What is 13/38 plus 10/21? (Answer: 653/798)

Exact Answer

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Problem: What is 13/38 plus 10/21?
Formula / Expression: 13/38 + 10/21
Final Answer: 653/798
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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 10/21 by 38 so both fractions share the common base 798.
Working: 13 × 21/38 × 21 = 273/798 and 10 × 38/21 × 38 = 380/798

Step 3: Add the Numerators
Now add the numerators (273 + 380 = 653) and keep the common denominator 798 unchanged.
Working: 273 + 380/798 = 653/798

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 653 and 798 is 1, confirming that 653/798 cannot be reduced further—it is already in its simplest irreducible form.
Working: 653/798

Step 5: Decimal & Percentage Representation
Dividing the numerator 653 by denominator 798 produces a repeating decimal (approximately 0.818296, or 81.8296%).
Working: 653 ÷ 798 = 0.818296 (81.8296%)

Key Values:
- Simplified Fraction: 653/798
- Mixed Number Form: 653/798
- Decimal Value: 0.818296
- Percentage: 81.8296%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-38-plus-10-21/
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13/38 + 10/21 = 653/798

Simplified Fraction

653/798

Mixed Number

Proper (653/798)

Decimal Value

0.818296

Percentage

81.8296%

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Step-by-Step Solution: 13/38 + 10/21

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 10/21 by 38 so both fractions share the common base 798.

13 × 21/38 × 21 = 273/798 and 10 × 38/21 × 38 = 380/798

Step 3

Add the Numerators

Now add the numerators (273 + 380 = 653) and keep the common denominator 798 unchanged.

273 + 380/798 = 653/798

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 653 and 798 is 1, confirming that 653/798 cannot be reduced further—it is already in its simplest irreducible form.

653/798

Step 5

Decimal & Percentage Representation

Dividing the numerator 653 by denominator 798 produces a repeating decimal (approximately 0.818296, or 81.8296%).

653 ÷ 798 = 0.818296 (81.8296%)

Visual Representation

The diagram below illustrates 13/38 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`653/798`
Mixed Number Form	`653/798`
Decimal Form	`0.818296`
Percentage	`81.8296%`

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Frequently Asked Questions

What is 13/38 plus 10/21 as a fraction?

13/38 + 10/21 in simplest fraction form is 653/798.

What is 13/38 plus 10/21 as a decimal?

13/38 + 10/21 converted to a decimal is 0.818296.

What is 13/38 plus 10/21 as a percentage?

13/38 + 10/21 expressed as a percentage is 81.8296%.

Does 13/38 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.818296...) because the denominator contains prime factors other than 2 and 5.