What is 1/39 plus 2/21? (Answer: 11/91)

Exact Answer

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Problem: What is 1/39 plus 2/21?
Formula / Expression: 1/39 + 2/21
Final Answer: 11/91
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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 1/39 by 7, and multiply the numerator and denominator of 2/21 by 13 so both fractions share the common base 273.
Working: 1 × 7/39 × 7 = 7/273 and 2 × 13/21 × 13 = 26/273

Step 3: Add the Numerators
Now add the numerators (7 + 26 = 33) and keep the common denominator 273 unchanged.
Working: 7 + 26/273 = 33/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/273 ÷ 3 = 11/91

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 91 produces a repeating decimal (approximately 0.120879, or 12.0879%).
Working: 11 ÷ 91 = 0.120879 (12.0879%)

Key Values:
- Simplified Fraction: 11/91
- Mixed Number Form: 11/91
- Decimal Value: 0.120879
- Percentage: 12.0879%

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Solved with FractionsCalc:
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1/39 + 2/21 = 11/91

Simplified Fraction

11/91

Mixed Number

Proper (11/91)

Decimal Value

0.120879

Percentage

12.0879%

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Step-by-Step Solution: 1/39 + 2/21

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 1/39 by 7, and multiply the numerator and denominator of 2/21 by 13 so both fractions share the common base 273.

1 × 7/39 × 7 = 7/273 and 2 × 13/21 × 13 = 26/273

Step 3

Add the Numerators

Now add the numerators (7 + 26 = 33) and keep the common denominator 273 unchanged.

7 + 26/273 = 33/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 273, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/273 ÷ 3 = 11/91

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 91 produces a repeating decimal (approximately 0.120879, or 12.0879%).

11 ÷ 91 = 0.120879 (12.0879%)

Visual Representation

The diagram below illustrates 1/39 plus 2/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/91`
Mixed Number Form	`11/91`
Decimal Form	`0.120879`
Percentage	`12.0879%`

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Frequently Asked Questions

What is 1/39 plus 2/21 as a fraction?

1/39 + 2/21 in simplest fraction form is 11/91.

What is 1/39 plus 2/21 as a decimal?

1/39 + 2/21 converted to a decimal is 0.120879.

What is 1/39 plus 2/21 as a percentage?

1/39 + 2/21 expressed as a percentage is 12.0879%.

Does 1/39 plus 2/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.120879...) because the denominator contains prime factors other than 2 and 5.