How to add mixed fractions with whole number?
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.
In this article we will learn how the mixed fractions are added with whole numbers along with definitions of various types of numbers in a number system.
Table of Content
- What is a Number System?
- How to add Whole Number with a Mixed Fraction?
- Sample Problems
What is a Number System?
A number system is a combination of natural numbers, whole numbers, integers, and real numbers.
Types of Numbers
The different types of numbers in a number system are:
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: Integers are the set of numbers 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.
How to add Whole Number with a Mixed Fraction?
- First we have to convert mixed fraction to p/q form.
- Convert the whole number to a fraction with the same denominator as the fraction part of the mixed fraction.
- Add the fractions together.
The detailed description of each step is given below:
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.
Let us consider an example for better understanding:
Example: Solve [Tex] 2 + 1\frac{3}{4} [/Tex]
Solution:
First, Convert 2 to a fraction with the same denominator as [Tex]1\frac{3}{4}[/Tex], which is 4. So, 2 = 8/4.
Second, Convert [Tex]1\frac{3}{4}[/Tex] to fraction
- Multiply whole number 1 with denominator 4 = 1 x 4 = 4.
- Adding numerator 3 with result in Step1 = 4 + 3 = 7.
- Hence [Tex]1\frac{3}{4}[/Tex] in p/q form is 7/4.
Now add 8/4 to 7/4.
[Tex]\frac{8}{4} + \frac{7}{4} = \frac{15}{4}[/Tex]
Also Check
Sample Problems
Problem 1: Solve the question below which is in the form of having whole numbers and mixed fraction addition?
10 + [Tex]10\frac{2}{3} [/Tex]
Solution:
To solve this problem we have to solve mixed fractions first.
Solving mixed fraction: [Tex]10\frac{2}{3} [/Tex] 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+[Tex]1\frac{2}{3} [/Tex]
Solution:
To solve this problem we have to solve mixed fractions first.
Solving mixed fraction:[Tex]1\frac{2}{3} [/Tex] 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+[Tex]2\frac{1}{3} [/Tex]
Solution:
To solve this problem we have to solve mixed fractions first.
Solving mixed fraction:[Tex]2\frac{1}{3} [/Tex] 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+[Tex]3\frac{1}{3} [/Tex]
Solution:
To solve this problem we have to solve mixed fractions first.
Solving mixed fraction: [Tex]3\frac{1}{3} [/Tex] 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.
FAQs on Mixed Fractions and Whole Numbers
What is a mixed fraction?
A mixed fraction consists of a whole number and a proper fraction. For example, [Tex]3\frac{1}{2}[/Tex] is a mixed fraction, where 3 is the whole number and 1/2 is the fraction part.
How do you convert a mixed fraction to an improper fraction?
To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. This sum becomes the numerator of the improper fraction, and the denominator remains the same.
How do you convert an improper fraction to a mixed fraction?
To convert an improper fraction to a mixed fraction, divide the numerator by the denominator. The quotient becomes the whole number part, and the remainder becomes the numerator of the fractional part, with the same denominator as the original fraction.
What is the difference between a mixed fraction and a whole number?
A whole number is an integer without any fractional or decimal parts. It can be positive, negative, or zero. A mixed fraction, on the other hand, combines a whole number and a proper fraction.
How do you add or subtract mixed fractions and whole numbers?
To add or subtract mixed fractions and whole numbers, first convert the mixed fractions to improper fractions if necessary. Then, perform the addition or subtraction as you would with regular fractions, ensuring that the denominators are the same.
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