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Improper Fractions – Explanation, Steps,& Examples

Grade 4
Sep 27, 2022

Key Concepts

  • Renaming improper fractions and mixed numbers.
  • Fraction of a set.
  • Line plots with fractions.
  • Mixed numbers.

Renaming Improper Fractions as Mixed numbers 

Use multiplication and division to rename improper fractions as mixed numbers 

Fraction Bar: The line that separates the numerator and the denominator in a fraction.  

Improper Fractions

Division Rule: Divide the numerator by the denominator.  

E.g.: 4 ÷ 2 = 2  

This is the division rule.  


Multiplication Rule: Multiplication is an operation used in math to multiply different types of numbers.  

Multiplication formula is:   

Multiplier × Multiplicand = Product  





Example: Rename  as a mixed number  

Sol:= 5 fourths  

= 4 fourth + 1 fourth  




Example: Rename as a mixed number  




Renaming Whole Numbers When Adding and Subtracting Fractions 

6.6.1 Add fractions to get a mixed number 

Example: Add and  to get a mixed number.  


6.6.2 Subtract fractions from whole numbers. 


  1. Convert the whole number to a fraction.  
  2. Convert to fractions of like denominators.  
Subtract fractions from whole numbers. 

6.7 Fraction of a Set 

Find a fractional part of a number: 

The fractional part of a set is a fraction of the set.  

EG: What is of 72?  


Find a fractional part of a number: 

So, of 72 is 24  

6.7.2 Multiply a fraction and a whole number. 

We know that multiplication is repeated addition. So, multiplying a fraction by a whole number is equivalent to adding the fraction for the whole number of times.  

Example: (a)   

Sol: can be shown as:   


Sol: 5×2 / 3=10 / 3

Real World Problems: Fractions 

Example: One-half of the students in a school are girls. of these girls are studying in lower classes. What fraction of girls are studying in lower classes?  

Sol: Fraction of girls studying in school =  

Fraction of girls studying in lower classes = of  

=3 / 5× 1 / 2

=3×1 / 5×1 / 2


 of girls are studying in lower classes.  

Line Plots with Fractions of a unit 

Line Plots: A line plot is a way to display data along a number line. Line plots are also called dot plots.  

Example: Marcia class measured the snowfall for 5 days. The line plot shows the height of the snowfall they recorded. How many inches of snow were recorded? What amount of snowfall occurred most often?  

Line Plots with Fractions of a unit 


Find the total number of inches of snowfall recorded.  

Sol: 1 / 4+2 / 4+2 / 4+2 / 4+3 / 4 = 10 / 4  = 224 inches  


  1. Rename 6/5  as a mixed number. 
  2. Add  8/4 to 1/2 get mixed number 
  3. Find    7- 1/2
  4. What is 2/4 of 56? 
  5. Find . 9 x 10/3
  6. Jack measured her dolls and showed the heights using a line plot. What was the most common height? 

Height of Jack’s Dolls

Height of Jack’s Dolls
  1. Two friends want to share 3 apples so that they each get same amount. How much would each friend get? 
  2. Two children are sharing 1/2 of a sandwich. How much will each child get? 

What have we learnt:

  • To change improper fractions to mixed numbers.
  • To change mixed numbers to improper fractions.
  • Representing a fraction as part of a whole or part of a set.
  • To show fractions with line plots.


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