Compare Different Denominators

Grade 4 · fractions · 67 practice problems · read aloud

🔊 Listen to this explanation

Comparing Fractions with Different Denominators

🧠 What is it and Why Learn It?

Comparing fractions with different denominators means figuring out which fraction is larger or smaller when the bottom numbers (denominators) aren't the same. This is super useful for real-life situations, like figuring out if you got 3/4 of a pizza or your friend got 5/8 of a pizza—who got more?

📝 Step-by-Step Guide

  1. Find a Common Denominator: Look for a number that both denominators can divide into. The easiest way is to multiply the two denominators together.
  2. Make Equivalent Fractions: Change both fractions so they have this new common denominator. Remember: whatever you do to the bottom, you MUST do to the top!
  3. Compare the Numerators: Now that the bottoms are the same, just look at the top numbers (numerators). The fraction with the larger numerator is the bigger fraction!

🔍 Visual Examples

Example 1: Compare 2/3 and 3/5

Step 1: Common denominator: 3 x 5 = 15.
Step 2: Make equivalent fractions.
    2/3 = (2x5)/(3x5) = 10/15
    3/5 = (3x3)/(5x3) = 9/15
Step 3: Compare 10 and 9. 10 > 9, so 2/3 > 3/5.

Example 2: Compare 1/4 and 2/6

Step 1: Common denominator: 4 x 6 = 24 (or use 12!).
Step 2: Make equivalent fractions.
    1/4 = (1x6)/(4x6) = 6/24
    2/6 = (2x4)/(6x4) = 8/24
Step 3: Compare 6 and 8. 6 < 8, so 1/4 < 2/6.

⚠️ Common Mistakes to Avoid

Don't just compare denominators! Just because one denominator is bigger, it doesn't mean the fraction is smaller. You MUST find a common denominator first.

Remember to multiply both parts! A common mistake is to change the denominator but forget to multiply the numerator by the same number.

Don't just compare numerators! 2/5 and 2/8 have the same numerator, but 2/5 is larger because the pieces are bigger.

💡 Tips & Tricks

The "Butterfly" Method (Cross-Multiply): Multiply the top of the first fraction by the bottom of the second. Write the answer above the first fraction. Then multiply the top of the second by the bottom of the first. Write that answer above the second fraction. The larger product shows you the larger fraction! 🦋

Use the Least Common Denominator (LCD): Sometimes you can find a common denominator smaller than just multiplying the two. For 4 and 6, the LCD is 12, not 24. This makes the numbers smaller and easier!

🎯 How to Practice

  • Use fraction circles or bars to see the comparisons visually.
  • Create flashcards with two fractions to compare.
  • Ask a friend or family member to give you two fractions and race to see who can find which is larger first!
  • Try these practice pairs: 3/4 vs 4/5, 2/8 vs 1/3, 5/6 vs 7/12.

Practice problems

6 of the 67, worked through step by step — try them before opening the answer.

1 3/4 > 2/3 ?

  1. A) yes
  2. B) no

Hint: To compare fractions with different denominators, find a common denominator by looking at the multiples of each denominator.

Show the answer

Answer: A) yes

  1. Find a common denominator. The denominators are 4 and 3. The smallest number that both 4 and 3 divide into is 12. So, 12 is our common denominator.
  2. Convert 3/4 to an equivalent fraction with denominator 12. To change the denominator from 4 to 12, we multiply 4 by 3. To keep the fraction equivalent, we must also multiply the numerator by 3. 3/4 = (3 * 3) / (4 * 3) = 9/12
  3. Convert 2/3 to an equivalent fraction with denominator 12. To change the denominator from 3 to 12, we multiply 3 by 4. To keep the fraction equivalent, we must also multiply the numerator by 4. 2/3 = (2 * 4) / (3 * 4) = 8/12
  4. Compare the two fractions. Now we compare 9/12 and 8/12. Since the denominators are the same, we simply compare the numerators. 9 is greater than 8. Therefore, 9/12 is greater than 8/12. Conclusion: Because 9/12 > 8/12, the original statement 3/4 > 2/3 is correct. ANSWER: yes

To determine if 3/4 is greater than 2/3, we need to compare the two fractions. The easiest way is to express both fractions with the same denominator.

2 2/3 > 3/5 ?

  1. A) no
  2. B) yes

Hint: To compare fractions with different denominators, find a common denominator by multiplying the denominators together, then compare the numerators.

Show the answer

Answer: B) yes

  1. To compare the fractions 2/3 and 3/5, we need a common denominator.
  2. The denominators are 3 and 5. The least common denominator is 15.
  3. Convert 2/3 to a fraction with denominator 15: Multiply numerator and denominator by 5: (2 × 5)/(3 × 5) = 10/15.
  4. Convert 3/5 to a fraction with denominator 15: Multiply numerator and denominator by 3: (3 × 3)/(5 × 3) = 9/15.
  5. Now compare 10/15 and 9/15. Since 10/15 is greater than 9/15, we conclude 2/3 > 3/5.
  6. Therefore, the answer to "2/3 > 3/5 ?" is yes.

3 2/3 > 1/2 ?

  1. A) yes
  2. B) no

Hint: To compare fractions with different denominators, find a common denominator by looking at the multiples of each denominator.

Show the answer

Answer: A) yes

  1. Understand the problem. We need to determine if 2/3 is greater than 1/2.
  2. To compare two fractions, it helps to have the same denominator. The denominators here are 3 and 2. The least common denominator is 6.
  3. Convert 2/3 to a fraction with denominator 6. Multiply numerator and denominator by 2: 2/3 = (2 × 2)/(3 × 2) = 4/6.
  4. Convert 1/2 to a fraction with denominator 6. Multiply numerator and denominator by 3: 1/2 = (1 × 3)/(2 × 3) = 3/6.
  5. Compare 4/6 and 3/6. Since 4/6 > 3/6, we conclude that 2/3 > 1/2. Final answer: yes

4 Mason is comparing two rectangular garden plots. Plot A is 7/8 of an acre, and Plot B is 5/6 of an acre. Which garden plot is larger?

Hint: Think about how to compare fractions with different denominators. You can find a common denominator or use fraction bars to visualize which piece is bigger.

Show the answer

Answer: Plot A (7/8)

  1. Write the fractions: 7/8 and 5/6. Since the denominators (8 and 6) are different, find a common denominator. The least common multiple of 8 and 6 is 24.
  2. Convert 7/8 to a fraction with denominator 24: Multiply numerator and denominator by 3 to get 21/24.
  3. Convert 5/6 to a fraction with denominator 24: Multiply numerator and denominator by 4 to get 20/24.
  4. Compare the numerators: 21 > 20, so 21/24 > 20/24. Therefore, 7/8 > 5/6. Plot A is larger. Answer: Plot A (7/8)

5 Noah and Sophia each have a pizza of the same size. Noah eats 5/8 of his pizza, and Sophia eats 7/12 of her pizza. Who eats more pizza?

Hint: Think about how to compare two fractions with different denominators. You can find a common denominator so both fractions have the same-sized pieces. Which fraction has more pieces when they are the same size?

Show the answer

Answer: Noah

  1. Compare 5/8 and 7/12. The denominators are different, so find a common denominator. The least common multiple of 8 and 12 is 24.
  2. Convert 5/8 to a fraction with denominator 24: 5/8 = (5 x 3)/(8 x 3) = 15/24.
  3. Convert 7/12 to a fraction with denominator 24: 7/12 = (7 x 2)/(12 x 2) = 14/24.
  4. Compare 15/24 and 14/24. Since 15 > 14, 15/24 > 14/24, so 5/8 > 7/12. Therefore, Noah eats more pizza.

The answer is Noah.

6 Aroha and Tane are each making a fruit smoothie. Aroha drinks 7/9 of her smoothie, and Tane drinks 9/11 of his smoothie. Who drank more of their smoothie?

Hint: Think about how to compare fractions with different denominators. You can find a common denominator or use benchmark fractions like 1/2 or 1 whole to help you decide which fraction is larger.

Show the answer

Answer: Tane

  1. Compare 7/9 and 9/11. Find a common denominator. The least common multiple of 9 and 11 is 99.
  2. Convert 7/9 to an equivalent fraction: 7/9 = (7 x 11)/(9 x 11) = 77/99.
  3. Convert 9/11 to an equivalent fraction: 9/11 = (9 x 9)/(11 x 9) = 81/99.
  4. Compare 77/99 and 81/99. Since 81 > 77, we have 81/99 > 77/99, so 9/11 > 7/9.
  5. Therefore, Tane drank more of his smoothie. Answer: Tane
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