Comparing Unlike Mixed Fractions Worksheets
Having the ability to accurately compare two fractions really helps students gain a bit of number sense for fractions. This is much different than comparing basic numeric values because they are composed of a numerator (part) and denominator (whole in one unit). This often confuses students because they are not sure which value is more important or where to even begin. We encourage teachers to start students off with the idea that you cannot compare anything unless it is in the same scale. In this case, denominators need to be the same before you can even begin. This is the strategy we have seen students to have the most success with. These worksheets help students learn how to find a common denominator and compare unlike fractions or simply compare like fractions.
Aligned Standard: Grade 4 Fractions - 4.NF.2
- Compare Like Fractions w/ Like Denominators Step-by-Step Lesson- Break out your >, <, or = symbols.
- Guided Lesson - Start with a filled shape comparison, order fractions, and decide on a sign to make a math sentence true.
- Guided Lesson Explanation - I was a little tired when writing this one, so you might need to put a little more effort in on this one.
- Practice Worksheet - Determine if the fractions are greater than, less than, or equal to each other.
- Matching Worksheet - Match the filled segmented pies with their fractions.
Unlike Fraction Comparisons
- Step-by-Step Lesson- We add a visual in here to help the students see what we are talking about.
- Guided Lesson - A straight unlike denominator comparison, a visual comparison, and ordering unlike fractions.
- Guided Lesson Explanation - I really took my time on these explanations.
- Independent Practice Worksheet 1 - I think you will really like what I put together here.
- Independent Practice Worksheet 2 - Yes, there are some equal comparisons here and I had them compare one part of everything.
- Answer Keys - These are for all the unlocked materials above.
We start off the easy way. Just use straight symbols. We then add some model-based comparisons. We end off by ordering fraction values.
- Homework 1 - The denominators in all fractions are same, so they do not need to be reworked. Now we have to compare numerators of both fractions.
- Homework 2 - Which sign makes the sentence true and put ˂ ____ ˃ ____ =
- Homework 3 - Complete the problems with a "___" by writing the ˃, ˂, or = signs. Rearrange the completed problems to make them true.
I always like to remind students to check if they are equal first. If not, point the arrow to the smaller fraction.
- Practice 1- Which symbol makes the most sense.
- Practice 2- Which sign makes the sentence true (>, <, or =)?
- Practice 3- Which set of fractions is ordered from least to greatest? Reorder sets that are incorrect.
Math Skill Quizzes
The quizzes are entirely fraction comparisons. This is the most common way to assess the skill.
- Quiz 1- Write the symbol that makes the math sentence true.
- Quiz 2- Make this sentence true.
- Quiz 3- Compare the fractions by writing a symbol. (<, >, or =).
How to Compare Mixed (Like and Unlike) Fractions
A fraction is meant to express a value that is less than one. It indicates how close or far from being one a value. Fractions are composed of two parts. The top part is called the numerator and indicates how many parts of the whole the value possesses. The bottom part of the fraction is called the denominator and indicates how many parts there are to be considered one whole unit.
When two fractions have the same denominators, they are said to be like fractions. When they do not have the same denominators, they are called unlike. Every student must be able to compare fractions both like and unlike. Comparison is used for determining which number is bigger and which one is smaller or in some cases to explain if they are equal.
There are three different situations you will come across when comparing two fractions:
Situation 1: They Have the Same Numerator, But Different Denominators - Students should understand that thirds are larger than sixths. The rule here is that the fraction with the smaller denominator is the bigger value. Did you know that when fast food chains attempted to give their customers more than the standard 1/4-pound hamburger and replace it with a 1/3-pound hamburgers, people simply thought it was less? If people only knew their fractions, they would realize they were getting a much better deal and larger burger to enjoy.
Situation 2: Different Numerator, But the Same Denominator - In this case, we can clearly see that there are different numbers of the same things. The same object is divided into 7/8th, and the other number is 3/8th. In this case, the number with the larger numerator is the bigger one.
Situation 3: Different Numerator and Different Denominator - In this case, the numerators and the denominators both are different. You can solve this by multiplying the top and bottom of the number with the same number as it will give the equivalent value. Once the multiplication is done, compare the two.