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Fraction

3.1 Fraction
 
 
Types of Fractions
Proper Fraction Improper Fractions and Mixed Numbers
  • Based on the diagram above, 3 out of 4 circles are shaded. 3 out of 4 is three over four.
  • Three over four is written as \(\dfrac{3}{4}\).
  • \(\dfrac{3}{4}=\dfrac{\text{numerator}}{\text{denominator}}\)

  • \(\dfrac{3}{4}\) is a proper fraction.

  • The numerator is smaller than the denominator.
  • There is one and three over four of the shaded area from the diagram above. 
  • One and three over four is written as \(1\dfrac{3}{4}\).
 
Equivalent Fractions
 
  • Equivalent fractions is two different fractions that have equal value.
     
  • For example: 
    \(\dfrac{1}{2}\) is equivalent to \(\dfrac{2}{4}\).

    \(\dfrac{1\times2}{2\times2}=\dfrac{2}{4}\)
 
Fractions in the Simplest Form
 
  • \(\dfrac{3}{9}\) has the same value as \(\dfrac{1}{3}\).
     
  • \(3\) and \(9\) can be divided by \(3\).

    \(\dfrac{3\div3}{9\div3}=\dfrac{1}{3}\)

 

  • So,  \(\dfrac{1}{3}\) the simplest form of  \(\dfrac{3}{9}\).
     
 
Addition of Fractions
 
Tips :
If the denominator is the same, just add the numenator.
 
Example :
\(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{5}\)
 
 
Substraction of Fractions
 
Tips :
If the denominator is the same, just substract the numenator.
 

Example :
\(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{8}\)

Simplify \(\dfrac{4}{8}\) , 
\(\dfrac{4\div2}{8\div2}=\dfrac{1}{2}\)

So, \(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{8}=\dfrac{1}{2}\)
 
Common Mistakes
 
  1. Incorrect equivalent fractions :
    (❌ wrong) (✅ correct)
    \(\dfrac{1}{2}=\dfrac{1}{4}\) \(\dfrac{1}{2}=\dfrac{2}{4}\)
       
  2. Wrong addition of fractions (same denominator) :
    (❌ wrong) (✅ correct)
    \(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{10}\) \(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{5}\)
       
  3. Wrong subtraction of fractions
    (❌ wrong) (✅ correct)
    \(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{16}\) \(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{8}=\dfrac{1}{2}\)
       
  4. Incorrect mixed number conversion
    (❌ wrong) (✅ correct)
    \(1\dfrac{3}{4}=\dfrac{4}{4}\) \(1\dfrac{3}{4}=\dfrac{7}{4}\)
       
 
Summary
Mixed Number Whole Number Proper Fraction

\(1\dfrac{3}{4}\)
 
\(1\)
 
\(\dfrac{3}{4}\)
 
 
🧪 Mini Quiz: Fraction
✅ 5 MCQ questions
 
⭐ Score at the end
 
⏱️ 2–3 minutes
Note: Interactive on website only. Print view shows intro only.
Question 1 of 5
 
 
 
 
 
Answer Review
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.

Fraction

3.1 Fraction
 
 
Types of Fractions
Proper Fraction Improper Fractions and Mixed Numbers
  • Based on the diagram above, 3 out of 4 circles are shaded. 3 out of 4 is three over four.
  • Three over four is written as \(\dfrac{3}{4}\).
  • \(\dfrac{3}{4}=\dfrac{\text{numerator}}{\text{denominator}}\)

  • \(\dfrac{3}{4}\) is a proper fraction.

  • The numerator is smaller than the denominator.
  • There is one and three over four of the shaded area from the diagram above. 
  • One and three over four is written as \(1\dfrac{3}{4}\).
 
Equivalent Fractions
 
  • Equivalent fractions is two different fractions that have equal value.
     
  • For example: 
    \(\dfrac{1}{2}\) is equivalent to \(\dfrac{2}{4}\).

    \(\dfrac{1\times2}{2\times2}=\dfrac{2}{4}\)
 
Fractions in the Simplest Form
 
  • \(\dfrac{3}{9}\) has the same value as \(\dfrac{1}{3}\).
     
  • \(3\) and \(9\) can be divided by \(3\).

    \(\dfrac{3\div3}{9\div3}=\dfrac{1}{3}\)

 

  • So,  \(\dfrac{1}{3}\) the simplest form of  \(\dfrac{3}{9}\).
     
 
Addition of Fractions
 
Tips :
If the denominator is the same, just add the numenator.
 
Example :
\(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{5}\)
 
 
Substraction of Fractions
 
Tips :
If the denominator is the same, just substract the numenator.
 

Example :
\(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{8}\)

Simplify \(\dfrac{4}{8}\) , 
\(\dfrac{4\div2}{8\div2}=\dfrac{1}{2}\)

So, \(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{8}=\dfrac{1}{2}\)
 
Common Mistakes
 
  1. Incorrect equivalent fractions :
    (❌ wrong) (✅ correct)
    \(\dfrac{1}{2}=\dfrac{1}{4}\) \(\dfrac{1}{2}=\dfrac{2}{4}\)
       
  2. Wrong addition of fractions (same denominator) :
    (❌ wrong) (✅ correct)
    \(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{10}\) \(\dfrac{1}{5}+\dfrac{2}{5}=\dfrac{3}{5}\)
       
  3. Wrong subtraction of fractions
    (❌ wrong) (✅ correct)
    \(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{16}\) \(\dfrac{7}{8}-\dfrac{3}{8}=\dfrac{4}{8}=\dfrac{1}{2}\)
       
  4. Incorrect mixed number conversion
    (❌ wrong) (✅ correct)
    \(1\dfrac{3}{4}=\dfrac{4}{4}\) \(1\dfrac{3}{4}=\dfrac{7}{4}\)
       
 
Summary
Mixed Number Whole Number Proper Fraction

\(1\dfrac{3}{4}\)
 
\(1\)
 
\(\dfrac{3}{4}\)
 
 
🧪 Mini Quiz: Fraction
✅ 5 MCQ questions
 
⭐ Score at the end
 
⏱️ 2–3 minutes
Note: Interactive on website only. Print view shows intro only.
Question 1 of 5
 
 
 
 
 
Answer Review
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of Pandai.
Chapter : Fractions, Decimals and Percentages
Topic : Fractions
Year 3 Mathematics
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