What are Fractions?

A fraction is a way of representing a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.

Ordering Fractions

When ordering fractions, you need to compare them and arrange them from least to greatest or greatest to least. To do this, you can use several methods:

Common Denominator Method

1. Find a common denominator for all the fractions.

2. Convert each fraction to an equivalent fraction with the common denominator.

3. Compare the numerators of the equivalent fractions to determine the order.

Cross Multiplication Method

1. Cross multiply the fractions to make them have a common denominator.

2. Compare the products obtained after cross multiplication to determine the order.

Example

Let's say we have the fractions 2/5, 3/8, and 1/2. We want to order them from least to greatest.

Common Denominator Method

First, find a common denominator. The least common denominator for 5, 8, and 2 is 40.

Convert each fraction to an equivalent fraction with a denominator of 40: 2/5 = 16/40, 3/8 = 15/40, and 1/2 = 20/40.

Now compare the numerators: 15/40 < 16/40 < 20/40.

So, the order from least to greatest is 3/8, 2/5, 1/2.

Cross Multiplication Method

First, cross multiply the fractions: 2/5 and 3/8: (2 * 8) and (3 * 5) 1/2 and 3/8: (1 * 8) and (3 * 2) 1/2 and 2/5: (1 * 5) and (2 * 2)

Compare the products: 16, 15, 10. So, the order from least to greatest is 3/8, 2/5, 1/2.

Practice Questions

1. Order the fractions 3/7, 4/9, and 2/5 from least to greatest using the common denominator method.

2. Order the fractions 5/8, 7/12, and 3/10 from greatest to least using the cross multiplication method.

Conclusion

Ordering fractions involves comparing their values to determine their order. Whether you use the common denominator method or the cross multiplication method, it's important to understand the concept of fractions and how to compare them accurately.

◂Math Worksheets and Study Guides Fifth Grade. Ordering Fractions

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Use models, benchmarks, and equivalent forms to judge the size of fractions.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.