What is 25/39 plus 15/21? (Answer: 370/273)

Exact Answer

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Problem: What is 25/39 plus 15/21?
Formula / Expression: 25/39 + 15/21
Final Answer: 1 97/273 (370/273)
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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 25/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.
Working: 25 × 7/39 × 7 = 175/273 and 15 × 13/21 × 13 = 195/273

Step 3: Add the Numerators
Now add the numerators (175 + 195 = 370) and keep the common denominator 273 unchanged.
Working: 175 + 195/273 = 370/273

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 370 and 273 is 1, confirming that 370/273 cannot be reduced further—it is already in its simplest irreducible form.
Working: 370/273

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (370) is greater than the denominator (273), divide 370 by 273: it goes in 1 whole time(s) with a remainder of 97, giving the mixed number 1 97/273.
Working: 370/273 = 1 97/273

Step 6: Decimal & Percentage Representation
Dividing the numerator 370 by denominator 273 produces a repeating decimal (approximately 1.355311, or 135.5311%).
Working: 370 ÷ 273 = 1.355311 (135.5311%)

Key Values:
- Simplified Fraction: 370/273
- Mixed Number Form: 1 97/273
- Decimal Value: 1.355311
- Percentage: 135.5311%

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Solved with FractionsCalc:
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25/39 + 15/21 = 370/273

Simplified Fraction

370/273

Mixed Number

1 97/273

Decimal Value

1.355311

Percentage

135.5311%

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Step-by-Step Solution: 25/39 + 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 25/39 by 7, and multiply the numerator and denominator of 15/21 by 13 so both fractions share the common base 273.

25 × 7/39 × 7 = 175/273 and 15 × 13/21 × 13 = 195/273

Step 3

Add the Numerators

Now add the numerators (175 + 195 = 370) and keep the common denominator 273 unchanged.

175 + 195/273 = 370/273

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 370 and 273 is 1, confirming that 370/273 cannot be reduced further—it is already in its simplest irreducible form.

370/273

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (370) is greater than the denominator (273), divide 370 by 273: it goes in 1 whole time(s) with a remainder of 97, giving the mixed number 1 97/273.

370/273 = 197/273

Step 6

Decimal & Percentage Representation

Dividing the numerator 370 by denominator 273 produces a repeating decimal (approximately 1.355311, or 135.5311%).

370 ÷ 273 = 1.355311 (135.5311%)

Visual Representation

The diagram below illustrates 25/39 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`370/273`
Mixed Number Form	`1 97/273`
Decimal Form	`1.355311`
Percentage	`135.5311%`

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Frequently Asked Questions

What is 25/39 plus 15/21 as a fraction?

25/39 + 15/21 in simplest fraction form is 370/273 (or 1 97/273 as a mixed number).

What is 25/39 plus 15/21 as a decimal?

25/39 + 15/21 converted to a decimal is 1.355311.

What is 25/39 plus 15/21 as a percentage?

25/39 + 15/21 expressed as a percentage is 135.5311%.

How do you write 25/39 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 370/273 can be written as the mixed number 1 97/273.

Does 25/39 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.355311...) because the denominator contains prime factors other than 2 and 5.