Improper Fractions – Explanation, Steps,& Examples

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.  

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  

E.g.: 

  

Example: Rename  as a mixed number  

Sol:  = 5 fourths  

= 4 fourth + 1 fourth  

=  

=  

= 

Example: Rename as a mixed number  

Sol:   

  

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. 

Steps:  

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

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?  

Sol:  

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:   

(b)  

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?  

  

Find the total number of inches of snowfall recorded.  

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

Exercise:

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

7. Two friends want to share 3 apples so that they each get same amount. How much would each friend get? 
8. 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.