What is 6/29 plus 10/21? (Answer: 416/609)

Exact Answer

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Problem: What is 6/29 plus 10/21?
Formula / Expression: 6/29 + 10/21
Final Answer: 416/609
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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 6/29 by 21, and multiply the numerator and denominator of 10/21 by 29 so both fractions share the common base 609.
Working: 6 × 21/29 × 21 = 126/609 and 10 × 29/21 × 29 = 290/609

Step 3: Add the Numerators
Now add the numerators (126 + 290 = 416) and keep the common denominator 609 unchanged.
Working: 126 + 290/609 = 416/609

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 416 and 609 is 1, confirming that 416/609 cannot be reduced further—it is already in its simplest irreducible form.
Working: 416/609

Step 5: Decimal & Percentage Representation
Dividing the numerator 416 by denominator 609 produces a repeating decimal (approximately 0.683087, or 68.3087%).
Working: 416 ÷ 609 = 0.683087 (68.3087%)

Key Values:
- Simplified Fraction: 416/609
- Mixed Number Form: 416/609
- Decimal Value: 0.683087
- Percentage: 68.3087%

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Solved with FractionsCalc:
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6/29 + 10/21 = 416/609

Simplified Fraction

416/609

Mixed Number

Proper (416/609)

Decimal Value

0.683087

Percentage

68.3087%

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Step-by-Step Solution: 6/29 + 10/21

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 6/29 by 21, and multiply the numerator and denominator of 10/21 by 29 so both fractions share the common base 609.

6 × 21/29 × 21 = 126/609 and 10 × 29/21 × 29 = 290/609

Step 3

Add the Numerators

Now add the numerators (126 + 290 = 416) and keep the common denominator 609 unchanged.

126 + 290/609 = 416/609

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 416 and 609 is 1, confirming that 416/609 cannot be reduced further—it is already in its simplest irreducible form.

416/609

Step 5

Decimal & Percentage Representation

Dividing the numerator 416 by denominator 609 produces a repeating decimal (approximately 0.683087, or 68.3087%).

416 ÷ 609 = 0.683087 (68.3087%)

Visual Representation

The diagram below illustrates 6/29 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`416/609`
Mixed Number Form	`416/609`
Decimal Form	`0.683087`
Percentage	`68.3087%`

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Frequently Asked Questions

What is 6/29 plus 10/21 as a fraction?

6/29 + 10/21 in simplest fraction form is 416/609.

What is 6/29 plus 10/21 as a decimal?

6/29 + 10/21 converted to a decimal is 0.683087.

What is 6/29 plus 10/21 as a percentage?

6/29 + 10/21 expressed as a percentage is 68.3087%.

Does 6/29 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.683087...) because the denominator contains prime factors other than 2 and 5.