What is 5/26 plus 10/21? (Answer: 365/546)

Exact Answer

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Problem: What is 5/26 plus 10/21?
Formula / Expression: 5/26 + 10/21
Final Answer: 365/546
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 26 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 21 = 546.
Working: LCD(26, 21) = 546

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 5/26 by 21, and multiply the numerator and denominator of 10/21 by 26 so both fractions share the common base 546.
Working: 5 × 21/26 × 21 = 105/546 and 10 × 26/21 × 26 = 260/546

Step 3: Add the Numerators
Now add the numerators (105 + 260 = 365) and keep the common denominator 546 unchanged.
Working: 105 + 260/546 = 365/546

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 365 and 546 is 1, confirming that 365/546 cannot be reduced further—it is already in its simplest irreducible form.
Working: 365/546

Step 5: Decimal & Percentage Representation
Dividing the numerator 365 by denominator 546 produces a repeating decimal (approximately 0.668498, or 66.8498%).
Working: 365 ÷ 546 = 0.668498 (66.8498%)

Key Values:
- Simplified Fraction: 365/546
- Mixed Number Form: 365/546
- Decimal Value: 0.668498
- Percentage: 66.8498%

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Solved with FractionsCalc:
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5/26 + 10/21 = 365/546

Simplified Fraction

365/546

Mixed Number

Proper (365/546)

Decimal Value

0.668498

Percentage

66.8498%

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Step-by-Step Solution: 5/26 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 26 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 26 × 21 = 546.

LCD(26, 21) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 5/26 by 21, and multiply the numerator and denominator of 10/21 by 26 so both fractions share the common base 546.

5 × 21/26 × 21 = 105/546 and 10 × 26/21 × 26 = 260/546

Step 3

Add the Numerators

Now add the numerators (105 + 260 = 365) and keep the common denominator 546 unchanged.

105 + 260/546 = 365/546

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 365 and 546 is 1, confirming that 365/546 cannot be reduced further—it is already in its simplest irreducible form.

365/546

Step 5

Decimal & Percentage Representation

Dividing the numerator 365 by denominator 546 produces a repeating decimal (approximately 0.668498, or 66.8498%).

365 ÷ 546 = 0.668498 (66.8498%)

Visual Representation

The diagram below illustrates 5/26 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`365/546`
Mixed Number Form	`365/546`
Decimal Form	`0.668498`
Percentage	`66.8498%`

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Frequently Asked Questions

What is 5/26 plus 10/21 as a fraction?

5/26 + 10/21 in simplest fraction form is 365/546.

What is 5/26 plus 10/21 as a decimal?

5/26 + 10/21 converted to a decimal is 0.668498.

What is 5/26 plus 10/21 as a percentage?

5/26 + 10/21 expressed as a percentage is 66.8498%.

Does 5/26 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.668498...) because the denominator contains prime factors other than 2 and 5.