Comparing Fractions with Like Numerators or Denominators Worksheets
When we are learning to compare values of any kind, we often use the greater than, less than, or equal symbols. Students usually are steady with their comparisons that is until fractions make their appearance in the curriculum, and they are asked to make sense of them. In this section we want to cover what can be considered the first trick to comparing fractional values. When you are comparing fractional values that have either the same numerator (top value) or like denominator (bottom value) the comparison is quick and easy to do. We go into further detail below, but when you can identify the same values at one of those regions, you just need to compare the other region. These worksheets and lessons will help students learn how to make these types of simple comparisons between multiple fractional values.
Aligned Standard: Grade 3 Fractions - 3.NF.3
- Comparing Visual Fractions Step-by-step Lesson- Here are two fraction models to compare. I walk through the concept of comparisons.
- Guided Lesson - I set up three completely different ways of looking at a comparison. I nice review for some.
- Guided Lesson Explanation - This explanation is very straight forward, some might say too straight forward.
- Practice Worksheet - Compare the two visual fraction models with the use of symbols.
- Matching Worksheet - Match the fraction model and their actual fraction.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
Start out by comparing different types of common fractions and end off moving that skill to using models.
- Homework 1 - Use the symbols >, <, or = to make the sentence true. Consider identifying which portion is equal.
- Homework 2 - Compare them all up. This is a real mix of numeric values and visuals.
- Homework 3 - Order the fractions from least to greatest. Focus on determining what they all have in common.
Practice Worksheets
I follow a similar pattern with the practice sheets.
- Practice 1 - It is funny how one single symbol can signify a math based relationship. Put it to work for you.
- Practice 2 - You will be comparing visual to actual fractions. Make it so bro!
- Practice 3 - Get them all in order from smallest to greatest.
Math Skill Quizzes
I always find it odd that students have a lot more trouble with the ordering of fractions than the visual fractions.
- Quiz 1 - Take your time and spot what they all have in common.
- Quiz 2 - Order these guys up. They are mostly bottom heavy.
How to Compare Fractions with Like Numerators or Denominators
Fractions are all fun until you encounter a problem that requires a comparison between two fractions having like numerators or denominators. The numerator indicates the number of parts of the whole that you possess, and the denominator indicates the total number of parts that a whole value is composed of. When we are learning this topic, solving them as they get more complex becomes more difficult as well. Similar is the case for comparing these values; because we need to find out which fraction is greater than the other or less than the other. We also need to learn to identify which of them are equivalent to each other. To do so, we must learn to identify fractional values with similar numerators or denominators and compare them to one another.
When comparing two fractions, keep in mind that the comparison is only valid when they both refer to the same whole. We will explore this more by figuring out how can we compare two fractions with like numerators or denominators.
Comparing Fractions That Have Like Denominators
When two fractions have the same (like) denominator, all we need to do is compare the numerator. The one with the larger numerator is larger and the smaller numerator is smaller.
Consider the example of these two values: 3/4, 2/4
Which of them is smaller?
Answer: When we have like denominators, we compare the numerators of the value. In this case, they both have the same denominator (4). The numerator, which is less, is a smaller fraction. 2/4 is smaller than 3/4.
Comparing Fractions That Have Numerators
Which of the fractions 5/6 and 5/8 is greater?
Answer: When you have like numerators, you simply compare the values of the denominators. The fraction with a higher denominator is the lesser of the two. This is the inverse of what we just learned when considering numerators. This is because the bottom value indicates how large a whole unit is. The smaller that value is, the less parts it makes to make a whole value. In this case, 5/6 is the greater fraction.
Now that you have learned how to compare simple fractions, start practicing now!