Improper Fractions

An improper fraction is a fraction in which the numerator is greater than or equal to the denominator.

Real-Life Example: If you have 10 slices from a pie that was originally cut into 8 slices, you have more than one whole pie. The fraction is 10/8.

This is an improper fraction because 10 (numerator) is greater than 8 (denominator), meaning you have more than one full pie.

On the basis of the numerator and denominator, fractions are of two types. i.e.,

1. A proper fraction is a fraction in which the numerator is less than the denominator, so its value is always less than 1.

• It represents a part of a whole.
• Examples of proper fractions are \frac{7}{13}, \frac{4}{5}, \frac{1}{2}, and \frac{2}{7}.

2. An improper fraction is a fraction in which the numerator is greater than or equal to the denominator, so its value is equal to or greater than 1.

• It can represent one whole or more.
• Examples of improper fractions are \frac{15}{13}, \frac{14}{5}, \frac{11}{2}, and \frac{12}{7}.

Fraction Conversion

Step to Convert Improper Fractions to Mixed Fractions

1. Divide the numerator by the denominator.
2. Write the quotient as the whole number.
3. Write the remainder as the new numerator.
4. Keep the original denominator

\text{Mixed Form} =\text{Quotient}\left(\frac{\text{Remainder}}{\text{Denominator}}\right)

Example: Convert \frac{17}{4} into a mixed fraction.

We have \frac{17}{4}
Dividing the fraction we get,
17 = 4 × 4 + 1

• Quotient = 4
• Remainder = 1

In Mixed Fraction Form,
4\frac{1}{4}
This is the required mixed fraction form.

Step to Convert Mixed Fraction to Improper Fraction

1. Multiply the whole number by the denominator.
2. Add the numerator to the product.
3. Write the result as the new numerator and keep the same denominator.

Example: Change 11\frac{3}{5} into an improper fraction.

Given, 11\frac{3}{5}
⇒ Multiply the whole number by the denominator.
11 ✕ 5 = 55
⇒ Add the numerator:
55 + 3
⇒\frac{58}{5}

Solved Examples

Example 1. Identify the improper fractions:

Solution: 

\frac{11}{5},\quad \frac{27}{15},\quad \frac{15}{7},\quad \frac{61}{6}  are improper fractions as the value of the numerator is greater than the value of the denominator for these fractions.

Example 2. Write \frac{22}{8} as mixed fraction.

Solution: 

We have \frac{22}{8}
Dividing the fraction we get,
22 = 2 × 8 + 6

• Quotient = 2
• Remainder = 6

In Mixed Fraction Form,
2\frac{6}{8}

Example 3. Write 1\frac{5}{6} as an improper fraction.

Solution: 

Given : 1\frac{5}{6}

⇒ Multiply the whole number by the denominator.
6 ✕ 1 = 6
⇒ Add the numerator:
6 + 5
⇒\frac{11}{6}

Practice Questions

1. Convert \frac{9}{4} into a mixed number
2. Convert \frac{5}{2} into a mixed number
3. Convert 4\frac{2}{7} into an improper fraction.
4. Convert \frac{47}{9} into a mixed number.
5. A cake is cut into 4 equal pieces. Riya has 13 pieces of that size. Write this as an improper fraction and a mixed number.

Solution :

1. 2\frac{1}{4}
2. 2\frac{1}{2}
3. \frac{30}{7}
4. 5\frac{2}{9}
5. Improper fraction: \frac{13}{4} Mixed number: 3\frac{1}{4}