Question

What are mixed numbers?

Answer 1

Hint: Mixed numbers are partly whole numbers and partly fractions. In this question, we are going to see what mixed numbers are, their properties and how to convert fractions into mixed numbers. There are three types of fractions: mixed fractions, improper fractions and proper fractions. We must know the definition of all these to solve the question.

Complete step by step solution:
A mixed number is a combination of a whole number and a fraction represented together. It lies between two whole numbers.
For example: $ 1\dfrac{1}{2} $ lies between two whole numbers $ 1 $ and $ 2 $ .
Similarly $ 3\dfrac{5}{6} $ lies between two whole numbers 3 and 4.
Some other examples of mixed numbers are $ 2\dfrac{1}{2},5\dfrac{1}{3},6\dfrac{1}{7} $ , etc.
Parts of a mixed number: A mixed number is made up of three parts, a whole number, numerator and denominator which forms a fraction. These three together make a mixed number. The whole number part tells us the number of whole entities represented by the mixed fraction. The fractional part consisting of numerator and denominator represents a part of the whole.
Some of the properties of Mixed number:
 $ \Rightarrow $ It is half the whole number.
 $ \Rightarrow $ It is a half fractional number.
Conversion of fractions to mixed number includes multiple steps:
STEP $ 1 $ : Divide the numerator by denominator.
STEP $ 2 $ : Write the obtained quotient as the whole number.
STEP $ 3 $ : Remainder will be written as numerator.
STEP $ 4 $ : Divisor will be written as denominator.
For example: Let us convert $ \dfrac{8}{5} $ into a mixed fraction.
Step 1: Divide 8 by 5.
We know that we can write the number $ 8 $ in the terms of multiples of five as:
 $ 8 = 5 \times 1 + 3 $
Step 2: Here, the quotient is $ 1 $ so, the whole number will be $ 1 $ .
Step 3: The remainder is $ 3 $ so $ 3 $ will be written in numerator.
Step 4: The divisor is $ 5 $ so $ 5 $ will be written in denominator.
Hence, our mixed number is $ 1\dfrac{3}{5} $ .
Addition of mixed numbers:
Suppose we are given two mixed numbers and, then to obtain their addition add the whole numbers separately and fractions separately.
Addition of whole numbers is carried out as: $ 1 + 3 = 4 $
Addition of fractions is carried out as: $ \dfrac{1}{5} + \dfrac{3}{5} = \dfrac{4}{5} $ .
Therefore, we add the mixed fractions as: $ 1\dfrac{3}{5} + 2\dfrac{1}{5} = \left( {1 + 2} \right) + \left( {\dfrac{3}{5} + \dfrac{1}{5}} \right) $ .


Note: Reverse Conversion of mixed number to fraction can be done through these easy steps:
Step 1: Multiply the denominator with the whole number.
Step 2: Add the numerator to the obtained result.
Step 3: The result obtained will be written in numerator.
Step 4: The denominator of the mixed number will remain the denominator for the fraction.
Example: $ 1\dfrac{3}{5} = \dfrac{{1 \times 5 + 3}}{5} = \dfrac{{5 + 3}}{5} = \dfrac{8}{5} $ .
We should know the conversion of different types of fractions as it helps in such simple problems and complex word problems also. One should take care while carrying out the calculative steps.