What is 12/39 plus 15/21? (Answer: 93/91)

Exact Answer

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Problem: What is 12/39 plus 15/21?
Formula / Expression: 12/39 + 15/21
Final Answer: 1 2/91 (93/91)
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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 12/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 12 × 7/39 × 7 = 84/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (84 + 195 = 279) and keep the common denominator 273 unchanged.
Working: 84 + 195/273 = 279/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 279 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 279 ÷ 3/273 ÷ 3 = 93/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (93) is greater than the denominator (91), divide 93 by 91: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/91.
Working: 93/91 = 1 2/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 93 by denominator 91 produces a repeating decimal (approximately 1.021978, or 102.1978%).
Working: 93 ÷ 91 = 1.021978 (102.1978%)

Key Values:
- Simplified Fraction: 93/91
- Mixed Number Form: 1 2/91
- Decimal Value: 1.021978
- Percentage: 102.1978%

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Solved with FractionsCalc:
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12/39 + 15/21 = 93/91

Simplified Fraction

93/91

Mixed Number

1 2/91

Decimal Value

1.021978

Percentage

102.1978%

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Step-by-Step Solution: 12/39 + 15/21

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 12/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

12 × 7/39 × 7 = 84/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (84 + 195 = 279) and keep the common denominator 273 unchanged.

84 + 195/273 = 279/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 279 and 273, which is 3. Divide both the numerator and denominator by 3.

279 ÷ 3/273 ÷ 3 = 93/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (93) is greater than the denominator (91), divide 93 by 91: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/91.

93/91 = 12/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 93 by denominator 91 produces a repeating decimal (approximately 1.021978, or 102.1978%).

93 ÷ 91 = 1.021978 (102.1978%)

Visual Representation

The diagram below illustrates 12/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`93/91`
Mixed Number Form	`1 2/91`
Decimal Form	`1.021978`
Percentage	`102.1978%`

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Frequently Asked Questions

What is 12/39 plus 15/21 as a fraction?

12/39 + 15/21 in simplest fraction form is 93/91 (or 1 2/91 as a mixed number).

What is 12/39 plus 15/21 as a decimal?

12/39 + 15/21 converted to a decimal is 1.021978.

What is 12/39 plus 15/21 as a percentage?

12/39 + 15/21 expressed as a percentage is 102.1978%.

How do you write 12/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 93/91 can be written as the mixed number 1 2/91.

Does 12/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.021978...) because the denominator contains prime factors other than 2 and 5.