What is 3/61 plus 9/21? (Answer: 204/427)

Exact Answer

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Problem: What is 3/61 plus 9/21?
Formula / Expression: 3/61 + 9/21
Final Answer: 204/427
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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 3/61 by 21, and multiply the numerator and denominator of 9/21 by 61 so both fractions share the common base 1281.
Working: 3 × 21/61 × 21 = 63/1281 and 9 × 61/21 × 61 = 549/1281

Step 3: Add the Numerators
Now add the numerators (63 + 549 = 612) and keep the common denominator 1281 unchanged.
Working: 63 + 549/1281 = 612/1281

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 612 and 1281, which is 3. Divide both the numerator and denominator by 3.
Working: 612 ÷ 3/1281 ÷ 3 = 204/427

Step 5: Decimal & Percentage Representation
Dividing the numerator 204 by denominator 427 produces a repeating decimal (approximately 0.477752, or 47.7752%).
Working: 204 ÷ 427 = 0.477752 (47.7752%)

Key Values:
- Simplified Fraction: 204/427
- Mixed Number Form: 204/427
- Decimal Value: 0.477752
- Percentage: 47.7752%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-61-plus-9-21/
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3/61 + 9/21 = 204/427

Simplified Fraction

204/427

Mixed Number

Proper (204/427)

Decimal Value

0.477752

Percentage

47.7752%

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Step-by-Step Solution: 3/61 + 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 3/61 by 21, and multiply the numerator and denominator of 9/21 by 61 so both fractions share the common base 1281.

3 × 21/61 × 21 = 63/1281 and 9 × 61/21 × 61 = 549/1281

Step 3

Add the Numerators

Now add the numerators (63 + 549 = 612) and keep the common denominator 1281 unchanged.

63 + 549/1281 = 612/1281

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 612 and 1281, which is 3. Divide both the numerator and denominator by 3.

612 ÷ 3/1281 ÷ 3 = 204/427

Step 5

Decimal & Percentage Representation

Dividing the numerator 204 by denominator 427 produces a repeating decimal (approximately 0.477752, or 47.7752%).

204 ÷ 427 = 0.477752 (47.7752%)

Visual Representation

The diagram below illustrates 3/61 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`204/427`
Mixed Number Form	`204/427`
Decimal Form	`0.477752`
Percentage	`47.7752%`

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Frequently Asked Questions

What is 3/61 plus 9/21 as a fraction?

3/61 + 9/21 in simplest fraction form is 204/427.

What is 3/61 plus 9/21 as a decimal?

3/61 + 9/21 converted to a decimal is 0.477752.

What is 3/61 plus 9/21 as a percentage?

3/61 + 9/21 expressed as a percentage is 47.7752%.

Does 3/61 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.477752...) because the denominator contains prime factors other than 2 and 5.