Benchmark fractions are common fractions.
They’re called benchmarks because you know how big they are from working with them a lot.
You probably have these fractions memorized.
Reasoning about fraction size means using what you know about fractions to compare them.
What do you know about 2/4 & 3/4 that can help you when using reasoning skills to compare them?
2/4 is equivalent to 1/2, and 1/2 is less than 3/4.
Fractions on a Number Line
You can use benchmark fractions and reasoning skills to compare fractions on number lines, too.
How many sixths will be greater than 2/3?
5/6 and 6/6
- Remember, thirds and sixths are related.
- Thirds partitioned in half make sixths.
- So, 4/6 is equivalent to 2/3 and any numerator greater than 4 with a denominator of 6 will be greater than thirds.
Benchmark Number: 1
The number 1 is an important benchmark because it represents a whole. Fractions that are equal to 1 have the same numerator and denominator, such as: 2/2, 10/10, 5/5, and 6/6.
When comparing fractions, recognizing when a fraction is close to 1 can help you estimate its size. For example, 3/4 is close to 1 because it’s only one piece away from a whole.
By using 1 as a benchmark, you can quickly determine whether a fraction is greater than, less than, or equal to 1 to help with comparisons and reasoning.
Use what you know to compare the fractions below.
4/4 is equilvanet to 1 whole.
2/3 is less than 1 whole.
4/4 > 2/3
6/6 is equivalent to 1 whole.
5/5 is equivalent to 1 whole.
6/6 = 5/5
3/3 is equivalent to 1.
5/4 is greater than 1.
3/3 < 5/4
Benchmark Number: 1/2
The fraction 1/2 is another essential benchmark because it represents a value that is exactly halfway between 0 and 1. Some fractions that are equal to 1/2 include: 3/6, 5/10, 4/8, and 2/4.
Using 1/2 as a benchmark helps you quickly decide if a fraction is closer to 0, closer to 1, or exactly in between.
Use what you know to compare the fractions below.
2/4 is equivalent to 1/2.
3/6 is also equivalent to 1/2.
2/4 = 3/6
4/8 is equivalent to 1/2.
2/3 is greater than 1/2.
4/8 < 2/3
6/12 is equivalent to 1/2.
4/10 is less than 1/2.
6/12 > 4/10
Practice Problems
Compare the fractions.
Compare the fractions.
Compare the fractions.
