Fraction Calculator - Convert Fractions

Fraction Calculator

Calculate fractions instantly with our free online calculator. Perform addition, subtraction, multiplication, division, and simplification of fractions with detailed step-by-step explanations.

Fraction Calculator

Operation: [Dropdown: Add, Subtract, Multiply, Divide]

First Fraction: [Numerator] / [Denominator]

Second Fraction: [Numerator] / [Denominator]

[Calculate Button]

Results:

• Result: [Fraction] = [Decimal]
• Simplified Form: [If applicable]
• Mixed Number: [If applicable]
• Step-by-Step: [Expand/Collapse]

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What is a Fraction?

A fraction represents a part of a whole. It consists of two numbers:

Numerator

• The top number
• Represents the number of parts we have

Denominator

• The bottom number
• Represents the total number of equal parts

Example:

3/4 (three-fourths or three quarters)
Numerator = 3 (we have 3 parts)
Denominator = 4 (whole divided into 4 parts)

Types of Fractions

1. Proper Fractions

• Numerator < Denominator
• Examples: 1/2, 3/4, 7/8

2. Improper Fractions

• Numerator > Denominator
• Examples: 5/4, 7/3, 11/5

3. Mixed Numbers

• Whole number + Proper fraction
• Examples: 1½, 2¾, 3⅓

4. Equivalent Fractions

• Different fractions representing same value
• Examples: 1/2 = 2/4 = 4/8

Fraction Operations

Adding Fractions

Same Denominator:

a/c + b/c = (a + b)/c

Example:

1/5 + 2/5 = (1 + 2)/5 = 3/5

Different Denominators:

a/b + c/d = (ad + bc)/(bd)

Example:

1/4 + 1/3
= (1×3 + 1×4)/(4×3)
= (3 + 4)/12
= 7/12

Subtracting Fractions

Same Denominator:

a/c - b/c = (a - b)/c

Example:

5/6 - 2/6 = (5 - 2)/6 = 3/6 = 1/2

Different Denominators:

a/b - c/d = (ad - bc)/(bd)

Example:

3/4 - 1/3
= (3×3 - 1×4)/(4×3)
= (9 - 4)/12
= 5/12

Multiplying Fractions

Formula:

a/b × c/d = (a × c)/(b × d)

Example 1:

1/2 × 3/4
= (1 × 3)/(2 × 4)
= 3/8

Example 2:

2/3 × 4/5
= (2 × 4)/(3 × 5)
= 8/15

Dividing Fractions

Formula:

(a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc

Remember: Flip the second fraction (reciprocal) and multiply

Example 1:

1/2 ÷ 1/4
= 1/2 × 4/1
= 4/2
= 2

Example 2:

3/4 ÷ 2/3
= 3/4 × 3/2
= 9/8
= 1⅛

Simplifying Fractions

What is Simplifying?

Finding an equivalent fraction with the smallest possible numerator and denominator.

Method 1: Divide by GCF

Example: Simplify 12/18

Step 1: Find GCF of 12 and 18

GCF(12, 18) = 6

Step 2: Divide both by GCF

(12 ÷ 6)/(18 ÷ 6) = 2/3

Result: 12/18 = 2/3

Method 2: Prime Factorization

Example: Simplify 24/36

Step 1: Prime factorize

24 = 2³ × 3
36 = 2² × 3²

Step 2: Cancel common factors

24/36 = (2³ × 3)/(2² × 3²)
     = 2/3

Result: 24/36 = 2/3

Examples of Simplification

1. Even Numbers:

8/12 = 4/6 = 2/3

2. Both Divisible by 3:

9/15 = 3/5

3. Both Divisible by 5:

15/25 = 3/5

4. Complex Example:

48/60 = 4/5
(divide by 12, the GCF)

Mixed Numbers and Improper Fractions

Converting Improper to Mixed

Formula:

a/b = (a ÷ b) remainder/b

Example 1: 7/3

7 ÷ 3 = 2 remainder 1
7/3 = 2⅓

Example 2: 17/5

17 ÷ 5 = 3 remainder 2
17/5 = 3⅖

Converting Mixed to Improper

Formula:

a(b/c) = (a × c + b)/c

Example 1: 2¾

2¾ = (2 × 4 + 3)/4
   = 11/4

Example 2: 3½

3½ = (3 × 2 + 1)/2
   = 7/2

Fraction Examples

Example 1: Addition

Calculate: 2/3 + 3/5

Solution:

LCD = 15
2/3 = 10/15
3/5 = 9/15
10/15 + 9/15 = 19/15 = 1⁴⁄₁₅

Example 2: Subtraction

Calculate: 5/6 - 1/4

Solution:

LCD = 12
5/6 = 10/12
1/4 = 3/12
10/12 - 3/12 = 7/12

Example 3: Multiplication

Calculate: 3/4 × 2/5

Solution:

3/4 × 2/5
= (3 × 2)/(4 × 5)
= 6/20
= 3/10 (simplified)

Example 4: Division

Calculate: 3/4 ÷ 1/2

Solution:

3/4 ÷ 1/2
= 3/4 × 2/1
= 6/4
= 3/2
= 1½

Example 5: Mixed Numbers

Calculate: 1½ + 2¾

Solution:

1½ = 3/2
2¾ = 11/4
LCD = 4
3/2 = 6/4
6/4 + 11/4 = 17/4 = 4¼

Finding Least Common Denominator (LCD)

Method 1: Listing Multiples

Example: LCD of 4 and 6

Multiples of 4: 4, 8, 12, 16, 20, ...
Multiples of 6: 6, 12, 18, 24, ...
LCD = 12

Method 2: Prime Factorization

Example: LCD of 12 and 18

12 = 2² × 3
18 = 2 × 3²
LCD = 2² × 3² = 4 × 9 = 36

Method 3: Using LCM Formula

LCD(a, b) = LCM(a, b)

Example: LCD of 8 and 12

LCM(8, 12) = 24
LCD = 24

Comparing Fractions

Method 1: Common Denominator

Compare: 3/4 and 2/3

LCD = 12
3/4 = 9/12
2/3 = 8/12
9/12 > 8/12
Therefore: 3/4 > 2/3

Method 2: Cross Multiplication

Compare: 5/8 and 3/5

5 × 5 = 25
3 × 8 = 24
25 > 24
Therefore: 5/8 > 3/5

Method 3: Decimal Conversion

Compare: 7/8 and 4/5

7/8 = 0.875
4/5 = 0.8
0.875 > 0.8
Therefore: 7/8 > 4/5

Fraction Rules and Properties

Identity Property

a/a = 1 (for a ≠ 0)

Examples:

5/5 = 1
100/100 = 1

Zero Property

0/a = 0 (for a ≠ 0) a/0 is undefined

Reciprocal Property

a/b × b/a = 1

Example:

2/3 × 3/2 = 6/6 = 1

Commutative Property

a/b + c/d = c/d + a/b a/b × c/d = c/d × a/b

Associative Property

(a/b + c/d) + e/f = a/b + (c/d + e/f) (a/b × c/d) × e/f = a/b × (c/d × e/f)

Real-World Applications

1. Cooking and Recipes

Example: Recipe serves 4, you need to serve 6

Scaling factor = 6/4 = 3/2 = 1½
Multiply all ingredients by 1½

2. Construction

Example: Board length needed

You need: 2⅓ + 1¾ + 3½
= 7/3 + 7/4 + 7/2
= 28/12 + 21/12 + 42/12
= 91/12
= 7⁷⁄₁₂ feet

3. Finance

Example: Interest rates

Quarterly rate = 6%/4 = 6/4% = 3/2%
Monthly rate = 6%/12 = 6/12% = 1/2%

4. Measurement

Example: Fabric pieces

Piece 1: 2⅝ yards
Piece 2: 3¼ yards
Total: 2⅝ + 3¼
= 21/8 + 13/4
= 21/8 + 26/8
= 47/8
= 5⅞ yards

Tips and Common Mistakes

Common Mistakes

1. Wrong operation for division: Not flipping second fraction
2. Forgetting LCD: Adding/subtracting without common denominator
3. Not simplifying: Leaving answers in unsimplified form
4. Confusing rules: Multiplying denominators when adding
5. Calculation errors: Making arithmetic mistakes

Best Practices

1. Always simplify: Final answers should be in simplest form
2. Find LCD first: For addition and subtraction
3. Check your work: Verify by converting to decimals
4. Use common sense: Estimate before calculating
5. Learn multiplication tables: Helps with finding factors

How do I add fractions with different denominators?

Find the LCD (least common denominator), convert both fractions to have the LCD, then add numerators. Example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12

How do I divide fractions?

Multiply the first fraction by the reciprocal (flipped version) of the second. Example: (1/2) ÷ (1/4) = (1/2) × (4/1) = 4/2 = 2

What is an improper fraction?

An improper fraction has a numerator greater than or equal to the denominator. Examples: 5/3, 7/4, 9/9

How do I convert mixed numbers to improper fractions?

Multiply whole number by denominator, add numerator, keep denominator. Example: 2¾ = (2 × 4 + 3)/4 = 11/4

What is the simplest form of a fraction?

The simplest form has numerator and denominator with no common factors other than 1. Example: 4/8 simplifies to 1/2

How do I find the LCD?

Find the LCM of the denominators. Example: LCD of 4 and 6 is LCM(4, 6) = 12

Can a fraction be negative?

Yes! Place the negative sign before the fraction or in the numerator. Example: -3/4 or (-3)/4

What is 0 divided by a fraction?

0 divided by any non-zero fraction equals 0. Example: 0 ÷ (3/4) = 0

What is a fraction divided by 0?

Division by zero is undefined, including fraction division by 0.

How do I compare fractions?

Convert to common denominator, cross multiply, or convert to decimals. Example: Compare 3/4 and 2/3: 9/12 > 8/12, so 3/4 > 2/3

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Practice Problems

Beginner Level

1. 1/2 + 1/4 = ?
2. 2/3 × 3/4 = ?
3. Simplify: 6/8

Intermediate Level

1. 3/4 + 2/5 = ?
2. 5/6 ÷ 1/3 = ?
3. Convert to mixed: 11/4

Advanced Level

1. 2⅓ + 1¾ = ?
2. (3/4 - 1/3) × 2/5 = ?
3. Which is larger: 7/8 or 5/6?

Answers: [Click to reveal]

1. Beginner: 3/4, 1/2, 3/4
2. Intermediate: 23/20, 2½, 2¾
3. Advanced: 49/12 = 4¹⁄₁₂, 7/30, 7/8 > 5/6

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