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Detailed Explanation of How to Compare Fractions 📏➗

When you compare fractions, you are finding out which fraction is bigger or smaller. In Year 3 Maths, we learn how to compare fractions by looking at the numerator, denominator, and using helpful tools like fraction bars and circles.

What Are Numerators and Denominators? 🧮

A fraction has two parts:

  • The numerator is the top number. It tells you how many pieces you have.
  • The denominator is the bottom number. It tells you how many equal parts the whole is divided into.

For example, in the fraction 3/4:

  • 3 is the numerator (3 pieces)
  • 4 is the denominator (the whole is split into 4 parts)

Step 1: Look at the Denominators 🔍

If the denominators are the same, it’s easy to compare fractions. The fraction with the bigger numerator is bigger because you have more parts of the same size.

Example:

  • 3/5 and 4/5
  • Because both have denominator 5, compare 3 and 4.
  • 4/5 is bigger because 4 is more than 3.

Step 2: Find a Common Denominator 🔄

If the denominators are different, you need to find a common denominator. This is a number both denominators can go into. You change both fractions so that they have the same denominator.

Example: Compare 1/3 and 2/5

  • The denominators are 3 and 5.
  • The smallest number that both 3 and 5 can go into is 15 (this is called the least common denominator).
  • Change 1/3 to a fraction with denominator 15: Multiply numerator and denominator by 5 → 1/3 = 5/15
  • Change 2/5 to a fraction with denominator 15: Multiply numerator and denominator by 3 → 2/5 = 6/15
  • Now compare 5/15 and 6/15: 6/15 is bigger, so 2/5 is bigger than 1/3.

Step 3: Use Visual Aids Like Fraction Bars or Circles 🎨

Sometimes it helps to see the fractions. You can draw fraction bars or circles divided into equal parts, then colour the parts to show each fraction.

  • Draw a rectangle divided into 4 parts and colour 3 parts for 3/4.
  • Draw another rectangle divided into 4 parts and colour 2 parts for 2/4.

Look at the coloured parts to see which is bigger.

Summary Tips for Comparing Fractions ✔️

  • If denominators are the same, compare numerators.
  • If denominators are different, find a common denominator.
  • Use fraction bars or circles to see the fractions.
  • Remember: bigger numerator means bigger fraction when denominators are equal.
  • Practice drawing fractions to understand sizes better.

By using these methods, you can easily compare fractions and understand which one is bigger or smaller! Keep practising with different fractions to get really good at it.

20 Examination-Style Questions on Comparing Fractions for Year 3 – Key Stage 2 Maths 📝

Here are 20 examination-style questions on how to compare fractions suitable for Year 3 students in Key Stage 2. These questions include multiple choice, fill-in-the-blanks, and ordering fractions from smallest to largest, all focusing on comparing fractions.

Multiple Choice Questions

  1. Which fraction is greater?
    • a) 1/4
    • b) 1/2
  2. Which fraction is smaller?
    • a) 3/5
    • b) 2/5
  3. Choose the bigger fraction:
    • a) 4/7
    • b) 5/7
  4. Which fraction is the smallest?
    • a) 1/3
    • b) 1/6
  5. Pick the biggest fraction:
    • a) 2/8
    • b) 3/8

Fill-in-the-Blanks

  1. Fill in the blank:
    1/3 is _____ than 1/4. (greater/less)
  2. True or False?
    2/6 is the same as 1/3. (Write True or False)
  3. Fill in the blank:
    3/4 is _____ than 2/4. (greater/less)
  4. Complete the sentence:
    5/10 is _____ than 4/10.
  5. Fill in the blank:
    1/5 is _____ than 3/5. (greater/less)

Ordering Fractions from Smallest to Largest

  1. Order these fractions from smallest to largest: 2/6, 1/6, 3/6
  2. Put these fractions in order from smallest to greatest: 3/4, 1/4, 2/4
  3. Arrange the fractions from smallest to largest: 1/8, 3/8, 2/8
  4. Write the fractions in order from smallest to largest: 4/10, 7/10, 1/10
  5. Order these from smallest to largest: 3/5, 1/5, 4/5

True or False Questions

  1. True or False: 3/7 is greater than 2/7.
  2. True or False: 1/2 is smaller than 2/3.
  3. True or False: 5/8 is the same as 10/16.
  4. True or False: 2/3 is less than 3/4.
  5. True or False: 1/9 is larger than 1/5.

These questions will help Year 3 students practise comparing fractions by identifying which fractions are greater or smaller, filling in comparison blanks, and ordering fractions correctly. Practising these will build a strong foundation in comparing fractions at Key Stage 2.

Answers to the Examination-Style Questions on Comparing Fractions ✅

Here are clear and easy-to-understand answers to 20 examination-style questions on comparing fractions for Year 3 students. The focus is on comparing fractions to help you understand which fraction is bigger, smaller, or if they are equal.

1. Which is larger: 1/4 or 1/3?

Answer: 1/3 is larger.
Explanation: When the numerator is the same (1), the fraction with the smaller denominator is bigger because the whole is divided into fewer parts.

2. Compare 2/5 and 3/5.

Answer: 3/5 is larger.
Explanation: When the denominators are the same, the fraction with the bigger numerator is larger.

3. Is 3/4 equal to 6/8?

Answer: Yes, they are equal.
Explanation: 6/8 can be simplified by dividing numerator and denominator by 2 to get 3/4.

4. Which fraction is smaller: 5/6 or 4/7?

Answer: 4/7 is smaller.
Explanation: Convert to decimals or use cross-multiplication to compare: 5×7=35 and 4×6=24, since 24 < 35, 4/7 < 5/6.

5. Arrange these fractions from smallest to largest: 2/3, 1/2, 3/4.

Answer: 1/2, 2/3, 3/4.
Explanation: 1/2 = 0.5, 2/3 ≈ 0.67, 3/4 = 0.75.

6. Is 7/10 bigger than 3/5?

Answer: Yes, 7/10 is bigger.
Explanation: 3/5 = 6/10, and 7/10 > 6/10.

7. Which is larger: 1/6 or 1/8?

Answer: 1/6 is larger.
Explanation: Smaller denominator means bigger fraction when numerators are equal.

8. Compare 3/10 and 2/5.

Answer: 2/5 is larger.
Explanation: 2/5 = 4/10 and 4/10 > 3/10.

9. Are 4/8 and 1/2 the same?

Answer: Yes, they are the same.
Explanation: 4/8 simplifies to 1/2.

10. Which fraction is bigger: 5/12 or 7/18?

Answer: 5/12 is bigger.
Explanation: Cross multiply: 5×18=90 and 7×12=84, since 90 > 84, 5/12 is bigger.

11. Is 9/10 greater than 8/9?

Answer: No, 8/9 is greater.
Explanation: 9×9=81 and 8×10=80, 81 > 80 means 8/9 > 9/10.

12. Put these in order: 1/3, 2/6, 3/9.

Answer: All are equal.
Explanation: Each simplifies to 1/3.

13. Which is smaller: 7/8 or 3/4?

Answer: 3/4 is smaller.
Explanation: 7/8 = 0.875 and 3/4 = 0.75.

14. Compare 4/5 and 2/3.

Answer: 4/5 is bigger.
Explanation: Cross multiply: 4×3=12, 2×5=10, 12 > 10.

15. Is 5/9 less than 1/2?

Answer: No, 5/9 is greater.
Explanation: 1/2 = 4.5/9, so 5/9 > 4.5/9.

16. Which fraction is larger: 8/12 or 6/9?

Answer: They are equal.
Explanation: 8/12 simplifies to 2/3 and 6/9 also simplifies to 2/3.

17. Compare 3/5 and 2/3.

Answer: 2/3 is bigger.
Explanation: Cross multiply: 3×3=9, 2×5=10, 10 > 9.

18. Is 1/7 smaller than 1/5?

Answer: Yes, 1/7 is smaller.
Explanation: Smaller denominator means bigger fraction when numerator is the same, so 1/7 < 1/5.

19. Which fraction is bigger: 5/7 or 4/6?

Answer: 5/7 is bigger.
Explanation: Cross multiply: 5×6=30, 4×7=28, 30 > 28.

20. Arrange these fractions from largest to smallest: 3/8, 2/5, 1/2.

Answer: 1/2, 2/5, 3/8.
Explanation: 1/2=0.5, 2/5=0.4, 3/8=0.375.

Study Tips for Comparing Fractions 📚

  • Remember: When the numerator is the same, the fraction with the smaller denominator is bigger.
  • When denominators are the same, the fraction with the bigger numerator is bigger.
  • Use cross multiplication to compare fractions with different denominators.
  • Simplify fractions to see if they are equal.

Keep practising and try explaining these steps to someone else—it really helps you understand better!

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