What is 6/39 plus 9/21? (Answer: 53/91)

Exact Answer

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Problem: What is 6/39 plus 9/21?
Formula / Expression: 6/39 + 9/21
Final Answer: 53/91
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).
Working: LCD(39, 21) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 6/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.
Working: 6 × 7/39 × 7 = 42/273 and 9 × 13/21 × 13 = 117/273

Step 3: Add the Numerators
Now add the numerators (42 + 117 = 159) and keep the common denominator 273 unchanged.
Working: 42 + 117/273 = 159/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 159 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 159 ÷ 3/273 ÷ 3 = 53/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 91 produces a repeating decimal (approximately 0.582418, or 58.2418%).
Working: 53 ÷ 91 = 0.582418 (58.2418%)

Key Values:
- Simplified Fraction: 53/91
- Mixed Number Form: 53/91
- Decimal Value: 0.582418
- Percentage: 58.2418%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-39-plus-9-21/
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6/39 + 9/21 = 53/91

Simplified Fraction

53/91

Mixed Number

Proper (53/91)

Decimal Value

0.582418

Percentage

58.2418%

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Step-by-Step Solution: 6/39 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 39 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 39 × 21 = 819, keeping the calculation simpler).

LCD(39, 21) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 6/39 by 7, and multiply the numerator and denominator of 9/21 by 13 so both fractions share the common base 273.

6 × 7/39 × 7 = 42/273 and 9 × 13/21 × 13 = 117/273

Step 3

Add the Numerators

Now add the numerators (42 + 117 = 159) and keep the common denominator 273 unchanged.

42 + 117/273 = 159/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 159 and 273, which is 3. Divide both the numerator and denominator by 3.

159 ÷ 3/273 ÷ 3 = 53/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 91 produces a repeating decimal (approximately 0.582418, or 58.2418%).

53 ÷ 91 = 0.582418 (58.2418%)

Visual Representation

The diagram below illustrates 6/39 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/91`
Mixed Number Form	`53/91`
Decimal Form	`0.582418`
Percentage	`58.2418%`

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Frequently Asked Questions

What is 6/39 plus 9/21 as a fraction?

6/39 + 9/21 in simplest fraction form is 53/91.

What is 6/39 plus 9/21 as a decimal?

6/39 + 9/21 converted to a decimal is 0.582418.

What is 6/39 plus 9/21 as a percentage?

6/39 + 9/21 expressed as a percentage is 58.2418%.

Does 6/39 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.582418...) because the denominator contains prime factors other than 2 and 5.