What is 16/39 plus 15/21? (Answer: 307/273)

Exact Answer

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Problem: What is 16/39 plus 15/21?
Formula / Expression: 16/39 + 15/21
Final Answer: 1 34/273 (307/273)
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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 15/21 by 13 so both fractions share the common base 273.
Working: 16 × 7/39 × 7 = 112/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (112 + 195 = 307) and keep the common denominator 273 unchanged.
Working: 112 + 195/273 = 307/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 307 and 273 is 1, confirming that 307/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 307/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (307) is greater than the denominator (273), divide 307 by 273: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/273.
Working: 307/273 = 1 34/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 307 by denominator 273 produces a repeating decimal (approximately 1.124542, or 112.4542%).
Working: 307 ÷ 273 = 1.124542 (112.4542%)

Key Values:
- Simplified Fraction: 307/273
- Mixed Number Form: 1 34/273
- Decimal Value: 1.124542
- Percentage: 112.4542%

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Solved with FractionsCalc:
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16/39 + 15/21 = 307/273

Simplified Fraction

307/273

Mixed Number

1 34/273

Decimal Value

1.124542

Percentage

112.4542%

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Step-by-Step Solution: 16/39 + 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 16/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

16 × 7/39 × 7 = 112/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (112 + 195 = 307) and keep the common denominator 273 unchanged.

112 + 195/273 = 307/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 307 and 273 is 1, confirming that 307/273 cannot be reduced further—it is already in its simplest irreducible form.

307/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (307) is greater than the denominator (273), divide 307 by 273: it goes in 1 whole time(s) with a remainder of 34, giving the mixed number 1 34/273.

307/273 = 134/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 307 by denominator 273 produces a repeating decimal (approximately 1.124542, or 112.4542%).

307 ÷ 273 = 1.124542 (112.4542%)

Visual Representation

The diagram below illustrates 16/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`307/273`
Mixed Number Form	`1 34/273`
Decimal Form	`1.124542`
Percentage	`112.4542%`

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Frequently Asked Questions

What is 16/39 plus 15/21 as a fraction?

16/39 + 15/21 in simplest fraction form is 307/273 (or 1 34/273 as a mixed number).

What is 16/39 plus 15/21 as a decimal?

16/39 + 15/21 converted to a decimal is 1.124542.

What is 16/39 plus 15/21 as a percentage?

16/39 + 15/21 expressed as a percentage is 112.4542%.

How do you write 16/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 307/273 can be written as the mixed number 1 34/273.

Does 16/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.124542...) because the denominator contains prime factors other than 2 and 5.