What is 4/13 plus 10/21? (Answer: 214/273)

Exact Answer

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Problem: What is 4/13 plus 10/21?
Formula / Expression: 4/13 + 10/21
Final Answer: 214/273
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 13 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 21 = 273.
Working: LCD(13, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 4/13 by 21, and multiply the numerator and denominator of 10/21 by 13 so both fractions share the common base 273.
Working: 4 × 21/13 × 21 = 84/273 and 10 × 13/21 × 13 = 130/273

Step 3: Add the Numerators
Now add the numerators (84 + 130 = 214) and keep the common denominator 273 unchanged.
Working: 84 + 130/273 = 214/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 214 and 273 is 1, confirming that 214/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 214/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 214 by denominator 273 produces a repeating decimal (approximately 0.783883, or 78.3883%).
Working: 214 ÷ 273 = 0.783883 (78.3883%)

Key Values:
- Simplified Fraction: 214/273
- Mixed Number Form: 214/273
- Decimal Value: 0.783883
- Percentage: 78.3883%

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Solved with FractionsCalc:
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4/13 + 10/21 = 214/273

Simplified Fraction

214/273

Mixed Number

Proper (214/273)

Decimal Value

0.783883

Percentage

78.3883%

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Step-by-Step Solution: 4/13 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 13 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 13 × 21 = 273.

LCD(13, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 4/13 by 21, and multiply the numerator and denominator of 10/21 by 13 so both fractions share the common base 273.

4 × 21/13 × 21 = 84/273 and 10 × 13/21 × 13 = 130/273

Step 3

Add the Numerators

Now add the numerators (84 + 130 = 214) and keep the common denominator 273 unchanged.

84 + 130/273 = 214/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 214 and 273 is 1, confirming that 214/273 cannot be reduced further—it is already in its simplest irreducible form.

214/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 214 by denominator 273 produces a repeating decimal (approximately 0.783883, or 78.3883%).

214 ÷ 273 = 0.783883 (78.3883%)

Visual Representation

The diagram below illustrates 4/13 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`214/273`
Mixed Number Form	`214/273`
Decimal Form	`0.783883`
Percentage	`78.3883%`

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Frequently Asked Questions

What is 4/13 plus 10/21 as a fraction?

4/13 + 10/21 in simplest fraction form is 214/273.

What is 4/13 plus 10/21 as a decimal?

4/13 + 10/21 converted to a decimal is 0.783883.

What is 4/13 plus 10/21 as a percentage?

4/13 + 10/21 expressed as a percentage is 78.3883%.

Does 4/13 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.783883...) because the denominator contains prime factors other than 2 and 5.