2/12 or 6/7- which one is greater? To answer this, one would have to calculate the lowest common denominator and then multiply both fractions so that they share a common denominator and then compare them. Want to simplify comparing and ordering fractions? Learn all about benchmark fractions, their definition, use, chart, and much more, as it is one of the best strategies to use these fractions when understanding the comparison of fractions. Their role and usage are the same as their name suggests. The word benchmark refers to a standard that other things can be compared to. So, what is a benchmark fraction?
In the following article, we’ll cover:
- What is a benchmark fraction?
- Benchmark fraction examples
- How to compare fractions using benchmark fractions?
- How to compare fractions by using benchmarks and number lines?
- Benchmark fractions chart
- Benchmark fraction calculator
What is a benchmark fraction?
Benchmark fraction definition: A common fraction that we can use to compare other fractions is a benchmark fraction.
So, a known size or amount helps understand a different size or amount.
They are simple common fractions that each of us is familiar with, and they make visualizing complicated fractions much easier. Using benchmark fractions for estimations helps students develop fraction number sense and advance their mental math skills.
We can easily divide any object to be measured or compared into two equal parts. Therefore, the most common benchmark fraction example is ½ (one-half). It lies right in the middle between zero and one. ½ can also be written in different forms or equivalent fractions, such as 2/4, 3/6, 4/8, and so on. Now, we can compare the other fractions with different denominators to one half.
Also, it is simple to determine whether a fraction is equivalent to one-half. We will first study the numerator and compare it to the denominator. If the numerator is exactly half the amount of the denominator, then the fraction is equivalent to one-half.
Suppose we have a fraction: 4/10. If we use 1/2 as a benchmark fraction, it simplifies the process. 5/10 is equivalent to ½ on simplification. So, a fraction with ten as the denominator can be compared to 5/10 as we know that it is exactly half.
So, on comparing 4/10 to 5/10, we can note that it is only 1/10 away from 5/10. Therefore, it is much closer to 5/10 (or ½) than 0 or 1.
Some common benchmark fraction examples are as follows:
How to compare fractions using benchmark fractions?
Consider the following examples to understand how to compare different fractions with benchmark fractions.
Example: Compare whether 3/8 is less or more than one-half?
We know that 4/8 equals ½. As three is less than four, 3/8 will be slightly less than one-half.
Example: Compare ½ and 7/12 to see which one is greater.
We will first make a list of multiples of 2 (the denominator of ½).
Multiples of 2, 4, 6, 8, 10, and 12.
We will stop when we get the denominator of the other number. Since there are six multiples involved in reaching up to 12 in the denominator, we will multiply ½ by 6 as follows:
1 62 6 = 612
Here we must multiply both the numerator and denominator with the same number.
Now, we can compare 7/ 12 to 6/12. We find that 7/12 is greater than 6/12.
Therefore, 7/12 is greater than ½.
|Real-life examples of benchmark fractions: A ruler used in everyday life has halves, fourths, and eighths as benchmark fractions. Measuring spoons and cups have several benchmark fractions marked on them. Measuring tape several carpentry and construction tools|
How to compare fractions by using benchmarks and number lines?
A number line is the most commonly used visual representation of fractions. We can use it to compare fractions.
Example: Compare which fraction is greater: ¼ or 5/12.
First, we will draw a number line to compare the two fractions, as shown below. Here 0/12 represents zero, 6/12 is for ½, and 12/12 is 1.
¼ is the same as 3/12. So, we will mark its length.
Next, we will mark the length of 5/12.
Thus, from the number line, we can conclude that 5/12 is greater than ¼.
Fraction Strips with Benchmark Fractions
Fraction strips are colored pieces of paper, similar in length, containing benchmark fractions. They are also called fraction bars or fraction tiles.
Colored fraction strips make it interesting for students to explore and visualize fraction relationships. These strips have several benchmark fractions marked on them that enable students to develop a concrete understanding of equivalent fractions, mixed numbers, comparing, and ordering fractions.
They help students see how different equal parts can represent a whole. Students can move these strips, put them side by side, and study fractional amounts.
|Interestingly, students can create fraction strips by themselves to understand the concept better. Here is how to do it: Take strips of paper that are the same in length. One strip represents one whole. Now, take a strip and fold it in half. The two parts represent two one-halves. So, students can learn that two one-halves make one whole. Take a strip and fold it into four equal parts. Each part represents one-fourth. So, four one-fourths make one whole. Repeat the process for another number of folds and study the relationships.|
Benchmark fractions chart
A benchmark fraction chart is a simple visual that allows students to see where a fraction lies on a number line when compared to a whole. They help students study equivalent fractions. They can be used to order and compare fractions with different denominators and numerators. It is also known as a fraction wall.
How to use a benchmark fraction chart?
It is simple to use a benchmark chart to compare two or more fractions. We have to consider the length of the corresponding fractions and draw conclusions. The process is similar to using fraction strips for estimations. The following example will help you understand using a benchmark fraction chart for comparing two fractions.
Example: Which one is greater: ½ or ⅚?
Now, we will consider the two fractions on a benchmark fraction chart. It shows that ⅚ is greater than ½.
|½One half||½One half|
|1/3One third||1/3One third||1/3One third|
|1/4One quarter||1/4One quarter||1/4One quarter||1/4One quarter|
|1/5One fifth||1/5One fifth||1/5One fifth||1/5One fifth||1/5One fifth|
Benchmark fraction calculator
Several benchmark fraction calculators are available online. They require you to enter at least two fractions for benchmark fraction calculation. You can also round to the nearest half, one-fourth, or one-eighth. You select from the available options, such as estimating sum, estimating difference, or comparing.
- What is a benchmark in Math?
Benchmarks in mathematics are the standard or reference points. You can measure, compare, or assess any quantity against these benchmarks. They can be in the form of integers or fractions. The most commonly used benchmark numbers are multiples of 10 or 100 and the fractions are ½ and ¼.
- What is an example of a benchmark fraction?
A commonly used fraction for comparing other fractions is ½ (one half). Other popular benchmark fractions are ⅓ (one-third) and ⅔ (two-thirds).
- What are some other strategies for comparing fractions?
In addition to benchmark fractions, several other strategies for comparing fractions are:
- You can easily compare fractions with the same denominator. The one that has the lowest numerator is the smallest fraction.
- Similarly, you can compare fractions with the same numerators. The one that has a bigger denominator is the smallest fraction.
- You can convert fractions with different numerators and denominators into decimals for quick estimations.
- Students can compare fractions by plotting the points on one or different number lines using number lines.
- What is the purpose of using fraction strips?
Fraction strips serve as a useful medium for students to grasp the fundamental theories of fractions. With several strips at hand, it gets easier to study the breakdown of fractions into ½, 1/3, ⅔, etc. These strips can be cut into different sizes and placed beside each other to study the relationships. They are also useful for understanding fractions’ addition, subtraction, and multiplication.
- How do you use benchmark fraction strips to find the largest fraction?
We can study the different benchmarks on the fraction strips. Place the required strips (side by side) for a number. Next, we will place the necessary strips (side by side) for the other number. If the length of the two sets of strips is the same, then the fractions are equal. The set that is the longest depicts the largest fraction.