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Mixed Fractions

To understand mixed fractions, it's important to first grasp the concept of fractions in general. A fraction shows a part of a whole or a part of a collection. It is written as a/b, where:  

a is the numerator (the number of parts we have)  

b is the denominator (the total number of equal parts the whole is divided into)  

 

Table of Content

 

Types of Fractions

  • Proper Fractions, where the numerator is less than the denominator (e.g., 3/4)  

 

  • Improper Fractions, where the numerator is greater than or equal to the denominator (e.g., 7/5, 4/4)  

 

  • Mixed Fractions, which combine a whole number and a proper fraction (e.g., 2 1/2)  

Fractions appear frequently in everyday life, such as when cooking, sharing a bill, or measuring distance or time.  

 

What are Mixed Fractions?

A mixed fraction, or mixed number, expresses numbers that include both a whole part and a fraction part. It is used when a quantity exceeds one whole but isn’t an exact multiple.  

Example:  

3 1/2 means 3 whole and 1 out of 2 equal parts.  

 

Why are Mixed Fractions Useful?

Mixed fractions are easier to understand than improper fractions in daily situations. For example, saying "I walked 1 1/2 kilometers" is more relatable than saying "I walked 3/2 kilometers."  

 

Converting Improper Fractions to Mixed Fractions

An improper fraction has a numerator greater than the denominator. To convert it into a mixed fraction:  

Steps:  

  • Divide the numerator by the denominator.  

  • The result is the whole number part.  

  • The remainder is the numerator of the fraction part.  

  • The denominator remains the same.  

 

Example:  

Convert 11/4  

11 ÷ 4 = 2 remainder 3  

So, 11/4 = 2 3/4  

This means that 11/4 equals 2 full parts and 3 out of 4 of the next part.  

 

Converting Mixed Fractions to Improper Fractions

For calculations, it’s often easier to convert mixed numbers into improper fractions first.  

Steps:  

  • Multiply the whole number by the denominator.  

  • Add the numerator to the result.  

  • The sum becomes the new numerator, and the denominator stays the same.  

 

Example:  

Convert 2 2/3  

2 × 3 = 6  

6 + 2 = 8  

So, 2 2/3 = 8/3  

 

Operations on Mixed Fractions

Addition and Subtraction  

  • Convert all mixed numbers to improper fractions.  

  • Find a common denominator if needed.  

  • Perform the addition or subtraction.  

  • Simplify and convert the result back to a mixed number if necessary.  

 

Example:  

Add: 2 1/3 + 1 1/6  

Convert:  

2 1/3 = 7/3, 1 1/6 = 7/6  

The least common multiple of 3 and 6 is 6.  

(7/3 = 14/6), so 14/6 + 7/6 = 21/6 = 3 1/2  

 

Multiplication  

  • Convert both mixed numbers to improper fractions.  

  • Multiply the numerators together and the denominators together.  

  • Simplify the result and convert back to a mixed number.  

 

Example:  

Multiply: 1 1/2 × 2 2/3  

1 1/2 = 3/2, 2 2/3 = 8/3  

(3/2 × 8/3 = 24/6 = 4)  

 

Division  

  • Convert both mixed numbers to improper fractions.  

  • Multiply the first by the reciprocal of the second.  

  • Simplify and convert back to a mixed number.  

 

Example:  

Divide: 2 1/4 ÷ 1 1/2  

2 1/4 = 9/4, 1 1/2 = 3/2  

9/4 ÷ 3/2 = 9/4 × 2/3 = 18/12 = 3/2 = 1 1/2  

 

Simplifying Mixed Fractions

After an operation, you often get a mixed number that needs simplification.  

Example:  

If the result is 3 4/8, simplify the fraction part:  

4/8 = 1/2, so the simplified mixed number is 3 1/2  

If the fractional part becomes improper (like 5 7/6), convert again:  

7/6 = 1 1/6 → 5 + 1 = 6 1/6  

 

Word Problems on Mixed Fractions  

Example 1:  

A recipe needs 2 1/2 cups of flour and 1 3/4 cups of sugar. How much do we need in total?  

Convert:  

2 1/2 = 5/2, 1 3/4 = 7/4  

The least common multiple of 2 and 4 is 4.  

(5/2 = 10/4), so 10/4 + 7/4 = 17/4 = 4 1/4  

Answer: 4 1/4 cups in total  

 

Example 2:  

Rahul ran 3 1/2 km in the morning and 2 2/3 km in the evening.  

Total distance = 3 1/2 + 2 2/3  

Convert and add: 7/2 + 8/3 = (21/6 + 16/6) = 37/6 = 6 1/6 km  

 

Common Mistakes and How to Avoid Them

  • Mixing up whole and fractional parts during conversion.  

  • Not simplifying the final answer.  

  • Incorrectly adding or subtracting whole and fractional parts separately.  

  • Forgetting to use the reciprocal when dividing.  

Tip: Always convert to improper fractions first when doing operations.  

 

Practice Questions

Convert the following to mixed numbers:  

a. 13/4  

b. 9/2  

 

Convert the following to improper fractions:  

a. 3 1/5  

b. 4 3/7  

 

Solve:  

a. 2 1/3 + 1 2/3  

b. 5 1/2 - 2 3/4  

c. 1 3/4 × 2 2/5  

d. 3 1/2 ÷ 1 3/4  

 

A water tank holds 5 1/4 liters. Another holds 3 2/3 liters. What is the total capacity?  

 

Conclusion

Mixed fractions are a practical and widely used way of expressing quantities that include whole numbers and parts of a whole. By mastering their identification, conversion, and operations, students can build a solid foundation for more advanced math topics like algebra, percentages, and ratios. With regular practice and application in everyday situations, understanding mixed fractions becomes intuitive and lasting.

 

Related Links

Fractions- Learn the basics of fractions, their operations, and real-life applications with step-by-step lessons.

Types of Fractions- Explore proper, improper, and mixed fractions with simple examples and visuals.

 

FAQs on Mixed Fractions

1. What is a mixed fraction with examples?

Answer:
A mixed fraction (or mixed number) is a number that combines a whole number and a proper fraction. It represents a value that is more than one whole but not a whole multiple.

Examples:

  • 2 1/2 → two wholes and one-half

  • 5 3/4 → five wholes and three-fourths

  • 7 2/3 → seven wholes and two-thirds

Mixed fractions are commonly used in real life, such as in recipes or measurements.

 

2. How do you solve a mixed fraction?

Answer:
To solve a problem involving mixed fractions (such as addition, subtraction, multiplication, or division), follow these steps:

  1. Convert the mixed fraction to an improper fraction.

  2. Perform the operation (add, subtract, multiply, divide) as you would with regular fractions.

  3. Simplify the result if needed.

  4. Convert the answer back to a mixed fraction, if applicable.

Example (Addition):
2 1/2 + 1 1/4
→ Convert to improper: 5/2 + 5/4
→ LCM = 4 → 10/4 + 5/4 = 15/4 = 3 3/4

 

3. What are 5 examples of mixed numbers?

Answer:
Here are five examples of mixed numbers:

  1. 1 1/2

  2. 2 3/4

  3. 4 2/3

  4. 6 1/5

  5. 7 5/8

Each of these includes a whole number and a proper fraction.

 

4. How do I convert to mixed fractions?

Answer:
To convert an improper fraction to a mixed fraction:

  1. Divide the numerator by the denominator.

  2. The quotient becomes the whole number.

  3. The remainder becomes the numerator of the fraction.

  4. Keep the same denominator.

Example:
Convert 11/4:
11 ÷ 4 = 2 remainder 3
So, 11/4 = 2 3/4

This means 11/4 equals 2 whole and 3 fourths.

 

Learn more and explore engaging math concepts at Orchids The International School. Build strong problem-solving skills with ease.

 

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