024. Ordering Fractions

Learning Intentions

• To know the meaning of the terms ascending and descending
• compare two fractions and decide which one is larger
• order a list of fractions in ascending or descending order

Pre-requisite Summary

• Understand that fractions represent parts of a whole
• Know the meaning of numerator and denominator
• Be able to Identify equivalent fractions
• Be able to Simplify fractions where helpful
• Understand that fractions can be compared by Use common denominators or by reasoning about size
• Know that ascending means smallest to largest
• Know that descending means largest to smallest

Worked Examples

Worked Example 1

a) Define ascending.

b) Define descending.

c) Write in ascending order.

Worked Example 2

Compare the fractions and decide which is larger:

a) and

b) and

c) and

Worked Example 3

Compare the fractions and decide which is larger:

a) and

b) and

c) and

Worked Example 4

Compare by using equivalent fractions or common denominators:

a) and

b) and

Worked Example 5

Write the fractions in ascending order:

a)

b)

Worked Example 6

Write the fractions in descending order:

a)

b)

Problems

Problem 1

a) Define ascending.

b) Define descending.

c) Write in ascending order.

Problem 2

Compare the fractions and decide which is larger:

a) and

b) and

c) and

Problem 3

Compare the fractions and decide which is larger:

a) and

b) and

c) and

Problem 4

Compare by using equivalent fractions or common denominators:

a) and

b) and

Problem 5

Write the fractions in ascending order:

a)

b)

Problem 6

Write the fractions in descending order:

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

State whether each list is in ascending or descending order:

a)

b)

c)

Exercise 2.

Compare the fractions and Choose the larger:

a) or

b) or

c) or

Exercise 3.

Compare the fractions and choose the larger:

a) or

b) or

c) or

Exercise 4.

Compare the fractions using common denominators:

a) and

b) and

c) and

Exercise 5.

Write in ascending order:

a)

b)

c)

Exercise 6.

Write in descending order:

a)

b)

c)

Exercise 7.

Order the fractions in ascending order:

a)

b)

c)

Exercise 8.

Order the fractions in descending order:

a)

b)

c)

Reasoning

Exercise 9.

Explain why even though .

Exercise 10.

A student says because . Explain the mistake.

Exercise 11.

Explain why using a common denominator helps compare and .

Exercise 12.

A student orders in ascending order because . Explain why this is incorrect.

Problem-solving

Exercise 13.

Three ribbons have lengths m, m and m. Order them from shortest to longest.

Exercise 14.

A recipe uses cup, cup and cup of different ingredients. Order these amounts from largest to smallest.

Exercise 15.

Four runners completed fractions of a lap: . Order these in ascending order.

Exercise 16.

A student shaded and of three rectangles. Order the shaded fractions in descending order.

Exercise 17.

A set of water bottles contains L, L and L. Order these amounts from smallest to largest.

Exercise 18.

A teacher lists scores as fractions: . Order them in descending order.

Potential Misunderstandings

• Students may think ascending means largest to smallest instead of smallest to largest
• Students may think descending means smallest to largest instead of largest to smallest
• Students may compare fractions by looking only at the numerator or only at the denominator
• Students may think a larger denominator always means a larger fraction
• Students may not Recognise that fractions with the same numerator can be compared by the size of their parts
• Students may not recognise that fractions with the same denominator can be compared by the number of parts taken
• Students may forget to convert to equivalent fractions when denominators are different
• Students may order fractions by the size of the denominator rather than the actual value of the fraction

Next: 025. Adding Fractions and Mixed Numerals