🔢 MathGrade 3Lesson 18
← Back🔒 PDF with full access

Compare and Order Fractions

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

Learning Objectives

  • 1Place fractions on a number line between 0 and 1 at the correct position
  • 2Compare two fractions with the same denominator using greater than, less than, or equal to
  • 3Order three fractions from least to greatest using a number line
📘

Mini Lesson

Fractions can be compared and ordered just like whole numbers. A number line from 0 to 1 is the best tool — the closer a fraction is to 1, the greater it is.

Fractions on a Number Line

  • Divide the space from 0 to 1 into equal sections matching the denominator.
  • Count up from 0 the number of sections shown by the numerator.
  • Example: 3/4 is 3 sections from 0 when the line is split into 4 equal parts.

Comparing Fractions with the Same Denominator

  • When denominators are equal, the larger numerator makes the larger fraction.
  • 2/6 < 5/6 because 2 < 5 (both are sixths, so more sixths = more).
  • Use < (less than), > (greater than), or = (equal to) between fractions.

Ordering Three Fractions

  • Place all three fractions on a number line and read them left to right.
  • Left to right = least to greatest.
  • Example: 1/4 < 1/2 < 3/4.
Fractions on a Number LineA number line from 0 to 1 showing ticks at 0, 1/4, 1/2, 3/4, and 1.Fractions on a Number Line01/41/23/411/4 < 1/2 < 3/4Reading left to right shows order.Closer to 1 = greater fraction.
Comparing Fractions with Same DenominatorTwo bar models comparing 2/6 and 5/6, showing that larger numerator means larger fraction.Comparing Fractions2/6 vs 5/6 — same denominator2/65/62/6 < 5/6Same denominator: bigger numerator= bigger fraction.5 > 2, so 5/6 > 2/6.
💡

When comparing fractions with the same denominator, just compare the numerators — bigger top number means bigger fraction.

Vocabulary
Compare
To look at two numbers to see which is greater, less, or equale.g. Compare 1/4 and 2/4 to see which is bigger.
Order
To put in a line from least to greatest or greatest to leaste.g. Order 1/4, 1/2, 3/4 from least to greatest.
Fraction
A number that shows part of a wholee.g. 3/4 is a fraction.
Numerator
The top number of a fractione.g. In 3/4, the numerator is 3.
Denominator
The bottom number of a fractione.g. In 3/4, the denominator is 4.
Equivalent
Equal in valuee.g. 1/2 and 2/4 are equivalent fractions.
Free · 7 days · No credit card

Unlock the full HSEA system for 7 days.

Add your first kid profile and your 7 days start: every lesson in every grade, saved progress for each child. Nothing to set up, no card required, nothing to cancel.

  • ✓ All 1,680 lessons, Grades 1–6, every subject
  • ✓ Profiles + saved progress for every kid
  • ✓ Printable lessons with answer key
Start your 7-day free trial →
Already convinced? See full membership plans →
← Lesson 17: Understand Fractions as Equal PartsLesson 19: Measure Length, Mass, and Capacity →