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Basic 4 · Mathematics · Fractions

Comparing and Ordering Fractions with Like Denominators

In this topic you will compare and order fractions that have the same denominator.

By the end of these notes you should be able to:

  • Compare fractions with the same denominator
  • Order fractions in ascending and descending order
  • Use < and > with fractions

What you already know

  • Equivalent and improper fractions

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

Strand
Number
Sub-strand
Fractions
Indicator
B4.1.3.2.1 – Compare and order fractions with like denominators

Introduction

Three friends shared pizzas of the same size cut into 8 slices. Kweku ate 5/8, Afua ate 3/8 and Yaw ate 7/8. Who ate the most?

1. Same Denominator Rule

When denominators are the same, the parts are the same size. The fraction with the bigger numerator is bigger.

7/8 > 5/8 > 3/8. Yaw ate the most.

Three bars cut into eighths showing 3/8, 5/8 and 7/8 shaded
Figure 1: Comparing eighths Draw bars to compare 2/5 and 4/5.Illustration: Sirbus

2. Ordering

Example

Arrange 4/9, 1/9, 8/9, 6/9 in ascending order.

  1. Same denominator: compare numerators 4, 1, 8, 6.
  2. Order numerators: 1, 4, 6, 8.

Answer: 1/9, 4/9, 6/9, 8/9

3. Including Improper Fractions

The same rule works: 9/5 > 7/5 > 3/5.

Compare with symbols
FractionsComparison
2/7 and 5/72/7 < 5/7
9/10 and 3/109/10 > 3/10
6/4 and 6/46/4 = 6/4

Remember: This rule only works when the denominators are the same.

New words

like denominators
The same bottom number.
compare
To decide which is greater.
ascending
From smallest to largest.
descending
From largest to smallest.
numerator
The top number of a fraction.
greater
Bigger.

Summary

  • With like denominators, compare the numerators.
  • The bigger numerator gives the bigger fraction.
  • Order fractions by ordering their numerators.
  • The rule also works for improper fractions.

Class activity: Fraction Line-Up

  1. Each member gets a fraction card with denominator 10.
  2. Line up in ascending order.
  3. Then line up in descending order.

You need: Fraction strips cut from old cartons, Bottle tops, Exercise books

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. Which is greater?

    • A. 5/6
    • B. 1/6
    • C. 2/6
    • D. 3/6
    Show answer
    Answer: 5/65 is the largest numerator.

  2. 2. Which is in ascending order?

    • A. 1/5, 3/5, 4/5
    • B. 4/5, 3/5, 1/5
    • C. 3/5, 1/5, 4/5
    • D. 4/5, 1/5, 3/5
    Show answer
    Answer: 1/5, 3/5, 4/5Smallest to largest.

  3. 3. Which symbol makes this true? 11/12 ___ 7/12

    • A. >
    • B. <
    • C. =
    • D. +
    Show answer
    Answer: >11 > 7.

  4. 4. 3/8 < 5/8

    • A. True
    • B. False
    Show answer
    Answer: True3 < 5.

  5. 5. 7/4 < 5/4

    • A. True
    • B. False
    Show answer
    Answer: False7/4 is greater.

  6. 6. Arrange in descending order: 2/9, 7/9, 5/9 → 7/9, ______, 2/9

    Show answer
    Answer: 5/97 > 5 > 2.

  7. 7. Order from smallest to largest: 6/11, 2/11, 9/11, 4/11.

    Show answer
    Answer: 2/11, 4/11, 6/11, 9/11Order the numerators.

  8. 8. Esi read 3/10 of a book on Monday and 5/10 on Tuesday. What fraction did she read in the two days, and how much is left?

    Show answer
    Answer: 8/10 read; 2/10 left3/10 + 5/10 = 8/10; 10/10 − 8/10 = 2/10.

Homework

  1. Cut a paper strip into 8 equal parts. Shade 3/8, 5/8 and 6/8 on separate strips and order them.