What is 21/39 plus 12/21? (Answer: 101/91)

Exact Answer

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Problem: What is 21/39 plus 12/21?
Formula / Expression: 21/39 + 12/21
Final Answer: 1 10/91 (101/91)
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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 21/39 by 7, and multiply the numerator and denominator of 12/21 by 13 so both fractions share the common base 273.
Working: 21 × 7/39 × 7 = 147/273 and 12 × 13/21 × 13 = 156/273

Step 3: Add the Numerators
Now add the numerators (147 + 156 = 303) and keep the common denominator 273 unchanged.
Working: 147 + 156/273 = 303/273

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 303 and 273, which is 3. Divide both the numerator and denominator by 3.
Working: 303 ÷ 3/273 ÷ 3 = 101/91

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (101) is greater than the denominator (91), divide 101 by 91: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/91.
Working: 101/91 = 1 10/91

Step 6: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 91 produces a repeating decimal (approximately 1.10989, or 110.989%).
Working: 101 ÷ 91 = 1.10989 (110.989%)

Key Values:
- Simplified Fraction: 101/91
- Mixed Number Form: 1 10/91
- Decimal Value: 1.10989
- Percentage: 110.989%

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Solved with FractionsCalc:
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21/39 + 12/21 = 101/91

Simplified Fraction

101/91

Mixed Number

1 10/91

Decimal Value

1.10989

Percentage

110.989%

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

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

21 × 7/39 × 7 = 147/273 and 12 × 13/21 × 13 = 156/273

Step 3

Add the Numerators

Now add the numerators (147 + 156 = 303) and keep the common denominator 273 unchanged.

147 + 156/273 = 303/273

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 303 and 273, which is 3. Divide both the numerator and denominator by 3.

303 ÷ 3/273 ÷ 3 = 101/91

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (101) is greater than the denominator (91), divide 101 by 91: it goes in 1 whole time(s) with a remainder of 10, giving the mixed number 1 10/91.

101/91 = 110/91

Step 6

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 91 produces a repeating decimal (approximately 1.10989, or 110.989%).

101 ÷ 91 = 1.10989 (110.989%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/91`
Mixed Number Form	`1 10/91`
Decimal Form	`1.10989`
Percentage	`110.989%`

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Frequently Asked Questions

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

21/39 + 12/21 in simplest fraction form is 101/91 (or 1 10/91 as a mixed number).

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

21/39 + 12/21 converted to a decimal is 1.10989.

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

21/39 + 12/21 expressed as a percentage is 110.989%.

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

Because the numerator is greater than the denominator, the improper fraction 101/91 can be written as the mixed number 1 10/91.

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

It results in a repeating decimal (approximately 1.10989...) because the denominator contains prime factors other than 2 and 5.