Quick Notes

Quick Notes

Mathematics Chapter 3: Fractions, Decimals and Percentages
3.1 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