we ask you to find equal fractions.
- Guided Lesson - We use a fractional numbers line again. It works well for this skill.
- Comparing Fractions 5 Pack - Comparing fractions over 5 pages of learning.
- Guided Lesson Explanation - Didn't take any chances this time, I wrote out every little step of these problems.
- Practice Worksheet - This is a three pager. I tried to cover it from every direction possible.
- Matching Worksheet - Match the fraction models to the fractions.

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

### Homework Sheets

Start by comparing models, compare fractions with numbers, and finish off with a nice coloring activity.

- Homework 1 - Compare the fractions using >, <, or =. Place your answer on the line.
- Homework 2 - Mr. Higgins class made model rockets. They shot off the models and measured the distance that they travelled from their starting point.
- Homework 3 - Draw a line to match the similar fractions. You will then fill in the missing numbers.

### Practice Worksheets

Put some symbols in their place and then tackle a rocket of a fractional word problem.

- Practice 1 - Write the fraction that each model represents. Circle the two fractions in each problem that are the same value.
- Practice 2 - Compare the fraction using <, >, or =. These are all the same denominators.
- Practice 3 - Color all the fractions that are equal to the key below. If a fraction is not equal to a value in the key, do not color it.

### Math Skill Quizzes

I fit all the skills in their including the word problem.

- Quiz 1 - The pole vaulting championship was very close. The difference between first place and fifth place were fractions of inches.
- Quiz 2 - Draw the symbol (>, <, or =) to make each statement correct. You will also work on a word problem.

### Tips for Comparing Fractions

Comparing fractions is one of the bigger struggles for elementary students. However, there are a few essential tips and tricks that make this a lot easier than what most students might think. When two fractions are in place, there a few tricks that can help you compare them with each other. They are based off of two core methods: decimal form and same denominator.

## Decimal Form Method

This method is pretty simple you need to rewrite each fraction in decimal form. This means that you just need to divide the numerator by the denominator. Once you have them in decimal form just compare the values.

Time to put this into action with this problem: Which of these values is larger: 4/9 or 7/12?

For both fractions we just divide the numerator (top) by the denominator (bottom). 4/9 = 0.44… and 7/12 = 0.583… 7/12 clearly represents the larger value.

## Denominator Method

If both fractions share the same denominator, you just need to look at the numerator. Whichever value has the larger numerator is the larger fraction.

If the fractions have different denominators, just convert them to have the same denominator. You can do this by simply determining a common denominator. The easiest way is to use one denominator as a multiple of the other.

For example: which fraction is smaller: 3/6 or 7/13?

We can make a common denominator by multiplying each fraction (top and bottom) by the denominator of the other. 3/6 (x13) = 39/78 and 7/13 (x6) = 42/78. To compare these, we just look back at our same denominator example. We can clearer see that 3/6 is smaller because the numerator is smaller.

## Advanced Method

You can also use an advance approach to this for students that are a bit more mathematically inclined. Example: compare 3/8 with 4/9.

You multiply the numerator of the first fractions by the denominator of the second fraction. Now compare the answers of the two.

3 x 9 = 27, 4 x 8 = 32, Since 32 is the larger number than 27, we know that 4/9 is a far greater number than 3/8. You need to make sure that your answer related to the numerator. So, in this example, 27 was related to 3/8, and 32 was related to 4/9. Hence, between the two fractions, 4/9 is greater.