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Comparing Rational Numbers

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Comparing Rational Numbers worksheet preview
Comparing Rational Numbers

Comparing Rational Numbers

Comparing fractions and decimals illustration

📊 Part 1: Comparison Symbols

Remember: < means less than, > means greater than, = means equal to

1. Fill in the correct symbol (<, >, or =) between each pair of numbers:

a) 0.6 _____ 0.5

b) ¾ _____ 0.75

c) ½ _____ 0.4

d) 0.3 _____ ⅓

e) ⅖ _____ 0.4

f) 0.8 _____ ¾

2. Circle the largest number in each group:

Group A:

0.6

½

¾

Group B:

0.7

📏 Part 2: Ordering on a Number Line

3. Place these numbers on the number line below in order from smallest to largest:

Numbers to order: 0.25, ½, ¾, 0.9, ⅓

4. Write the numbers from question 3 in ascending order (smallest to largest):

🏃‍♀️ Part 3: Real-World Context - School Sports Day

5. Four students ran different distances during sports day. Order their distances from shortest to longest:

Distances:

• Aroha: 0.75 kilometres

• Ben: ¾ kilometres

• Chloe: ⅔ kilometres

• David: 0.8 kilometres

Order from shortest to longest:

1st (shortest): ________________

2nd: ________________

3rd: ________________

4th (longest): ________________

6. Explain your reasoning for ordering Aroha's and Ben's distances:

🍰 Part 4: Recipe Comparisons

7. A recipe calls for different amounts of ingredients. Check all the ingredients that are MORE than half a cup:

Sugar: ⅗ cup

Flour: 0.4 cups

Butter: ¾ cup

Milk: 0.6 cups

Vanilla: ⅓ cup

8. Match each fraction to its equivalent decimal:
1. ¼
2. ½
3. ¾
4. ⅕
A. 0.5
B. 0.25
C. 0.75
D. 0.2

🧠 Part 5: Challenge Problems

9. Show your working to compare 0.7 and ⅝:

Therefore: 0.7 _____ ⅝

10. Create your own comparison problem using fractions and decimals, then solve it:

My problem: _________ _____ _________

11. Explain in your own words how you know when one rational number is greater than another:

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