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Basic 4 · Mathematics · Fractions

Equivalent Fractions and the Lowest Common Denominator

In this topic you will find equivalent fractions and the lowest common denominator.

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

  • Explain equivalent fractions
  • Make equivalent fractions by multiplying or dividing
  • Find the lowest common denominator of two fractions

What you already know

  • Comparing fractions (Basic 3)

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
B4.1.3.1.1 – Recognise and name equivalent fractions and use a number line to determine the lowest common denominator (LCD)

Introduction

Ama ate ½ of a loaf. Kojo ate 2/4 of the same size loaf. Who ate more? They ate the same amount! ½ and 2/4 are equivalent fractions.

1. Equivalent Fractions

Equivalent fractions: Fractions that look different but have the same value.

½ = 2/4 = 3/6 = 4/8 = 5/10

Fraction strips showing ½, 2/4, 3/6 and 4/8 shaded to the same length
Figure 1: Equivalent fractions Draw strips to show ⅓ = 2/6.Illustration: Sirbus

2. Making Equivalent Fractions

Multiply (or divide) the numerator and the denominator by the same number.

Example

Find two fractions equivalent to ⅔.

  1. ⅔ × 2/2 = 4/6
  2. ⅔ × 3/3 = 6/9

Answer: ⅔ = 4/6 = 6/9

3. Lowest Common Denominator (LCD)

Lowest common denominator: The LCM of the denominators.

Example

Find the LCD of ½ and ⅓.

  1. Denominators: 2 and 3.
  2. LCM of 2 and 3 = 6.
  3. ½ = 3/6 and ⅓ = 2/6.

Answer: The LCD is 6.

Common mistake: Multiplying only the denominator changes the value. Always do the same to the top and bottom.

New words

equivalent
Having the same value.
numerator
The top number of a fraction.
denominator
The bottom number of a fraction.
LCD
Lowest common denominator.
simplify
To divide top and bottom by the same number.
value
How much something is worth.

Summary

  • Equivalent fractions have the same value.
  • Multiply or divide top and bottom by the same number.
  • The LCD is the LCM of the denominators.
  • ½ = 3/6 and ⅓ = 2/6, so the LCD of ½ and ⅓ is 6.

Class activity: Fraction Wall

  1. Use fraction strips cut from old cartons to build a fraction wall.
  2. Find all the fractions equal to ½.
  3. Find the LCD of ¼ and ⅙ using the wall.

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 fraction is equivalent to ½?

    • A. 3/6
    • B. 2/3
    • C. 1/3
    • D. 3/4
    Show answer
    Answer: 3/61 × 3 over 2 × 3.

  2. 2. ⅗ = ?/10

    • A. 6
    • B. 5
    • C. 3
    • D. 8
    Show answer
    Answer: 6Multiply top and bottom by 2.

  3. 3. What is the LCD of ¼ and ⅙?

    • A. 12
    • B. 24
    • C. 10
    • D. 4
    Show answer
    Answer: 12LCM of 4 and 6 is 12.

  4. 4. 2/4 and 1/2 are equivalent.

    • A. True
    • B. False
    Show answer
    Answer: TrueBoth are a half.

  5. 5. ⅓ = 2/3

    • A. True
    • B. False
    Show answer
    Answer: FalseOnly the numerator changed.

  6. 6. ¾ = ______/8

    Show answer
    Answer: 6Multiply top and bottom by 2.

  7. 7. Write three fractions equivalent to ¼.

    Show answer
    Answer: E.g. 2/8, 3/12, 4/16Multiply top and bottom by the same number.

  8. 8. Find the LCD of ⅔ and ¾ and rewrite both fractions.

    Show answer
    Answer: LCD 12; ⅔ = 8/12 and ¾ = 9/12LCM of 3 and 4 is 12.

Homework

  1. Fold paper strips to show that ½ = 2/4 = 4/8.