What is 4/13 plus 4/8? (Answer: 21/26)

Exact Answer

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Problem: What is 4/13 plus 4/8?
Formula / Expression: 4/13 + 4/8
Final Answer: 21/26
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.
Working: LCD(13, 8) = 104

Step 2: Convert to Equivalent Fractions with Common Denominator 104
Multiply the numerator and denominator of 4/13 by 8, and multiply the numerator and denominator of 4/8 by 13 so both fractions share the common base 104.
Working: 4 × 8/13 × 8 = 32/104 and 4 × 13/8 × 13 = 52/104

Step 3: Add the Numerators
Now add the numerators (32 + 52 = 84) and keep the common denominator 104 unchanged.
Working: 32 + 52/104 = 84/104

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 104, which is 4. Divide both the numerator and denominator by 4.
Working: 84 ÷ 4/104 ÷ 4 = 21/26

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).
Working: 21 ÷ 26 = 0.807692 (80.7692%)

Key Values:
- Simplified Fraction: 21/26
- Mixed Number Form: 21/26
- Decimal Value: 0.807692
- Percentage: 80.7692%

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Solved with FractionsCalc:
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4/13 + 4/8 = 21/26

Simplified Fraction

21/26

Mixed Number

Proper (21/26)

Decimal Value

0.807692

Percentage

80.7692%

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Step-by-Step Solution: 4/13 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 8 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 8 = 104.

LCD(13, 8) = 104

Step 2

Convert to Equivalent Fractions with Common Denominator 104

Multiply the numerator and denominator of 4/13 by 8, and multiply the numerator and denominator of 4/8 by 13 so both fractions share the common base 104.

4 × 8/13 × 8 = 32/104 and 4 × 13/8 × 13 = 52/104

Step 3

Add the Numerators

Now add the numerators (32 + 52 = 84) and keep the common denominator 104 unchanged.

32 + 52/104 = 84/104

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 104, which is 4. Divide both the numerator and denominator by 4.

84 ÷ 4/104 ÷ 4 = 21/26

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 26 produces a repeating decimal (approximately 0.807692, or 80.7692%).

21 ÷ 26 = 0.807692 (80.7692%)

Visual Representation

The diagram below illustrates 4/13 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/26`
Mixed Number Form	`21/26`
Decimal Form	`0.807692`
Percentage	`80.7692%`

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Frequently Asked Questions

What is 4/13 plus 4/8 as a fraction?

4/13 + 4/8 in simplest fraction form is 21/26.

What is 4/13 plus 4/8 as a decimal?

4/13 + 4/8 converted to a decimal is 0.807692.

What is 4/13 plus 4/8 as a percentage?

4/13 + 4/8 expressed as a percentage is 80.7692%.

Does 4/13 plus 4/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.807692...) because the denominator contains prime factors other than 2 and 5.