CCSS.MATH.4.NF.A.2✓ New York State Education Department (NYSED) AlignedAcademic Year 2026–27
Comparing Fractions with Unlike Numerators & Denominators
Find common denominators and benchmark fractions (such as 1/2) to order and compare rational quantities.
Why It Matters:Essential for dosage measurements, woodworking tolerances, and probability comparisons.
Curated Video Instruction
● Verified Active EmbedSTEP-BY-STEP PROOF
Worked Example
Compare 3/4 and 5/6 using a common denominator:
1
Find least common multiple of 4 and 6
LCM(4, 6) = 12
Both 4 and 6 divide evenly into 12.
2
Convert both fractions to twelfths
3/4 = (3*3)/(4*3) = 9/12; 5/6 = (5*2)/(6*2) = 10/12
Express both with common denominator 12.
3
Compare numerators
9/12 < 10/12, therefore 3/4 < 5/6
Since 9 < 10, 3/4 is less than 5/6.
✓Verification Check
Cross multiply: 3 * 6 = 18 vs 4 * 5 = 20.
18
•
20 (18 < 20 Verified)
⚠️ Common Pitfalls & Misconceptions
Thinking larger denominator always means larger fraction
✗ Thinking 3/8 > 3/4 because 8 > 4✓ Larger denominator cuts the whole into SMALLER pieces, so 3/4 > 3/8
A greater number of pieces makes each unit fraction smaller.
INTERACTIVE DRILLS
Guided Practice
Practice Question1 of 1
Step-by-step Feedback
Which inequality correctly compares 2/3 and 3/5?
MASTERY BENCHMARK
Official Assessment Quiz
Formal Assessment
Comparing Fractions with Unlike Numerators & Denominators
Passing Criteria:70% or higher
Question 1 of 1
Which fraction is greater than 1/2?
Education to Career Navigation
Where This Lesson Leads
Carpenters and Lab Technicians compare fractional tolerances when cutting materials or measuring solutions.