What is 15/21 plus 28/39? (Answer: 391/273)

Exact Answer

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Problem: What is 15/21 plus 28/39?
Formula / Expression: 15/21 + 28/39
Final Answer: 1 118/273 (391/273)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).
Working: LCD(21, 39) = 273

Step 2: Convert to Equivalent Fractions with Common Denominator 273
Multiply the numerator and denominator of 15/21 by 13, and multiply the numerator and denominator of 28/39 by 7 so both fractions share the common base 273.
Working: 15 × 13/21 × 13 = 195/273 and 28 × 7/39 × 7 = 196/273

Step 3: Add the Numerators
Now add the numerators (195 + 196 = 391) and keep the common denominator 273 unchanged.
Working: 195 + 196/273 = 391/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 391 and 273 is 1, confirming that 391/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 391/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (391) is greater than the denominator (273), divide 391 by 273: it goes in 1 whole time(s) with a remainder of 118, giving the mixed number 1 118/273.
Working: 391/273 = 1 118/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 391 by denominator 273 produces a repeating decimal (approximately 1.432234, or 143.2234%).
Working: 391 ÷ 273 = 1.432234 (143.2234%)

Key Values:
- Simplified Fraction: 391/273
- Mixed Number Form: 1 118/273
- Decimal Value: 1.432234
- Percentage: 143.2234%

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Solved with FractionsCalc:
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15/21 + 28/39 = 391/273

Simplified Fraction

391/273

Mixed Number

1 118/273

Decimal Value

1.432234

Percentage

143.2234%

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Step-by-Step Solution: 15/21 + 28/39

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 39 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 273 (which is smaller than their product 21 × 39 = 819, keeping the calculation simpler).

LCD(21, 39) = 273

Step 2

Convert to Equivalent Fractions with Common Denominator 273

Multiply the numerator and denominator of 15/21 by 13, and multiply the numerator and denominator of 28/39 by 7 so both fractions share the common base 273.

15 × 13/21 × 13 = 195/273 and 28 × 7/39 × 7 = 196/273

Step 3

Add the Numerators

Now add the numerators (195 + 196 = 391) and keep the common denominator 273 unchanged.

195 + 196/273 = 391/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 391 and 273 is 1, confirming that 391/273 cannot be reduced further—it is already in its simplest irreducible form.

391/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (391) is greater than the denominator (273), divide 391 by 273: it goes in 1 whole time(s) with a remainder of 118, giving the mixed number 1 118/273.

391/273 = 1118/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 391 by denominator 273 produces a repeating decimal (approximately 1.432234, or 143.2234%).

391 ÷ 273 = 1.432234 (143.2234%)

Visual Representation

The diagram below illustrates 15/21 plus 28/39 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`391/273`
Mixed Number Form	`1 118/273`
Decimal Form	`1.432234`
Percentage	`143.2234%`

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Frequently Asked Questions

What is 15/21 plus 28/39 as a fraction?

15/21 + 28/39 in simplest fraction form is 391/273 (or 1 118/273 as a mixed number).

What is 15/21 plus 28/39 as a decimal?

15/21 + 28/39 converted to a decimal is 1.432234.

What is 15/21 plus 28/39 as a percentage?

15/21 + 28/39 expressed as a percentage is 143.2234%.

How do you write 15/21 plus 28/39 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 391/273 can be written as the mixed number 1 118/273.

Does 15/21 plus 28/39 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.432234...) because the denominator contains prime factors other than 2 and 5.