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Study with Ghada› Math Fifth Grade, Primary› Unit 6

Lesson ⁦6-5⁩: Compare Fractions and Mixed Numbers

Math · Fifth Grade, Primary · Unit 6: Fractions · First Semester

A 10-question quiz; after every question you'll see the right answer with an explanation.
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What will you learn in this lesson?

Students compare fractions and mixed numbers using models, number lines, and common denominators, and decide which is greater or less.

  • Compares two fractions with the same denominator or the same numerator
  • Compares two fractions with different denominators by writing equivalent fractions
  • Compares mixed numbers and improper fractions

💡 Tip: When the numerators are equal, the fraction with the smaller denominator is greater: 1/3 > 1/5, because the piece is bigger when we divide into fewer parts.

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Worked examples from the Compare Fractions and Mixed Numbers lesson questions

Which of the following statements is true?
  • 3/7 < 5/7
  • 4/9 > 7/9
  • 2/5 > 4/5
  • 6/8 < 3/8
✓ 3/7 < 5/7
When the denominators are equal, we compare the numerators: 3 < 5, so 3/7 < 5/7. The other statements are the reverse of what is correct.
Which of the following fractions is the greatest?
  • 7/10
  • 3/10
  • 1/10
  • 5/10
✓ 7/10
The denominators are equal, so the fraction with the greatest numerator is the greatest, and 7 is the greatest numerator.
Show more examples (3)
Which of the following fractions is the least?
  • 1/9
  • 1/3
  • 1/5
  • 1/2
✓ 1/9
The numerators are equal (1), so the fraction with the greatest denominator has the smallest parts; the least is 1/9.
Which of the following numbers is the greatest?
  • 3 1/5
  • 2 4/5
  • 2 3/5
  • 1 4/5
✓ 3 1/5
We compare the whole numbers first: 3 is greater than 2 and 1, so 3 1/5 is the greatest.
What is the correct relationship between 9/4 and 2 1/4?
  • 9/4 = 2 1/4
  • 9/4 > 2 1/4
  • 9/4 < 2 1/4
  • 9/4 = 2 1/9
✓ 9/4 = 2 1/4
Convert 2 1/4 to an improper fraction: 2 × 4 + 1 = 9, which gives 9/4, so the two numbers are equal.

FAQ about the Compare Fractions and Mixed Numbers lesson

How do I compare 2/3 and 3/4?

Write them with a common denominator of 12: 2/3 = 8/12 and 3/4 = 9/12. Since 9 > 8, 3/4 > 2/3.

How do I compare a mixed number with an improper fraction, such as 2 1/4 and 7/4?

Convert the mixed number to an improper fraction: 2 1/4 = 9/4. Since 9/4 > 7/4, the mixed number is greater.

How do I study the lesson Compare Fractions and Mixed Numbers and test myself on it?

Start the lesson quiz on Study with Ghada: 10 questions from the Math Fifth Grade, Primary question bank. After each answer you'll see the right answer with an explanation, and any questions you miss move to “Review my mistakes” until you master them.

Are Study with Ghada quizzes free and aligned with the curriculum?

Yes, completely free. They're built on the Math - Grade 5 - Semester 1 lessons in the same order as the book, and every question is reviewed and approved by a teacher before students see it.

Unit 6 lessons: Fractions

⁦6-1⁩ Division and Fractions ⁦6-2⁩ Improper Fractions ⁦6-3⁩ Problem-Solving Strategy: Use Venn Diagrams ⁦6-4⁩ Mixed Numbers ⁦6-6⁩ Round Fractions ⁦6-7⁩ Problem-Solving Investigation All Math Fifth Grade, Primary lessons →
← ⁦6-4⁩ Mixed Numbers ⁦6-6⁩ Round Fractions →