What is 21/34 plus 9/13? (Answer: 579/442)

Exact Answer

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Problem: What is 21/34 plus 9/13?
Formula / Expression: 21/34 + 9/13
Final Answer: 1 137/442 (579/442)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 34 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 13 = 442.
Working: LCD(34, 13) = 442

Step 2: Convert to Equivalent Fractions with Common Denominator 442
Multiply the numerator and denominator of 21/34 by 13, and multiply the numerator and denominator of 9/13 by 34 so both fractions share the common base 442.
Working: 21 × 13/34 × 13 = 273/442 and 9 × 34/13 × 34 = 306/442

Step 3: Add the Numerators
Now add the numerators (273 + 306 = 579) and keep the common denominator 442 unchanged.
Working: 273 + 306/442 = 579/442

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 579 and 442 is 1, confirming that 579/442 cannot be reduced further—it is already in its simplest irreducible form.
Working: 579/442

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (579) is greater than the denominator (442), divide 579 by 442: it goes in 1 whole time(s) with a remainder of 137, giving the mixed number 1 137/442.
Working: 579/442 = 1 137/442

Step 6: Decimal & Percentage Representation
Dividing the numerator 579 by denominator 442 produces a repeating decimal (approximately 1.309955, or 130.9955%).
Working: 579 ÷ 442 = 1.309955 (130.9955%)

Key Values:
- Simplified Fraction: 579/442
- Mixed Number Form: 1 137/442
- Decimal Value: 1.309955
- Percentage: 130.9955%

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Solved with FractionsCalc:
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21/34 + 9/13 = 579/442

Simplified Fraction

579/442

Mixed Number

1 137/442

Decimal Value

1.309955

Percentage

130.9955%

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Step-by-Step Solution: 21/34 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 34 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 34 × 13 = 442.

LCD(34, 13) = 442

Step 2

Convert to Equivalent Fractions with Common Denominator 442

Multiply the numerator and denominator of 21/34 by 13, and multiply the numerator and denominator of 9/13 by 34 so both fractions share the common base 442.

21 × 13/34 × 13 = 273/442 and 9 × 34/13 × 34 = 306/442

Step 3

Add the Numerators

Now add the numerators (273 + 306 = 579) and keep the common denominator 442 unchanged.

273 + 306/442 = 579/442

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 579 and 442 is 1, confirming that 579/442 cannot be reduced further—it is already in its simplest irreducible form.

579/442

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (579) is greater than the denominator (442), divide 579 by 442: it goes in 1 whole time(s) with a remainder of 137, giving the mixed number 1 137/442.

579/442 = 1137/442

Step 6

Decimal & Percentage Representation

Dividing the numerator 579 by denominator 442 produces a repeating decimal (approximately 1.309955, or 130.9955%).

579 ÷ 442 = 1.309955 (130.9955%)

Visual Representation

The diagram below illustrates 21/34 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`579/442`
Mixed Number Form	`1 137/442`
Decimal Form	`1.309955`
Percentage	`130.9955%`

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Frequently Asked Questions

What is 21/34 plus 9/13 as a fraction?

21/34 + 9/13 in simplest fraction form is 579/442 (or 1 137/442 as a mixed number).

What is 21/34 plus 9/13 as a decimal?

21/34 + 9/13 converted to a decimal is 1.309955.

What is 21/34 plus 9/13 as a percentage?

21/34 + 9/13 expressed as a percentage is 130.9955%.

How do you write 21/34 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 579/442 can be written as the mixed number 1 137/442.

Does 21/34 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.309955...) because the denominator contains prime factors other than 2 and 5.