What is 4/21 plus 5/26? (Answer: 209/546)

Exact Answer

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Problem: What is 4/21 plus 5/26?
Formula / Expression: 4/21 + 5/26
Final Answer: 209/546
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 546
Multiply the numerator and denominator of 4/21 by 26, and multiply the numerator and denominator of 5/26 by 21 so both fractions share the common base 546.
Working: 4 × 26/21 × 26 = 104/546 and 5 × 21/26 × 21 = 105/546

Step 3: Add the Numerators
Now add the numerators (104 + 105 = 209) and keep the common denominator 546 unchanged.
Working: 104 + 105/546 = 209/546

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 209 and 546 is 1, confirming that 209/546 cannot be reduced further—it is already in its simplest irreducible form.
Working: 209/546

Step 5: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 546 produces a repeating decimal (approximately 0.382784, or 38.2784%).
Working: 209 ÷ 546 = 0.382784 (38.2784%)

Key Values:
- Simplified Fraction: 209/546
- Mixed Number Form: 209/546
- Decimal Value: 0.382784
- Percentage: 38.2784%

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Solved with FractionsCalc:
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4/21 + 5/26 = 209/546

Simplified Fraction

209/546

Mixed Number

Proper (209/546)

Decimal Value

0.382784

Percentage

38.2784%

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Step-by-Step Solution: 4/21 + 5/26

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 26) = 546

Step 2

Convert to Equivalent Fractions with Common Denominator 546

Multiply the numerator and denominator of 4/21 by 26, and multiply the numerator and denominator of 5/26 by 21 so both fractions share the common base 546.

4 × 26/21 × 26 = 104/546 and 5 × 21/26 × 21 = 105/546

Step 3

Add the Numerators

Now add the numerators (104 + 105 = 209) and keep the common denominator 546 unchanged.

104 + 105/546 = 209/546

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 209 and 546 is 1, confirming that 209/546 cannot be reduced further—it is already in its simplest irreducible form.

209/546

Step 5

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 546 produces a repeating decimal (approximately 0.382784, or 38.2784%).

209 ÷ 546 = 0.382784 (38.2784%)

Visual Representation

The diagram below illustrates 4/21 plus 5/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/546`
Mixed Number Form	`209/546`
Decimal Form	`0.382784`
Percentage	`38.2784%`

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Frequently Asked Questions

What is 4/21 plus 5/26 as a fraction?

4/21 + 5/26 in simplest fraction form is 209/546.

What is 4/21 plus 5/26 as a decimal?

4/21 + 5/26 converted to a decimal is 0.382784.

What is 4/21 plus 5/26 as a percentage?

4/21 + 5/26 expressed as a percentage is 38.2784%.

Does 4/21 plus 5/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.382784...) because the denominator contains prime factors other than 2 and 5.