What is 13/34 plus 10/21? (Answer: 613/714)

Exact Answer

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Problem: What is 13/34 plus 10/21?
Formula / Expression: 13/34 + 10/21
Final Answer: 613/714
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 21 = 714.
Working: LCD(34, 21) = 714

Step 2: Convert to Equivalent Fractions with Common Denominator 714
Multiply the numerator and denominator of 13/34 by 21, and multiply the numerator and denominator of 10/21 by 34 so both fractions share the common base 714.
Working: 13 × 21/34 × 21 = 273/714 and 10 × 34/21 × 34 = 340/714

Step 3: Add the Numerators
Now add the numerators (273 + 340 = 613) and keep the common denominator 714 unchanged.
Working: 273 + 340/714 = 613/714

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 613 and 714 is 1, confirming that 613/714 cannot be reduced further—it is already in its simplest irreducible form.
Working: 613/714

Step 5: Decimal & Percentage Representation
Dividing the numerator 613 by denominator 714 produces a repeating decimal (approximately 0.858543, or 85.8543%).
Working: 613 ÷ 714 = 0.858543 (85.8543%)

Key Values:
- Simplified Fraction: 613/714
- Mixed Number Form: 613/714
- Decimal Value: 0.858543
- Percentage: 85.8543%

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Solved with FractionsCalc:
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13/34 + 10/21 = 613/714

Simplified Fraction

613/714

Mixed Number

Proper (613/714)

Decimal Value

0.858543

Percentage

85.8543%

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Step-by-Step Solution: 13/34 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 21 = 714.

LCD(34, 21) = 714

Step 2

Convert to Equivalent Fractions with Common Denominator 714

Multiply the numerator and denominator of 13/34 by 21, and multiply the numerator and denominator of 10/21 by 34 so both fractions share the common base 714.

13 × 21/34 × 21 = 273/714 and 10 × 34/21 × 34 = 340/714

Step 3

Add the Numerators

Now add the numerators (273 + 340 = 613) and keep the common denominator 714 unchanged.

273 + 340/714 = 613/714

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 613 and 714 is 1, confirming that 613/714 cannot be reduced further—it is already in its simplest irreducible form.

613/714

Step 5

Decimal & Percentage Representation

Dividing the numerator 613 by denominator 714 produces a repeating decimal (approximately 0.858543, or 85.8543%).

613 ÷ 714 = 0.858543 (85.8543%)

Visual Representation

The diagram below illustrates 13/34 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`613/714`
Mixed Number Form	`613/714`
Decimal Form	`0.858543`
Percentage	`85.8543%`

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Frequently Asked Questions

What is 13/34 plus 10/21 as a fraction?

13/34 + 10/21 in simplest fraction form is 613/714.

What is 13/34 plus 10/21 as a decimal?

13/34 + 10/21 converted to a decimal is 0.858543.

What is 13/34 plus 10/21 as a percentage?

13/34 + 10/21 expressed as a percentage is 85.8543%.

Does 13/34 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.858543...) because the denominator contains prime factors other than 2 and 5.