What is 3/29 plus 5/21? (Answer: 208/609)

Exact Answer

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Problem: What is 3/29 plus 5/21?
Formula / Expression: 3/29 + 5/21
Final Answer: 208/609
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 29 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 21 = 609.
Working: LCD(29, 21) = 609

Step 2: Convert to Equivalent Fractions with Common Denominator 609
Multiply the numerator and denominator of 3/29 by 21, and multiply the numerator and denominator of 5/21 by 29 so both fractions share the common base 609.
Working: 3 × 21/29 × 21 = 63/609 and 5 × 29/21 × 29 = 145/609

Step 3: Add the Numerators
Now add the numerators (63 + 145 = 208) and keep the common denominator 609 unchanged.
Working: 63 + 145/609 = 208/609

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 208 and 609 is 1, confirming that 208/609 cannot be reduced further—it is already in its simplest irreducible form.
Working: 208/609

Step 5: Decimal & Percentage Representation
Dividing the numerator 208 by denominator 609 produces a repeating decimal (approximately 0.341544, or 34.1544%).
Working: 208 ÷ 609 = 0.341544 (34.1544%)

Key Values:
- Simplified Fraction: 208/609
- Mixed Number Form: 208/609
- Decimal Value: 0.341544
- Percentage: 34.1544%

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3/29 + 5/21 = 208/609

Simplified Fraction

208/609

Mixed Number

Proper (208/609)

Decimal Value

0.341544

Percentage

34.1544%

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Step-by-Step Solution: 3/29 + 5/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 29 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 29 × 21 = 609.

LCD(29, 21) = 609

Step 2

Convert to Equivalent Fractions with Common Denominator 609

Multiply the numerator and denominator of 3/29 by 21, and multiply the numerator and denominator of 5/21 by 29 so both fractions share the common base 609.

3 × 21/29 × 21 = 63/609 and 5 × 29/21 × 29 = 145/609

Step 3

Add the Numerators

Now add the numerators (63 + 145 = 208) and keep the common denominator 609 unchanged.

63 + 145/609 = 208/609

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 208 and 609 is 1, confirming that 208/609 cannot be reduced further—it is already in its simplest irreducible form.

208/609

Step 5

Decimal & Percentage Representation

Dividing the numerator 208 by denominator 609 produces a repeating decimal (approximately 0.341544, or 34.1544%).

208 ÷ 609 = 0.341544 (34.1544%)

Visual Representation

The diagram below illustrates 3/29 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`208/609`
Mixed Number Form	`208/609`
Decimal Form	`0.341544`
Percentage	`34.1544%`

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Frequently Asked Questions

What is 3/29 plus 5/21 as a fraction?

3/29 + 5/21 in simplest fraction form is 208/609.

What is 3/29 plus 5/21 as a decimal?

3/29 + 5/21 converted to a decimal is 0.341544.

What is 3/29 plus 5/21 as a percentage?

3/29 + 5/21 expressed as a percentage is 34.1544%.

Does 3/29 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.341544...) because the denominator contains prime factors other than 2 and 5.