Mixed Numbers

A mixed number consists of a whole number and a proper fraction combined. It represents a value greater than a whole, but it is not a whole number by itself. The parts of a mixed number include the whole number, the numerator, and the denominator. The numerator represents how many parts are taken, and the denominator shows the total number of equal parts in one whole.
 

 The properties of mixed numbers are mentioned below:

• A combination of whole numbers and fractions
• Can be converted to an improper fraction
• Can be converted to a decimal
• Can be used in basic arithmetic operations
• Obeys the commutative property (for addition and multiplication)
• Does not follow the commutative property for subtraction and division
• Follows the associative property (for addition and multiplication)
• Follows the identity property
   

To add mixed numbers, we have to follow the steps mentioned below:

Step 1: Convert Mixed Numbers to Improper Fractions (Optional, but Useful for Complex Problems)
For easier addition, you can convert mixed numbers into improper fractions.

Step 2: Find a Common Denominator (If Necessary)

If the fractions have different denominators, find the Least Common Denominator (LCD) and convert both fractions.

Step 3: Add Whole Numbers and Fractions Separately
Separately add the whole numbers and the fractions

Step 4: Simplify (If Necessary)
If the fraction part is improper, convert it to a mixed number and adjust the final answer. If possible, simplify the fraction.
 

To subtract mixed numbers, the steps are mentioned below:

Step 1: Convert Mixed Numbers to Improper Fractions (Optional, but Useful for Complex Problems)
If the mixed numbers have different denominators or borrowing is needed, converting them into improper fractions makes subtraction easier.
However, if the whole numbers and fractions can be subtracted directly, you may skip this step.

Step 2: Find a Common Denominator (If Necessary)
If the fractions have different denominators, find the Least Common Denominator (LCD) and convert both fractions.

Step 3: Subtract Whole Numbers and Fractions Separately

As it is mentioned above, subtract the whole numbers and the fractions separately

Step 4: Borrowing (If the First Fraction is Smaller than the Second)
If the fraction in the first number is smaller than that in the second, borrow 1 from the whole number and convert it into an equivalent fraction.
 

For converting improper fractions to mixed numbers, the following steps are used:

Step 1: Divide the Numerator by the Denominator
Perform long division to divide the numerator by the denominator.

Step 2: Write the Whole Number
The quotient from Step 1 becomes the whole number of the mixed number.

Step 3: Use the Remainder as the New Numerator
The remainder from Step 1 becomes the numerator of the fraction.
The denominator remains the same.

Step 4: Write the Mixed Number
Combine the whole number and fraction to form the mixed number.
 

To convert mixed numbers to improper fractions, follow the steps mentioned below:

Step 1: Identify the Whole Number and Fraction
A mixed number consists of a whole number and a fraction (numerator/denominator)

Step 2: Multiply the Whole Number by the Denominator
Multiply the whole number by the denominator of the fraction.
Whole Number×Denominator

Step 3: Add the Numerator to the Result
Take the result from Step 2 and add the numerator of the fraction.

Step 4: Place the Sum Over the Original Denominator
Write the result from Step 3 as the numerator, keeping the denominator the same.
 

To convert mixed numbers to decimals, follow the steps mentioned below:

Step 1: Identify the Whole Number and Fraction
A mixed number consists of a whole number and a fraction.
Example: Convert 3 ½ to a decimal.
Whole number = 3
Fraction = ½

Step 2: Convert the Fraction to a Decimal
To convert the fraction to a decimal, divide the numerator by the denominator.
​1/2  = 1 ÷ 2 = 0.5
So, ½ = 0.5

Step 3: Add the Decimal to the Whole Number
Now, add the decimal from Step 2 to the whole number.
3+0.5=3.5
Therefore, 3 ½ = 3.5 in decimal form.
 

The mixed numbers have numerous applications across various fields. Let us explore how mixed numbers are used in different areas:

Cooking and Baking: Mixed numbers are essential in cooking and baking, where ingredients are measured precisely, such as 2 ½ cups of flour or 3 ¾ teaspoons of sugar. These measurements ensure that flavors and textures are balanced and that recipes turn out as expected.

Construction and Carpentry: Mixed numbers are used in measuring materials for construction. For measuring the dimensions like 4 ⅜ inches or 6 ½ feet for door frame, such mixed numbers are used for accuracy.
6 ½ feet for a door frame. These precise measurements ensure that parts fit together correctly, preventing structural issues.

Time Management and Scheduling: Mixed numbers are commonly used when planning and managing time. Appointments, travel durations, and schedules often involve expressions like 1 ½ hours or 2 ¾ hours. For example, if a movie starts at 6:30 PM and lasts 1 ¾ hours, knowing how to work with mixed numbers helps determine when it will end. It will end at 8:15 PM