Comparing and Ordering Fractions
4A · Chapter 6 · Lesson 2 · MATH-4A-C06-L02
Learning goal. Compare fractions with common denominators/numerators or equivalent forms and a number line.
Before you begin
Recall: Grade 3B: fractions of equal wholes, equivalence, number lines and simplifying; Equivalent Fractions. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
Are 2/3 and 6/9 equivalent? Explain.
Show answer & reasoning
Multiply numerator and denominator of 2/3 by the same factor 3; the represented amount is unchanged.
Are 2/4 and 8/16 equivalent? Explain.
Show answer & reasoning
Multiply numerator and denominator of 2/4 by the same factor 4; the represented amount is unchanged.
Complete an equivalent fraction: 3/5 = ?/20.
Show answer & reasoning
The denominator was multiplied by 4, so the numerator must also be multiplied by 4.
Key vocabulary
- equivalent fractions
- different numerators and denominators representing the same quantity
- mixed number
- whole number plus proper fraction
- improper fraction
- fraction with numerator at least its denominator
- denominator
- number of equal parts in one whole
Understand the concept
To compare unlike fractions, rename them using equally sized parts. For 2/3 versus 3/4, twelfths give 8/12 and 9/12, so 3/4 is greater. On a number line, every fraction is positioned relative to the same 0 and 1. A denominator alone never tells you which fraction is larger when numerators also differ.
Model it: aligned fraction strips and a shared number line. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
Insert <, >, or =: 11/12 ___ 3/4.
Rename fractions using common denominator 12 and compare equal-size parts.
Check your understanding 1
Insert <, >, or =: 5/8 ___ 2/5.
Show answer & reasoning
Rename fractions using common denominator 40 and compare equal-size parts.
Worked example 2
Insert <, >, or =: 1/12 ___ 3/10.
Rename fractions using common denominator 60 and compare equal-size parts.
Check your understanding 2
Insert <, >, or =: 4/6 ___ 1/3.
Show answer & reasoning
Rename fractions using common denominator 6 and compare equal-size parts.
Worked example 3
Insert <, >, or =: 5/10 ___ 2/6.
Rename fractions using common denominator 30 and compare equal-size parts.
Check your understanding 3
Insert <, >, or =: 2/12 ___ 1/4.
Show answer & reasoning
Rename fractions using common denominator 12 and compare equal-size parts.
Guided practice
Insert <, >, or =: 3/6 ___ 2/3.
Show answer & reasoning
Rename fractions using common denominator 6 and compare equal-size parts.
Insert <, >, or =: 1/10 ___ 1/8.
Show answer & reasoning
Rename fractions using common denominator 40 and compare equal-size parts.
Insert <, >, or =: 8/10 ___ 5/10.
Show answer & reasoning
Rename fractions using common denominator 10 and compare equal-size parts.
Order these fractions from least to greatest: 3/4, 5/6, 1/5.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Order these fractions from least to greatest: 4/6, 3/8, 1/10.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Independent practice
Insert <, >, or =: 3/4 ___ 7/10.
Show answer & reasoning
Rename fractions using common denominator 20 and compare equal-size parts.
Insert <, >, or =: 7/12 ___ 2/3.
Show answer & reasoning
Rename fractions using common denominator 12 and compare equal-size parts.
Order these fractions from least to greatest: 9/10, 1/4, 5/6.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Order these fractions from least to greatest: 1/2, 5/10, 1/10.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Order these fractions from least to greatest: 5/8, 6/8, 5/10.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Insert <, >, or =: 1/4 ___ 2/4.
Show answer & reasoning
Rename fractions using common denominator 4 and compare equal-size parts.
Insert <, >, or =: 1/5 ___ 9/10.
Show answer & reasoning
Rename fractions using common denominator 10 and compare equal-size parts.
Insert <, >, or =: 5/6 ___ 2/8.
Show answer & reasoning
Rename fractions using common denominator 24 and compare equal-size parts.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
Two students each shade 2/5 of a rectangle, but one rectangle has twice the area of the other. Are the shaded areas necessarily equal? Explain.
Show answer & reasoning
Both shade 2/5 of their own reference whole. Because one whole has twice the area, that shaded region also has twice the area.
Insert <, >, or =: 3/10 ___ 2/10.
Show answer & reasoning
Rename fractions using common denominator 10 and compare equal-size parts.
Exit check
Order these fractions from least to greatest: 9/12, 1/3, 6/8.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Order these fractions from least to greatest: 3/8, 5/6, 4/8.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.
Order these fractions from least to greatest: 2/8, 2/4, 1/5.
Show answer & reasoning
Rename all three fractions using a common denominator, then compare numerators for equal-size parts.