What is 13/38 plus 8/21? (Answer: 577/798)

Exact Answer

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Problem: What is 13/38 plus 8/21?
Formula / Expression: 13/38 + 8/21
Final Answer: 577/798
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 38 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 21 = 798.
Working: LCD(38, 21) = 798

Step 2: Convert to Equivalent Fractions with Common Denominator 798
Multiply the numerator and denominator of 13/38 by 21, and multiply the numerator and denominator of 8/21 by 38 so both fractions share the common base 798.
Working: 13 × 21/38 × 21 = 273/798 and 8 × 38/21 × 38 = 304/798

Step 3: Add the Numerators
Now add the numerators (273 + 304 = 577) and keep the common denominator 798 unchanged.
Working: 273 + 304/798 = 577/798

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 577 and 798 is 1, confirming that 577/798 cannot be reduced further—it is already in its simplest irreducible form.
Working: 577/798

Step 5: Decimal & Percentage Representation
Dividing the numerator 577 by denominator 798 produces a repeating decimal (approximately 0.723058, or 72.3058%).
Working: 577 ÷ 798 = 0.723058 (72.3058%)

Key Values:
- Simplified Fraction: 577/798
- Mixed Number Form: 577/798
- Decimal Value: 0.723058
- Percentage: 72.3058%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-38-plus-8-21/
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13/38 + 8/21 = 577/798

Simplified Fraction

577/798

Mixed Number

Proper (577/798)

Decimal Value

0.723058

Percentage

72.3058%

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Step-by-Step Solution: 13/38 + 8/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 38 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 38 × 21 = 798.

LCD(38, 21) = 798

Step 2

Convert to Equivalent Fractions with Common Denominator 798

Multiply the numerator and denominator of 13/38 by 21, and multiply the numerator and denominator of 8/21 by 38 so both fractions share the common base 798.

13 × 21/38 × 21 = 273/798 and 8 × 38/21 × 38 = 304/798

Step 3

Add the Numerators

Now add the numerators (273 + 304 = 577) and keep the common denominator 798 unchanged.

273 + 304/798 = 577/798

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 577 and 798 is 1, confirming that 577/798 cannot be reduced further—it is already in its simplest irreducible form.

577/798

Step 5

Decimal & Percentage Representation

Dividing the numerator 577 by denominator 798 produces a repeating decimal (approximately 0.723058, or 72.3058%).

577 ÷ 798 = 0.723058 (72.3058%)

Visual Representation

The diagram below illustrates 13/38 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`577/798`
Mixed Number Form	`577/798`
Decimal Form	`0.723058`
Percentage	`72.3058%`

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Frequently Asked Questions

What is 13/38 plus 8/21 as a fraction?

13/38 + 8/21 in simplest fraction form is 577/798.

What is 13/38 plus 8/21 as a decimal?

13/38 + 8/21 converted to a decimal is 0.723058.

What is 13/38 plus 8/21 as a percentage?

13/38 + 8/21 expressed as a percentage is 72.3058%.

Does 13/38 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.723058...) because the denominator contains prime factors other than 2 and 5.