How to Use Benchmark Fraction? Benchmark Fraction Definition

A Step-by-step Guide to understanding benchmark fractions

In mathematics, benchmark fractions may be described as common fractions. One is able to measure or judge against, whenever comparing, measuring, or arranging other fractions. These benchmark fractions are simple to see and distinguish, and so, assist in assessing the parts. Whenever doing a comparison of two fractions with varied denominators and numerators, one may either make the denominators common else do a comparison of them with a benchmark fraction. Common benchmark fractions are \(\frac{1}{4},\frac{1}{2}\).

Here’s a step-by-step guide to understanding benchmark fractions:

Step 1: Know the common benchmark fractions:

First, familiarize yourself with the most common benchmark fractions. These are usually simple fractions with small denominators, such as:

0 (which represents 0/1)

1/4

1/2

3/4

1 (which represents a whole, e.g., 4/4, 5/5, etc.)

Step 2: Understand what benchmark fractions represent:

Benchmark fractions represent easily recognizable values that lie between 0 and 1. They help you understand and estimate the value of other fractions. For example, knowing that 1/2 is a benchmark fraction helps you understand that 3/5 is a little more than 1/2.

Step 3: Compare other fractions to benchmark fractions:

When comparing fractions, use benchmark fractions to make estimations. For example, if you need to compare 3/8 and 5/8, you can use the benchmark fraction 1/2 (4/8) to determine that 3/8 is less than 1/2 and 5/8 is greater than 1/2.

Step 4: Use benchmark fractions to estimate sums and differences:

Benchmark fractions can also help you make quick estimates when adding or subtracting fractions. For example, if you’re adding 1/3 and 1/6, you can estimate that their sum is a little more than 1/2 (since 1/3 is slightly more than 1/4 and 1/6 is half of 1/3).

Step 5: Place benchmark fractions on a number line:

To visualize benchmark fractions and their relationships to other fractions, place them on a number line. Divide the line into four equal parts and label the segments with the benchmark fractions 0, 1/4, 1/2, and 3/4. You can then use this number line to compare other fractions to the benchmark fractions.

Step 6: Practice with various fractions:

To solidify your understanding of benchmark fractions, practice comparing different fractions to benchmark fractions. As you gain experience, you’ll develop a better intuition for estimating the value of a fraction and its relationship to benchmark fractions.

Understanding and using benchmark fractions can help students develop a strong foundation in fractions and their relationships, making it easier to compare, add, and subtract fractions.

Benchmark Fractions Definition-Example 1:

Which fraction is closer to \(0\)?\(\frac{1}{2},\frac{1}{4},\:\frac{3}{4}\)

Solution: \(\frac{1}{2}\) is the middle of \(0\) and \(1\). \(\frac{1}{4}\) is the middle of \(0\) and \(\frac{1}{2}\). \(\frac{3}{4}\) is the middle of \(\frac{1}{2}\) and \(1\). Therefore, \(\frac{1}{4}\) is closer to \(0\).