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How to add mixed fractions with whole number?

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  • Last Updated : 30 Jun, 2022

Before going to know how we can add mixed fractions with whole numbers we have to know what is fractions and whole numbers. The number system is the main concept behind whole numbers and mixed fractions. If we have clarity regarding the number system we can easily solve the concept of adding mixed fractions with whole numbers. The number system has concepts like integers, natural numbers, whole numbers, and real numbers.

A number system is a combination of natural numbers, whole numbers, integers, and real numbers.

Natural numbers: Natural numbers are the numbers that can able to count numbers. We can also say that numbers start from 1 to infinity without 0 included. Examples,

Natural numbers={1,2,3,4,5,6,7,8,9,10,11,12,13….}

Whole numbers: Whole numbers are the numbers in the union of natural numbers and Zero(0). The whole number is one type of number system having zero included in natural numbers. Examples,

Whole numbers= {0,1,2,3,4,5,6,7,8,9,10,11,12,13.15,16,17,18….}

Integers: Integer system is the number system having negative numbers and positive natural numbers included with zero(0). Integers are numbers having a union of negative integers and whole numbers. Examples,

Integers={…-2,-1,0,1,2…..}

Rational numbers: Rational numbers are the number that is in the form of r/a only where a should not equal zero. Rational numbers are also called terminating numbers.

Examples, 

Rational numbers: 0/1, 1/1, 2/1, 3/1,1.9999 etc.

Irrational numbers: Irrational numbers are the numbers that are not represented in the form of r/b where b must not equal zero and also they are called non-terminating numbers.

Examples,

Irrational numbers: √2,√3, 0.12356… 

Real numbers: Real numbers are part of a number system having a fusion of both rational and irrational numbers.

Fractions: Fractions are based on the numerator and denominator. Fractions are like rational numbers represented as part of whole numbers. Suppose consider a rectangle is divided into four parts so that each part is divided into 1/3 also represents 1:3, where 1/3 or 1:3 is a fraction part of a rectangle.

Examples of fractions: 

7/8 where 7 is the numerator and 2 is the denominator.

1/4 where 1 is the numerator and 4 is the denominator.

9/3 where 9 is the numerator and 3 is the denominator.

Fractions are of three types. They are,

  1. Proper fraction: Proper fraction is one of the types of the fraction. A proper fraction is explained as a numerator that should be less than the denominator.
    Examples of proper fractions: 1/2, 3/5, 6/8 ….
  2. Improper fraction: Improper fraction is one of the types of fraction. It is defined as a numerator that should be greater than the denominator.
    Examples of improper fractions: 8/6, 9/7, 3/2, and so on.
  3. Mixed fraction: The mixed fraction is the union of fraction part( contains both proper and improper )and natural numbers.
    Examples of mixed fractions are shown below:
     1\frac{2}{3} here, 1 is a whole number, 2 is a numerator and 3 is a denominator.

How to convert mixed fractions into p/q form?

Step 1: First multiply the whole number with the denominator.

Step 2: Add the numerator and result of multiplication of the whole number with denominator.

Step 3: Result from Step2 should be placed in the numerator part where the denominator is the same as in the mixed fraction. Hence we got the mixed fraction into proper p/q form.

How to convert improper fractions to mixed fractions?

Let’s take 8/6 as an improper fraction

Step 1: First, divide the numerator with denominator 8//6 = 1 as quotient and remainder as 2.

Step 2: Remainder 2  which divides by 6.

Step 3: Remainder should divide with denominator. If there is a cancellation that occurs cancel with the appropriate factor.

Step 4: When we rationalize 2/6 we get 1/3. Combining Step 1 answer and Step 4 we get 1\frac{1}{3}

How to add a whole number with a mixed fraction?

  1. First we have to convert mixed fraction to p/q form.
  2. Next convert that p/q form into decimal form.
  3. Then the addition of a whole number with a decimal form of p/q.

Sample Problems

Problem 1: Solve the question below which is in the form of having whole numbers and mixed fraction addition?

                                                       1010\frac{2}{3}

Solution:

To solve this problem we have to solve mixed fractions first.

Solving mixed fraction: 10\frac{2}{3} is converted into p/q  form as follows.

Step 1: Multiply whole number 10  with denominator 3 as shown in diagram = 10×3=30.

Step 2: Adding numerator 2 with result in Step1 = 2+30=32.

Step 3: In p/q form numerator p=32 and denominator q=3. Therefore 32/3=10.7 is the proper p/q form.

After converting the mixed fraction part to the proper p/q form. Add the whole number with a mixed fraction.

Add 10 with 32/3=10.7 we get 20.7 as a result of the addition.

Therefore by solving the above problem we will get the result of 20.7 which is also represented in p/q=207/10.

Problem 2: Solve the question below which is in the form of having whole numbers and mixed fraction addition?

                                                     20+1\frac{2}{3}

Solution:

To solve this problem we have to solve mixed fractions first.

Solving mixed fraction:1\frac{2}{3} is converted into p/q  form as follows.

Step 1: Multiply whole number 1 with denominator 3 as shown in diagram = 1×3=3.

Step 2: Adding numerator 2 with result in Step1 = 2+3=5.

Step 3: In P/q form numerator p=5and denominator q=3. Therefore 5/3=1.7 is the proper p/q form.

After converting the mixed fraction part to the proper p/q form. Add the whole number with a mixed fraction.

Add 20 with 5/3=1.7 we get 21.7 as a result of the addition.

Therefore by solving the above problem we will get the result of 21.7 which is also denoted as p/q form 217/10.

Problem 3: Solve the question below which is in the form of having whole numbers and mixed fraction addition?

                                                  13+2\frac{1}{3}                                                     

Solution:

To solve this problem we have to solve mixed fractions first.

Solving mixed fraction:2\frac{1}{3}  is converted into p/q  form as follows.

Step 1: Multiply whole number 2 with denominator 3 as shown in diagram = 2×3=6.

Step 2: Adding numerator 1 with result in Step1 = 1+6=7.

Step 3: In p/q form numerator p=7and denominator q=3. Therefore 7/3=2.33 is the proper p/q form.

After converting the mixed fraction part to the proper p/q form. Add the whole number with a mixed fraction.

Add 13 with 7/3=2.33 we get 15.33as a result of the addition.

Therefore by solving the above problem we will get the result of 15.33 which is also denoted as p/q form 153.3/10.

Problem 4: Solve the question below which is in the form of having whole numbers and mixed fraction addition?

                                                16+3\frac{1}{3}

Solution:

To solve this problem we have to solve mixed fractions first.

Solving mixed fraction: 3\frac{1}{3} is converted into p/q  form as follows.

Step 1: Multiply whole number 3 with denominator 3 as shown in diagram = 3×3=9.

Step 2: Adding numerator 1 with result in Step1 = 1+9=10.

Step 3: In p/q form numerator p=10 and denominator q=3. Therefore 10/3=3.33 is the proper p/q form.

After converting the mixed fraction part to the proper p/q form. Add the whole number with a mixed fraction.

Add 16 with 10/3=3.33 we get 19.33as a result of the addition.

Therefore by solving the above problem we will get the result of 19.33 which is also denoted as p/q form 193.3/10.


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