Mathematics 3 : Comparing and Ordering Fractions

Mathematics 3 - Grade 3: Comparing and Ordering Fractions

In this lesson, students will learn how to compare and order fractions. They will understand fractions better by using simple examples and visual aids like number lines, fraction bars, and pie charts.

What Are Fractions?
A fraction is a part of a whole, made up of a numerator (top number) and denominator (bottom number). The numerator tells how many parts are being considered, while the denominator tells how many equal parts the whole is divided into.

Comparing Fractions
Students will learn how to compare fractions using these methods:

Same denominator: The fraction with the larger numerator is greater.
Same numerator: The fraction with the smaller denominator is greater.
Visual aids: Number lines and fraction bars help students visualize which fraction is larger or smaller.
Cross-multiplication: Students can multiply the numerator of one fraction by the denominator of the other to compare them.
Ordering Fractions
Once students can compare fractions, they will learn how to order them from least to greatest or greatest to least. This is useful in everyday situations like sharing or measuring.

Examples:
Same denominator: Compare 3/8 and 5/8. Since the denominators are the same, 5/8 is greater because 5 is larger than 3.
Same numerator: Compare 2/7 and 2/5. Since 5 is smaller than 7, 2/5 is greater.
Visual Models
Using fraction strips, circles, or number lines helps students see the size of fractions and compare them more easily.

Activity at the End
After learning about comparing and ordering fractions, students will apply their knowledge through a fun hands-on activity, using number lines and visual models to compare and order a set of fractions.

1. C o m p a r i n g a n d O r d e r i n g F r a c t i o n s

2. Comparing Two Fractions ⸭ Similar fractions are fractions with the same denominator. When comparing similar fractions, the fraction with the greater numerator has the greater value or the fraction with the lesser numerator has the lesser value. 3 4 1 4 > Same denominator, 3 > 1 Hence ¾ > ¼.

3. Comparing Two Fractions ⸭ Dissimilar fractions are fractions with the different denominators. If the fractions have the same numerator, the fraction with the lesser denominator has the greater value. 1 4 1 2 < Same numerator, 4 > 2 Hence ¼ < ½.

4. Comparing Two Fractions ⸭ Dissimilar fractions are fractions with the different denominators. If the fractions have the same numerator, the fraction with the lesser denominator has the greater value. 2 5 2 3 < Same numerator, 2 = 2 Hence 2/5 < 2/3. Example 2:

5. We may compare fractions by using cross multiplication. 1 2 4 8 1 2 4 8 8 8 1 2 4 8 = The fraction that has the greater cross product is greater. The fraction with less cross product is less than the other fraction.

6. We may compare fractions by using cross multiplication. 2 3 3 4 2 3 3 4 8 9 2 3 3 4 < The fraction that has the greater cross product is greater. The fraction with less cross product is less than the other fraction. Example 2:

7. Comparing Two Fractions ⸭ Mixed number is a sum of a whole number and a proper fraction. Compare the whole number parts. If they are the same compare the fraction parts. 1 4 2 4 1 1

8. The whole number parts are the same, so compare the fraction parts. 1 4 2 4 < Hence, 1 1/4 < 1 2/4.

9. Comparing Two Fractions ⸭ Mixed number is a sum of a whole number and a proper fraction. Compare the whole number parts. If they are the same compare the fraction parts. 3 4 3 5 1 1 Example 2:

10. The whole number parts are the same, so compare the fraction parts. 3 4 3 5 > Hence, 1 3/4 > 1 3/5.

11. ORDERING FRACTIONS Fractions can also be arranged in ascending order, that is, from least to greatest, or in descending order, that is, from greatest to least. Look at the examples: Given Descending Order Ascending Order 3 11 7 11 13 11 , , 13 11 7 11 3 11 , , 3 11 7 11 13 11 , ,

12. Simply use the rules in comparing similar fractions. 13 11 13 11 7 11 7 11 3 11 3 11 Descending Order Ascending Order

13. Example: Arrange ¾, 5/6, 7/12 in ascending order and in descending order. Compare two fractions at a time. 3 4 5 6 18 20 5 6 7 12 60 42 3 4 7 12 36 28 Hence, ¾ < 5/6 Hence, 7/12 < 5/6 Hence, 7/12 < ¾ Ascending order: 7/12, ¾, 5/6 Descending order: 5/6, ¾, 7/12

14. ACTIVITY 1

15. Compare. Use >, < or = 7 10 3 10 _____ 2 5 4 5 _____ 3 3 1 10 1 4 _____ 3 8 5 9 _____ 9 13 5 16 _____ 1. 2. 3. 4. 5.

16. Arrange the fractions from least to greatest. 5 11 8 11 2 11 , , 3 14 3 7 3 16 , , 1 4 2 5 3 10 , , _____, _____, _____ _____, _____, _____ _____, _____, _____ 6. 7. 8.

17. Arrange the fractions from greatest to least . 11 18 5 18 13 18 , , 3 8 3 10 3 5 , , _____, _____, _____ _____, _____, _____ 9. 10.

18. ACTIVITY 2

19. Compare. Use >, < or = 4 8 3 6 _____ 1 4 1 3 _____ 3 3 1 7 1 4 _____ 3 6 1 2 _____ 9 12 2 3 _____ 1. 2. 3. 4. 5.

20. Arrange the fractions from least to greatest. 2 6 3 6 1 6 , , 1 4 1 7 1 6 , , 2 6 1 5 2 10 , , _____, _____, _____ _____, _____, _____ _____, _____, _____ 6. 7. 8.

21. Arrange the fractions from greatest to least . 1 8 3 8 2 8 , , 5 10 5 5 5 12 , , _____, _____, _____ _____, _____, _____ 9. 10.