What is 16/39 plus 12/21? (Answer: 268/273)

Exact Answer

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Problem: What is 16/39 plus 12/21?
Formula / Expression: 16/39 + 12/21
Final Answer: 268/273
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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 16/39 by 7, and multiply the numerator and denominator of 12/21 by 13 so both fractions share the common base 273.
Working: 16 × 7/39 × 7 = 112/273 and 12 × 13/21 × 13 = 156/273

Step 3: Add the Numerators
Now add the numerators (112 + 156 = 268) and keep the common denominator 273 unchanged.
Working: 112 + 156/273 = 268/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 268 and 273 is 1, confirming that 268/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 268/273

Step 5: Decimal & Percentage Representation
Dividing the numerator 268 by denominator 273 produces a repeating decimal (approximately 0.981685, or 98.1685%).
Working: 268 ÷ 273 = 0.981685 (98.1685%)

Key Values:
- Simplified Fraction: 268/273
- Mixed Number Form: 268/273
- Decimal Value: 0.981685
- Percentage: 98.1685%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-16-39-plus-12-21/
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16/39 + 12/21 = 268/273

Simplified Fraction

268/273

Mixed Number

Proper (268/273)

Decimal Value

0.981685

Percentage

98.1685%

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Step-by-Step Solution: 16/39 + 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 16/39 by 7, and multiply the numerator and denominator of 12/21 by 13 so both fractions share the common base 273.

16 × 7/39 × 7 = 112/273 and 12 × 13/21 × 13 = 156/273

Step 3

Add the Numerators

Now add the numerators (112 + 156 = 268) and keep the common denominator 273 unchanged.

112 + 156/273 = 268/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 268 and 273 is 1, confirming that 268/273 cannot be reduced further—it is already in its simplest irreducible form.

268/273

Step 5

Decimal & Percentage Representation

Dividing the numerator 268 by denominator 273 produces a repeating decimal (approximately 0.981685, or 98.1685%).

268 ÷ 273 = 0.981685 (98.1685%)

Visual Representation

The diagram below illustrates 16/39 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`268/273`
Mixed Number Form	`268/273`
Decimal Form	`0.981685`
Percentage	`98.1685%`

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Frequently Asked Questions

What is 16/39 plus 12/21 as a fraction?

16/39 + 12/21 in simplest fraction form is 268/273.

What is 16/39 plus 12/21 as a decimal?

16/39 + 12/21 converted to a decimal is 0.981685.

What is 16/39 plus 12/21 as a percentage?

16/39 + 12/21 expressed as a percentage is 98.1685%.

Does 16/39 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.981685...) because the denominator contains prime factors other than 2 and 5.