What is 13/61 plus 9/21? (Answer: 274/427)

Exact Answer

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Problem: What is 13/61 plus 9/21?
Formula / Expression: 13/61 + 9/21
Final Answer: 274/427
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 61 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 61 × 21 = 1281.
Working: LCD(61, 21) = 1281

Step 2: Convert to Equivalent Fractions with Common Denominator 1281
Multiply the numerator and denominator of 13/61 by 21, and multiply the numerator and denominator of 9/21 by 61 so both fractions share the common base 1281.
Working: 13 × 21/61 × 21 = 273/1281 and 9 × 61/21 × 61 = 549/1281

Step 3: Add the Numerators
Now add the numerators (273 + 549 = 822) and keep the common denominator 1281 unchanged.
Working: 273 + 549/1281 = 822/1281

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 822 and 1281, which is 3. Divide both the numerator and denominator by 3.
Working: 822 ÷ 3/1281 ÷ 3 = 274/427

Step 5: Decimal & Percentage Representation
Dividing the numerator 274 by denominator 427 produces a repeating decimal (approximately 0.641686, or 64.1686%).
Working: 274 ÷ 427 = 0.641686 (64.1686%)

Key Values:
- Simplified Fraction: 274/427
- Mixed Number Form: 274/427
- Decimal Value: 0.641686
- Percentage: 64.1686%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-61-plus-9-21/
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13/61 + 9/21 = 274/427

Simplified Fraction

274/427

Mixed Number

Proper (274/427)

Decimal Value

0.641686

Percentage

64.1686%

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Step-by-Step Solution: 13/61 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 61 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 61 × 21 = 1281.

LCD(61, 21) = 1281

Step 2

Convert to Equivalent Fractions with Common Denominator 1281

Multiply the numerator and denominator of 13/61 by 21, and multiply the numerator and denominator of 9/21 by 61 so both fractions share the common base 1281.

13 × 21/61 × 21 = 273/1281 and 9 × 61/21 × 61 = 549/1281

Step 3

Add the Numerators

Now add the numerators (273 + 549 = 822) and keep the common denominator 1281 unchanged.

273 + 549/1281 = 822/1281

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 822 and 1281, which is 3. Divide both the numerator and denominator by 3.

822 ÷ 3/1281 ÷ 3 = 274/427

Step 5

Decimal & Percentage Representation

Dividing the numerator 274 by denominator 427 produces a repeating decimal (approximately 0.641686, or 64.1686%).

274 ÷ 427 = 0.641686 (64.1686%)

Visual Representation

The diagram below illustrates 13/61 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`274/427`
Mixed Number Form	`274/427`
Decimal Form	`0.641686`
Percentage	`64.1686%`

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Frequently Asked Questions

What is 13/61 plus 9/21 as a fraction?

13/61 + 9/21 in simplest fraction form is 274/427.

What is 13/61 plus 9/21 as a decimal?

13/61 + 9/21 converted to a decimal is 0.641686.

What is 13/61 plus 9/21 as a percentage?

13/61 + 9/21 expressed as a percentage is 64.1686%.

Does 13/61 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.641686...) because the denominator contains prime factors other than 2 and 5.