What is 3/21 plus 9/59? (Answer: 122/413)

Exact Answer

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Problem: What is 3/21 plus 9/59?
Formula / Expression: 3/21 + 9/59
Final Answer: 122/413
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 59 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 59 = 1239.
Working: LCD(21, 59) = 1239

Step 2: Convert to Equivalent Fractions with Common Denominator 1239
Multiply the numerator and denominator of 3/21 by 59, and multiply the numerator and denominator of 9/59 by 21 so both fractions share the common base 1239.
Working: 3 × 59/21 × 59 = 177/1239 and 9 × 21/59 × 21 = 189/1239

Step 3: Add the Numerators
Now add the numerators (177 + 189 = 366) and keep the common denominator 1239 unchanged.
Working: 177 + 189/1239 = 366/1239

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 366 and 1239, which is 3. Divide both the numerator and denominator by 3.
Working: 366 ÷ 3/1239 ÷ 3 = 122/413

Step 5: Decimal & Percentage Representation
Dividing the numerator 122 by denominator 413 produces a repeating decimal (approximately 0.2954, or 29.54%).
Working: 122 ÷ 413 = 0.2954 (29.54%)

Key Values:
- Simplified Fraction: 122/413
- Mixed Number Form: 122/413
- Decimal Value: 0.2954
- Percentage: 29.54%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-9-59/
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3/21 + 9/59 = 122/413

Simplified Fraction

122/413

Mixed Number

Proper (122/413)

Decimal Value

0.2954

Percentage

29.54%

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Step-by-Step Solution: 3/21 + 9/59

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 59 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 59 = 1239.

LCD(21, 59) = 1239

Step 2

Convert to Equivalent Fractions with Common Denominator 1239

Multiply the numerator and denominator of 3/21 by 59, and multiply the numerator and denominator of 9/59 by 21 so both fractions share the common base 1239.

3 × 59/21 × 59 = 177/1239 and 9 × 21/59 × 21 = 189/1239

Step 3

Add the Numerators

Now add the numerators (177 + 189 = 366) and keep the common denominator 1239 unchanged.

177 + 189/1239 = 366/1239

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 366 and 1239, which is 3. Divide both the numerator and denominator by 3.

366 ÷ 3/1239 ÷ 3 = 122/413

Step 5

Decimal & Percentage Representation

Dividing the numerator 122 by denominator 413 produces a repeating decimal (approximately 0.2954, or 29.54%).

122 ÷ 413 = 0.2954 (29.54%)

Visual Representation

The diagram below illustrates 3/21 plus 9/59 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`122/413`
Mixed Number Form	`122/413`
Decimal Form	`0.2954`
Percentage	`29.54%`

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Frequently Asked Questions

What is 3/21 plus 9/59 as a fraction?

3/21 + 9/59 in simplest fraction form is 122/413.

What is 3/21 plus 9/59 as a decimal?

3/21 + 9/59 converted to a decimal is 0.2954.

What is 3/21 plus 9/59 as a percentage?

3/21 + 9/59 expressed as a percentage is 29.54%.

Does 3/21 plus 9/59 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.2954...) because the denominator contains prime factors other than 2 and 5.