Fractions : Proper, Improper, and Mixed fractions

maths > fractions

Proper, Improper, and Mixed fractions

what you'll learn...

overview

In this, the following are explained.

• proper fraction: smaller than a whole and properly a fraction of a whole

• improper fraction: larger than a whole in fraction form

• mixed fraction: larger than a whole given as mix of a whole number and a fraction

mixing proper and improper

$proper fraction 1$

Consider the given figure. The colored part is the representation of a fraction and the gray part is shown only as a representation of the whole.

The fraction is $\frac{1}{4}$ $1/4$ .

$proper fraction 2$

The fraction represented by the colored part in the given figure is $\frac{2}{4}$ $2/4$

$improper fraction 6/4$

The fraction represented by the colored part in the given figure is $\frac{6}{4}$ $6/4$

The picture represents the fraction $\frac{6}{4}$ $6/4$ . Number of parts in the given fraction: $6$ $6$
Number of parts making a whole: $4$ $4$
The number of parts in the given fraction is greater than the number of parts making a whole.

$improper fraction 6/4$

The picture represents the fraction $\frac{6}{4}$ $6/4$ . The $4$ $4$ parts of the given fraction is rearranged to make a whole and remaining $2$ $2$ parts are shown nearby. So, $\frac{6}{4}$ $6/4$ can be given as $1 \frac{2}{4}$ $1 2/4$ .

naming them

$improper fraction 6/4$

The picture represents three fractions

• Fraction given by green part: $\frac{1}{4}$ $1/4$

• Fraction given by purple parts : $\frac{6}{4}$ $6/4$

• Fraction given by orange parts : $1 \frac{2}{4}$ $1 2/4$

The word "fraction" means "part of a whole".

• In the three given fractions, only $\frac{1}{4}$ $1/4$ is strictly part of whole. The value of the fraction is less than $1$ $1$ , which is properly part of whole. Such fractions are called proper fractions.

• The fraction $\frac{6}{4}$ $6/4$ is greater than $1$ $1$ , and is represented as numerator by denominator. Such fractions are called improper fractions.

• The fraction $1 \frac{2}{4}$ $1 2/4$ is greater than $1$ $1$ , and is represented as a whole number along with a fraction. Such fractions are called mixed fractions.

The word "proper" means: required or correct type. Proper fractions are fractions that are smaller than a whole and properly a fraction of a whole.

The word "improper" means: not of correct type. Improper fractions are fractions that are larger than a whole.

The word "mixed" means: consisting of different quantities or elements. Mixed fractions are fraction that have an integer count of whole and a proper fraction.

Proper Fraction: number of parts in the fraction (numerator) is less than the number of parts making a whole(denominator) given as numerator divided by denominator. Proper fractions are less than 1.

Improper Fraction: number of parts in the fraction (numerator) is greater than the number of parts making a whole(denominator) given as numerator by denominator. Improper fractions are greater than 1 given as numerator by denominator.

Mixed Fraction: Specified as number of wholes with a fraction. Mixed fractions are greater than 1 and given as whole number followed by a numerator by denominator.

examples

What type of fraction is $\frac{3}{7}$ $3/7$ ?
The answer is 'proper fraction'.

What type of fraction is $\frac{17}{7}$ $17/7$ ?
The answer is 'improper fraction'.

What type of fraction is $2 \frac{3}{7}$ $2 3/7$ ?
The answer is 'mixed fraction'.

What type of fraction is $7 \frac{30}{35}$ $7 (30)/(35)$ ?
The answer is 'mixed fraction'.

summary

» Proper Fraction
    → fraction is smaller than the whole
    → eg: $\frac{2}{4}$ $2/4$
» Improper Fraction
    → fraction is larger than the whole
    → eg: $\frac{6}{4}$ $6/4$
» Mixed Fraction
    → a whole number and a fraction given together
    → eg: $1 \frac{2}{4}$ $1 2/4$

Outline

The outline of material to learn "fractions" is as follows.

• click here for detailed outline of Fractions

→ Part of whole

→ Dividing a group

→ Fractions as Directed numbers

→ Like and Unlike Fractions

→ Proper and Improper Fractions

→ Equivalent & Simplest form

→ Converting unlike and like Fractions

→ Simplest form of a Fraction

→ Comparing Fractions

→ Addition & Subtraction

→ Multiplication

→ Reciprocal

→ Division

→ Numerical Expressions with Fractions

→ PEMA / BOMA